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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ -->
<title>src/Control/Lens/Plated.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE Rank2Types #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE DefaultSignatures #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE FlexibleInstances #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE FlexibleContexts #-}</span>
<a name="line-6"></a><span class='hs-comment'>{-# LANGUAGE TypeOperators #-}</span>
<a name="line-7"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-8"></a>
<a name="line-9"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &lt; 710</span>
<a name="line-10"></a><span class='hs-comment'>{-# LANGUAGE OverlappingInstances #-}</span>
<a name="line-11"></a><span class='hs-cpp'>#define OVERLAPPING_PRAGMA</span>
<a name="line-12"></a><span class='hs-cpp'>#else</span>
<a name="line-13"></a><span class='hs-cpp'>#define OVERLAPPING_PRAGMA {-# OVERLAPPING #-}</span>
<a name="line-14"></a><span class='hs-cpp'>#endif</span>
<a name="line-15"></a>
<a name="line-16"></a><span class='hs-cpp'>#ifdef TRUSTWORTHY</span>
<a name="line-17"></a><span class='hs-cpp'># if MIN_VERSION_template_haskell(2,12,0)</span>
<a name="line-18"></a><span class='hs-comment'>{-# LANGUAGE Safe #-}</span>
<a name="line-19"></a><span class='hs-cpp'># else</span>
<a name="line-20"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy #-}</span> <span class='hs-comment'>-- template-haskell</span>
<a name="line-21"></a><span class='hs-cpp'># endif</span>
<a name="line-22"></a><span class='hs-cpp'>#endif</span>
<a name="line-23"></a>
<a name="line-24"></a><span class='hs-cpp'>#ifndef MIN_VERSION_template_haskell</span>
<a name="line-25"></a><span class='hs-cpp'>#define MIN_VERSION_template_haskell(x,y,z) 1</span>
<a name="line-26"></a><span class='hs-cpp'>#endif</span>
<a name="line-27"></a>
<a name="line-28"></a><span class='hs-cpp'>#ifndef MIN_VERSION_free</span>
<a name="line-29"></a><span class='hs-cpp'>#define MIN_VERSION_free(x,y,z) 1</span>
<a name="line-30"></a><span class='hs-cpp'>#endif</span>
<a name="line-31"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-32"></a><span class='hs-comment'>-- |</span>
<a name="line-33"></a><span class='hs-comment'>-- Module      :  Control.Lens.Plated</span>
<a name="line-34"></a><span class='hs-comment'>-- Copyright   :  (C) 2012-16 Edward Kmett</span>
<a name="line-35"></a><span class='hs-comment'>-- License     :  BSD-style (see the file LICENSE)</span>
<a name="line-36"></a><span class='hs-comment'>-- Maintainer  :  Edward Kmett &lt;ekmett@gmail.com&gt;</span>
<a name="line-37"></a><span class='hs-comment'>-- Stability   :  provisional</span>
<a name="line-38"></a><span class='hs-comment'>-- Portability :  Rank2Types</span>
<a name="line-39"></a><span class='hs-comment'>--</span>
<a name="line-40"></a><span class='hs-comment'>-- The name \"plate\" stems originally from \"boilerplate\", which was the term</span>
<a name="line-41"></a><span class='hs-comment'>-- used by the \"Scrap Your Boilerplate\" papers, and later inherited by Neil</span>
<a name="line-42"></a><span class='hs-comment'>-- Mitchell's \"Uniplate\".</span>
<a name="line-43"></a><span class='hs-comment'>--</span>
<a name="line-44"></a><span class='hs-comment'>-- &lt;<a href="http://community.haskell.org/~ndm/uniplate/">http://community.haskell.org/~ndm/uniplate/</a>&gt;</span>
<a name="line-45"></a><span class='hs-comment'>--</span>
<a name="line-46"></a><span class='hs-comment'>-- The combinators in here are designed to be compatible with and subsume the</span>
<a name="line-47"></a><span class='hs-comment'>-- @uniplate@ API with the notion of a 'Traversal' replacing</span>
<a name="line-48"></a><span class='hs-comment'>-- a 'Data.Data.Lens.uniplate' or 'Data.Data.Lens.biplate'.</span>
<a name="line-49"></a><span class='hs-comment'>--</span>
<a name="line-50"></a><span class='hs-comment'>-- By implementing these combinators in terms of 'plate' instead of</span>
<a name="line-51"></a><span class='hs-comment'>-- 'Data.Data.Lens.uniplate' additional type safety is gained, as the user is</span>
<a name="line-52"></a><span class='hs-comment'>-- no longer responsible for maintaining invariants such as the number of</span>
<a name="line-53"></a><span class='hs-comment'>-- children they received.</span>
<a name="line-54"></a><span class='hs-comment'>--</span>
<a name="line-55"></a><span class='hs-comment'>-- Note: The @Biplate@ is /deliberately/ excluded from the API here, with the</span>
<a name="line-56"></a><span class='hs-comment'>-- intention that you replace them with either explicit traversals, or by using the</span>
<a name="line-57"></a><span class='hs-comment'>-- @On@ variants of the combinators below with 'Data.Data.Lens.biplate' from</span>
<a name="line-58"></a><span class='hs-comment'>-- @Data.Data.Lens@. As a design, it forced the user into too many situations where</span>
<a name="line-59"></a><span class='hs-comment'>-- they had to choose between correctness and ease of use, and it was brittle in the</span>
<a name="line-60"></a><span class='hs-comment'>-- face of competing imports.</span>
<a name="line-61"></a><span class='hs-comment'>--</span>
<a name="line-62"></a><span class='hs-comment'>-- The sensible use of these combinators makes some simple assumptions.  Notably, any</span>
<a name="line-63"></a><span class='hs-comment'>-- of the @On@ combinators are expecting a 'Traversal', 'Setter' or 'Fold'</span>
<a name="line-64"></a><span class='hs-comment'>-- to play the role of the 'Data.Data.Lens.biplate' combinator, and so when the</span>
<a name="line-65"></a><span class='hs-comment'>-- types of the contents and the container match, they should be the 'id' 'Traversal',</span>
<a name="line-66"></a><span class='hs-comment'>-- 'Setter' or 'Fold'.</span>
<a name="line-67"></a><span class='hs-comment'>--</span>
<a name="line-68"></a><span class='hs-comment'>-- It is often beneficial to use the combinators in this module with the combinators</span>
<a name="line-69"></a><span class='hs-comment'>-- from @Data.Data.Lens@ or @GHC.Generics.Lens@ to make it easier to automatically</span>
<a name="line-70"></a><span class='hs-comment'>-- derive definitions for 'plate', or to derive custom traversals.</span>
<a name="line-71"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-72"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Plated</span>
<a name="line-73"></a>  <span class='hs-layout'>(</span>
<a name="line-74"></a>  <span class='hs-comment'>-- * Uniplate</span>
<a name="line-75"></a>    <span class='hs-conid'>Plated</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-76"></a>
<a name="line-77"></a>  <span class='hs-comment'>-- * Uniplate Combinators</span>
<a name="line-78"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>children</span>
<a name="line-79"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>rewrite</span><span class='hs-layout'>,</span> <span class='hs-varid'>rewriteOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>rewriteOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>rewriteOnOf</span>
<a name="line-80"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>rewriteM</span><span class='hs-layout'>,</span> <span class='hs-varid'>rewriteMOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>rewriteMOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>rewriteMOnOf</span>
<a name="line-81"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>universe</span><span class='hs-layout'>,</span> <span class='hs-varid'>universeOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>universeOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>universeOnOf</span>
<a name="line-82"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>cosmos</span><span class='hs-layout'>,</span> <span class='hs-varid'>cosmosOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>cosmosOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>cosmosOnOf</span>
<a name="line-83"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>transform</span><span class='hs-layout'>,</span> <span class='hs-varid'>transformOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>transformOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>transformOnOf</span>
<a name="line-84"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>transformM</span><span class='hs-layout'>,</span> <span class='hs-varid'>transformMOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>transformMOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>transformMOnOf</span>
<a name="line-85"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>contexts</span><span class='hs-layout'>,</span> <span class='hs-varid'>contextsOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>contextsOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>contextsOnOf</span>
<a name="line-86"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>holes</span><span class='hs-layout'>,</span> <span class='hs-varid'>holesOn</span><span class='hs-layout'>,</span> <span class='hs-varid'>holesOnOf</span>
<a name="line-87"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>para</span><span class='hs-layout'>,</span> <span class='hs-varid'>paraOf</span>
<a name="line-88"></a>  <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>...</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>deep</span>
<a name="line-89"></a>
<a name="line-90"></a>  <span class='hs-comment'>-- * Compos</span>
<a name="line-91"></a>  <span class='hs-comment'>-- $compos</span>
<a name="line-92"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>composOpFold</span>
<a name="line-93"></a>
<a name="line-94"></a>  <span class='hs-comment'>-- * Parts</span>
<a name="line-95"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>parts</span>
<a name="line-96"></a>
<a name="line-97"></a>  <span class='hs-comment'>-- * Generics</span>
<a name="line-98"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>gplate</span>
<a name="line-99"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>GPlated</span>
<a name="line-100"></a>  <span class='hs-layout'>)</span>
<a name="line-101"></a>  <span class='hs-keyword'>where</span>
<a name="line-102"></a>
<a name="line-103"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-104"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span><span class='hs-varop'>.</span><span class='hs-conid'>Cofree</span>
<a name="line-105"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Cofree</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>CoTrans</span>
<a name="line-106"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Fold</span>
<a name="line-107"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Getter</span>
<a name="line-108"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Indexed</span>
<a name="line-109"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Context</span>
<a name="line-110"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Type</span>
<a name="line-111"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Setter</span>
<a name="line-112"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversal</span>
<a name="line-113"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Monad</span>
<a name="line-114"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span><span class='hs-varop'>.</span><span class='hs-conid'>Church</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Church</span>
<a name="line-115"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Trans</span>
<a name="line-116"></a><span class='hs-cpp'>#if !(MIN_VERSION_free(4,6,0))</span>
<a name="line-117"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>MonadPlus</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>MonadPlus</span>
<a name="line-118"></a><span class='hs-cpp'>#endif</span>
<a name="line-119"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Language</span><span class='hs-varop'>.</span><span class='hs-conid'>Haskell</span><span class='hs-varop'>.</span><span class='hs-conid'>TH</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>TH</span>
<a name="line-120"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span>
<a name="line-121"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span>
<a name="line-122"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span>
<a name="line-123"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tree</span>
<a name="line-124"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>GHC</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span>
<a name="line-125"></a>
<a name="line-126"></a><span class='hs-cpp'>#ifdef HLINT</span>
<a name="line-127"></a><span class='hs-comment'>{-# ANN module "HLint: ignore Reduce duplication" #-}</span>
<a name="line-128"></a><span class='hs-cpp'>#endif</span>
<a name="line-129"></a>
<a name="line-130"></a><span class='hs-comment'>-- | A 'Plated' type is one where we know how to extract its immediate self-similar children.</span>
<a name="line-131"></a><span class='hs-comment'>--</span>
<a name="line-132"></a><span class='hs-comment'>-- /Example 1/:</span>
<a name="line-133"></a><span class='hs-comment'>--</span>
<a name="line-134"></a><span class='hs-comment'>-- @</span>
<a name="line-135"></a><span class='hs-comment'>-- import Control.Applicative</span>
<a name="line-136"></a><span class='hs-comment'>-- import Control.Lens</span>
<a name="line-137"></a><span class='hs-comment'>-- import Control.Lens.Plated</span>
<a name="line-138"></a><span class='hs-comment'>-- import Data.Data</span>
<a name="line-139"></a><span class='hs-comment'>-- import Data.Data.Lens ('Data.Data.Lens.uniplate')</span>
<a name="line-140"></a><span class='hs-comment'>-- @</span>
<a name="line-141"></a><span class='hs-comment'>--</span>
<a name="line-142"></a><span class='hs-comment'>-- @</span>
<a name="line-143"></a><span class='hs-comment'>-- data Expr</span>
<a name="line-144"></a><span class='hs-comment'>--   = Val 'Int'</span>
<a name="line-145"></a><span class='hs-comment'>--   | Neg Expr</span>
<a name="line-146"></a><span class='hs-comment'>--   | Add Expr Expr</span>
<a name="line-147"></a><span class='hs-comment'>--   deriving ('Eq','Ord','Show','Read','Data','Typeable')</span>
<a name="line-148"></a><span class='hs-comment'>-- @</span>
<a name="line-149"></a><span class='hs-comment'>--</span>
<a name="line-150"></a><span class='hs-comment'>-- @</span>
<a name="line-151"></a><span class='hs-comment'>-- instance 'Plated' Expr where</span>
<a name="line-152"></a><span class='hs-comment'>--   'plate' f (Neg e) = Neg '&lt;$&gt;' f e</span>
<a name="line-153"></a><span class='hs-comment'>--   'plate' f (Add a b) = Add '&lt;$&gt;' f a '&lt;*&gt;' f b</span>
<a name="line-154"></a><span class='hs-comment'>--   'plate' _ a = 'pure' a</span>
<a name="line-155"></a><span class='hs-comment'>-- @</span>
<a name="line-156"></a><span class='hs-comment'>--</span>
<a name="line-157"></a><span class='hs-comment'>-- /or/</span>
<a name="line-158"></a><span class='hs-comment'>--</span>
<a name="line-159"></a><span class='hs-comment'>-- @</span>
<a name="line-160"></a><span class='hs-comment'>-- instance 'Plated' Expr where</span>
<a name="line-161"></a><span class='hs-comment'>--   'plate' = 'Data.Data.Lens.uniplate'</span>
<a name="line-162"></a><span class='hs-comment'>-- @</span>
<a name="line-163"></a><span class='hs-comment'>--</span>
<a name="line-164"></a><span class='hs-comment'>-- /Example 2/:</span>
<a name="line-165"></a><span class='hs-comment'>--</span>
<a name="line-166"></a><span class='hs-comment'>-- @</span>
<a name="line-167"></a><span class='hs-comment'>-- import Control.Applicative</span>
<a name="line-168"></a><span class='hs-comment'>-- import Control.Lens</span>
<a name="line-169"></a><span class='hs-comment'>-- import Control.Lens.Plated</span>
<a name="line-170"></a><span class='hs-comment'>-- import Data.Data</span>
<a name="line-171"></a><span class='hs-comment'>-- import Data.Data.Lens ('Data.Data.Lens.uniplate')</span>
<a name="line-172"></a><span class='hs-comment'>-- @</span>
<a name="line-173"></a><span class='hs-comment'>--</span>
<a name="line-174"></a><span class='hs-comment'>-- @</span>
<a name="line-175"></a><span class='hs-comment'>-- data Tree a</span>
<a name="line-176"></a><span class='hs-comment'>--   = Bin (Tree a) (Tree a)</span>
<a name="line-177"></a><span class='hs-comment'>--   | Tip a</span>
<a name="line-178"></a><span class='hs-comment'>--   deriving ('Eq','Ord','Show','Read','Data','Typeable')</span>
<a name="line-179"></a><span class='hs-comment'>-- @</span>
<a name="line-180"></a><span class='hs-comment'>--</span>
<a name="line-181"></a><span class='hs-comment'>-- @</span>
<a name="line-182"></a><span class='hs-comment'>-- instance 'Plated' (Tree a) where</span>
<a name="line-183"></a><span class='hs-comment'>--   'plate' f (Bin l r) = Bin '&lt;$&gt;' f l '&lt;*&gt;' f r</span>
<a name="line-184"></a><span class='hs-comment'>--   'plate' _ t = 'pure' t</span>
<a name="line-185"></a><span class='hs-comment'>-- @</span>
<a name="line-186"></a><span class='hs-comment'>--</span>
<a name="line-187"></a><span class='hs-comment'>-- /or/</span>
<a name="line-188"></a><span class='hs-comment'>--</span>
<a name="line-189"></a><span class='hs-comment'>-- @</span>
<a name="line-190"></a><span class='hs-comment'>-- instance 'Data' a =&gt; 'Plated' (Tree a) where</span>
<a name="line-191"></a><span class='hs-comment'>--   'plate' = 'uniplate'</span>
<a name="line-192"></a><span class='hs-comment'>-- @</span>
<a name="line-193"></a><span class='hs-comment'>--</span>
<a name="line-194"></a><span class='hs-comment'>-- Note the big distinction between these two implementations.</span>
<a name="line-195"></a><span class='hs-comment'>--</span>
<a name="line-196"></a><span class='hs-comment'>-- The former will only treat children directly in this tree as descendents,</span>
<a name="line-197"></a><span class='hs-comment'>-- the latter will treat trees contained in the values under the tips also</span>
<a name="line-198"></a><span class='hs-comment'>-- as descendants!</span>
<a name="line-199"></a><span class='hs-comment'>--</span>
<a name="line-200"></a><span class='hs-comment'>-- When in doubt, pick a 'Traversal' and just use the various @...Of@ combinators</span>
<a name="line-201"></a><span class='hs-comment'>-- rather than pollute 'Plated' with orphan instances!</span>
<a name="line-202"></a><span class='hs-comment'>--</span>
<a name="line-203"></a><span class='hs-comment'>-- If you want to find something unplated and non-recursive with 'Data.Data.Lens.biplate'</span>
<a name="line-204"></a><span class='hs-comment'>-- use the @...OnOf@ variant with 'ignored', though those usecases are much better served</span>
<a name="line-205"></a><span class='hs-comment'>-- in most cases by using the existing 'Lens' combinators! e.g.</span>
<a name="line-206"></a><span class='hs-comment'>--</span>
<a name="line-207"></a><span class='hs-comment'>-- @</span>
<a name="line-208"></a><span class='hs-comment'>-- 'toListOf' 'biplate' ≡ 'universeOnOf' 'biplate' 'ignored'</span>
<a name="line-209"></a><span class='hs-comment'>-- @</span>
<a name="line-210"></a><span class='hs-comment'>--</span>
<a name="line-211"></a><span class='hs-comment'>-- This same ability to explicitly pass the 'Traversal' in question is why there is no</span>
<a name="line-212"></a><span class='hs-comment'>-- analogue to uniplate's @Biplate@.</span>
<a name="line-213"></a><span class='hs-comment'>--</span>
<a name="line-214"></a><span class='hs-comment'>-- Moreover, since we can allow custom traversals, we implement reasonable defaults for</span>
<a name="line-215"></a><span class='hs-comment'>-- polymorphic data types, that only 'Control.Traversable.traverse' into themselves, and /not/ their</span>
<a name="line-216"></a><span class='hs-comment'>-- polymorphic arguments.</span>
<a name="line-217"></a>
<a name="line-218"></a><a name="Traversal'"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-219"></a>  <span class='hs-comment'>-- | 'Traversal' of the immediate children of this structure.</span>
<a name="line-220"></a>  <span class='hs-comment'>--</span>
<a name="line-221"></a>  <span class='hs-comment'>-- If you're using GHC 7.2 or newer and your type has a 'Data' instance,</span>
<a name="line-222"></a>  <span class='hs-comment'>-- 'plate' will default to 'uniplate' and you can choose to not override</span>
<a name="line-223"></a>  <span class='hs-comment'>-- it with your own definition.</span>
<a name="line-224"></a>  <span class='hs-varid'>plate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Traversal'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-225"></a>  <span class='hs-keyword'>default</span> <span class='hs-varid'>plate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Data</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Traversal'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-226"></a>  <span class='hs-varid'>plate</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>uniplate</span>
<a name="line-227"></a>
<a name="line-228"></a><a name="instance%20Plated%20%5ba%5d"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyword'>where</span>
<a name="line-229"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span>
<a name="line-230"></a>  <span class='hs-varid'>plate</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-conid'>[]</span>
<a name="line-231"></a>
<a name="line-232"></a><a name="instance%20Plated%20(Monad.Free%20f%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-233"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>as</span>
<a name="line-234"></a>  <span class='hs-varid'>plate</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span>         <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span>
<a name="line-235"></a>
<a name="line-236"></a><a name="instance%20Plated%20(Trans.FreeT%20f%20m%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>FreeT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-237"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>FreeT</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>FreeT</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-layout'>(</span><span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-238"></a>
<a name="line-239"></a><span class='hs-cpp'>#if !(MIN_VERSION_free(4,6,0))</span>
<a name="line-240"></a><a name="instance%20Plated%20(MonadPlus.Free%20f%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadPlus</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-241"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadPlus</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>MonadPlus</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>as</span>
<a name="line-242"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadPlus</span><span class='hs-varop'>.</span><span class='hs-conid'>Plus</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>MonadPlus</span><span class='hs-varop'>.</span><span class='hs-conid'>Plus</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>as</span>
<a name="line-243"></a>  <span class='hs-varid'>plate</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span>         <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span>
<a name="line-244"></a><span class='hs-cpp'>#endif</span>
<a name="line-245"></a>
<a name="line-246"></a><a name="instance%20Plated%20(Church.F%20f%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>Church</span><span class='hs-varop'>.</span><span class='hs-conid'>F</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-247"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-conid'>Church</span><span class='hs-varop'>.</span><span class='hs-varid'>toF</span> <span class='hs-varop'>.</span> <span class='hs-varid'>plate</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-conid'>Church</span><span class='hs-varop'>.</span><span class='hs-varid'>fromF</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Church</span><span class='hs-varop'>.</span><span class='hs-varid'>toF</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Church</span><span class='hs-varop'>.</span><span class='hs-varid'>fromF</span>
<a name="line-248"></a>
<a name="line-249"></a><span class='hs-comment'>-- -- This one can't work</span>
<a name="line-250"></a><span class='hs-comment'>--</span>
<a name="line-251"></a><span class='hs-comment'>-- instance (Traversable f, Traversable m) =&gt; Plated (ChurchT.FT f m a) where</span>
<a name="line-252"></a><span class='hs-comment'>--   plate f = fmap ChurchT.toFT . plate (fmap ChurchT.fromFT . f . ChurchT.toFT) . ChurchT.fromFT</span>
<a name="line-253"></a>
<a name="line-254"></a><a name="instance%20Plated%20(CoTrans.CofreeT%20f%20w%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>CoTrans</span><span class='hs-varop'>.</span><span class='hs-conid'>CofreeT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-255"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>CoTrans</span><span class='hs-varop'>.</span><span class='hs-conid'>CofreeT</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>CoTrans</span><span class='hs-varop'>.</span><span class='hs-conid'>CofreeT</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-layout'>(</span><span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-256"></a>
<a name="line-257"></a><a name="instance%20Plated%20(Cofree%20f%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cofree</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-258"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:&lt;</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conop'>:&lt;</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>as</span>
<a name="line-259"></a>
<a name="line-260"></a><a name="instance%20Plated%20(Tree%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-261"></a>  <span class='hs-varid'>plate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>a</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>as</span>
<a name="line-262"></a>
<a name="line-263"></a><a name="instance%20Plated%20TH.Exp"></a><span class='hs-comment'>{- Default uniplate instances -}</span>
<a name="line-264"></a><a name="instance%20Plated%20TH.Exp"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Exp</span>
<a name="line-265"></a><a name="instance%20Plated%20TH.Dec"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Dec</span>
<a name="line-266"></a><a name="instance%20Plated%20TH.Con"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Con</span>
<a name="line-267"></a><a name="instance%20Plated%20TH.Type"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Type</span>
<a name="line-268"></a><span class='hs-cpp'>#if !(MIN_VERSION_template_haskell(2,8,0))</span>
<a name="line-269"></a><a name="instance%20Plated%20TH.Kind"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Kind</span> <span class='hs-comment'>-- in 2.8 Kind is an alias for Type</span>
<a name="line-270"></a><span class='hs-cpp'>#endif</span>
<a name="line-271"></a><a name="instance%20Plated%20TH.Stmt"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Stmt</span>
<a name="line-272"></a><a name="instance%20Plated%20TH.Pat"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Plated</span> <span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Pat</span>
<a name="line-273"></a>
<a name="line-274"></a>
<a name="line-275"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>9</span> <span class='hs-varop'>...</span>
<a name="line-276"></a><a name="..."></a><span class='hs-comment'>-- | Compose through a plate</span>
<a name="line-277"></a><span class='hs-layout'>(</span><span class='hs-varop'>...</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>c</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Over</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c</span> <span class='hs-varid'>c</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Over</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-278"></a><a name="l"></a><span class='hs-definition'>l</span> <span class='hs-varop'>...</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>l</span> <span class='hs-varop'>.</span> <span class='hs-varid'>plate</span> <span class='hs-varop'>.</span> <span class='hs-varid'>m</span>
<a name="line-279"></a><span class='hs-comment'>{-# INLINE (...) #-}</span>
<a name="line-280"></a>
<a name="line-281"></a>
<a name="line-282"></a><a name="deep"></a><span class='hs-comment'>-- | Try to apply a traversal to all transitive descendants of a 'Plated' container, but</span>
<a name="line-283"></a><span class='hs-comment'>-- do not recurse through matching descendants.</span>
<a name="line-284"></a><span class='hs-comment'>--</span>
<a name="line-285"></a><span class='hs-comment'>-- @</span>
<a name="line-286"></a><span class='hs-comment'>-- 'deep' :: 'Plated' s =&gt; 'Fold' s a                 -&gt; 'Fold' s a</span>
<a name="line-287"></a><span class='hs-comment'>-- 'deep' :: 'Plated' s =&gt; 'IndexedFold' s a          -&gt; 'IndexedFold' s a</span>
<a name="line-288"></a><span class='hs-comment'>-- 'deep' :: 'Plated' s =&gt; 'Traversal' s s a b        -&gt; 'Traversal' s s a b</span>
<a name="line-289"></a><span class='hs-comment'>-- 'deep' :: 'Plated' s =&gt; 'IndexedTraversal' s s a b -&gt; 'IndexedTraversal' s s a b</span>
<a name="line-290"></a><span class='hs-comment'>-- @</span>
<a name="line-291"></a><span class='hs-definition'>deep</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Conjoined</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Traversing</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Over</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-292"></a><span class='hs-definition'>deep</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>deepOf</span> <span class='hs-varid'>plate</span>
<a name="line-293"></a>
<a name="line-294"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-295"></a><span class='hs-comment'>-- Children</span>
<a name="line-296"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-297"></a>
<a name="line-298"></a><a name="children"></a><span class='hs-comment'>-- | Extract the immediate descendants of a 'Plated' container.</span>
<a name="line-299"></a><span class='hs-comment'>--</span>
<a name="line-300"></a><span class='hs-comment'>-- @</span>
<a name="line-301"></a><span class='hs-comment'>-- 'children' ≡ 'toListOf' 'plate'</span>
<a name="line-302"></a><span class='hs-comment'>-- @</span>
<a name="line-303"></a><span class='hs-definition'>children</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-304"></a><span class='hs-definition'>children</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toListOf</span> <span class='hs-varid'>plate</span>
<a name="line-305"></a><span class='hs-comment'>{-# INLINE children #-}</span>
<a name="line-306"></a>
<a name="line-307"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-308"></a><span class='hs-comment'>-- Rewriting</span>
<a name="line-309"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-310"></a>
<a name="line-311"></a><a name="rewrite"></a><span class='hs-comment'>-- | Rewrite by applying a rule everywhere you can. Ensures that the rule cannot</span>
<a name="line-312"></a><span class='hs-comment'>-- be applied anywhere in the result:</span>
<a name="line-313"></a><span class='hs-comment'>--</span>
<a name="line-314"></a><span class='hs-comment'>-- @</span>
<a name="line-315"></a><span class='hs-comment'>-- propRewrite r x = 'all' ('Data.Just.isNothing' '.' r) ('universe' ('rewrite' r x))</span>
<a name="line-316"></a><span class='hs-comment'>-- @</span>
<a name="line-317"></a><span class='hs-comment'>--</span>
<a name="line-318"></a><span class='hs-comment'>-- Usually 'transform' is more appropriate, but 'rewrite' can give better</span>
<a name="line-319"></a><span class='hs-comment'>-- compositionality. Given two single transformations @f@ and @g@, you can</span>
<a name="line-320"></a><span class='hs-comment'>-- construct @\a -&gt; f a `mplus` g a@ which performs both rewrites until a fixed point.</span>
<a name="line-321"></a><span class='hs-definition'>rewrite</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-322"></a><span class='hs-definition'>rewrite</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rewriteOf</span> <span class='hs-varid'>plate</span>
<a name="line-323"></a><span class='hs-comment'>{-# INLINE rewrite #-}</span>
<a name="line-324"></a>
<a name="line-325"></a><a name="rewriteOf"></a><span class='hs-comment'>-- | Rewrite by applying a rule everywhere you can. Ensures that the rule cannot</span>
<a name="line-326"></a><span class='hs-comment'>-- be applied anywhere in the result:</span>
<a name="line-327"></a><span class='hs-comment'>--</span>
<a name="line-328"></a><span class='hs-comment'>-- @</span>
<a name="line-329"></a><span class='hs-comment'>-- propRewriteOf l r x = 'all' ('Data.Just.isNothing' '.' r) ('universeOf' l ('rewriteOf' l r x))</span>
<a name="line-330"></a><span class='hs-comment'>-- @</span>
<a name="line-331"></a><span class='hs-comment'>--</span>
<a name="line-332"></a><span class='hs-comment'>-- Usually 'transformOf' is more appropriate, but 'rewriteOf' can give better</span>
<a name="line-333"></a><span class='hs-comment'>-- compositionality. Given two single transformations @f@ and @g@, you can</span>
<a name="line-334"></a><span class='hs-comment'>-- construct @\a -&gt; f a `mplus` g a@ which performs both rewrites until a fixed point.</span>
<a name="line-335"></a><span class='hs-comment'>--</span>
<a name="line-336"></a><span class='hs-comment'>-- @</span>
<a name="line-337"></a><span class='hs-comment'>-- 'rewriteOf' :: 'Control.Lens.Iso.Iso'' a a       -&gt; (a -&gt; 'Maybe' a) -&gt; a -&gt; a</span>
<a name="line-338"></a><span class='hs-comment'>-- 'rewriteOf' :: 'Lens'' a a      -&gt; (a -&gt; 'Maybe' a) -&gt; a -&gt; a</span>
<a name="line-339"></a><span class='hs-comment'>-- 'rewriteOf' :: 'Traversal'' a a -&gt; (a -&gt; 'Maybe' a) -&gt; a -&gt; a</span>
<a name="line-340"></a><span class='hs-comment'>-- 'rewriteOf' :: 'Setter'' a a    -&gt; (a -&gt; 'Maybe' a) -&gt; a -&gt; a</span>
<a name="line-341"></a><span class='hs-comment'>-- @</span>
<a name="line-342"></a><span class='hs-definition'>rewriteOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span>
<a name="line-343"></a><span class='hs-definition'>rewriteOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-344"></a>  <span class='hs-varid'>go</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transformOf</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>maybe</span> <span class='hs-varid'>x</span> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-345"></a><span class='hs-comment'>{-# INLINE rewriteOf #-}</span>
<a name="line-346"></a>
<a name="line-347"></a><a name="rewriteOn"></a><span class='hs-comment'>-- | Rewrite recursively over part of a larger structure.</span>
<a name="line-348"></a><span class='hs-comment'>--</span>
<a name="line-349"></a><span class='hs-comment'>-- @</span>
<a name="line-350"></a><span class='hs-comment'>-- 'rewriteOn' :: 'Plated' a =&gt; 'Control.Lens.Iso.Iso'' s a       -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-351"></a><span class='hs-comment'>-- 'rewriteOn' :: 'Plated' a =&gt; 'Lens'' s a      -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-352"></a><span class='hs-comment'>-- 'rewriteOn' :: 'Plated' a =&gt; 'Traversal'' s a -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-353"></a><span class='hs-comment'>-- 'rewriteOn' :: 'Plated' a =&gt; 'ASetter'' s a   -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-354"></a><span class='hs-comment'>-- @</span>
<a name="line-355"></a><span class='hs-definition'>rewriteOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span>
<a name="line-356"></a><span class='hs-definition'>rewriteOn</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>over</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rewrite</span>
<a name="line-357"></a><span class='hs-comment'>{-# INLINE rewriteOn #-}</span>
<a name="line-358"></a>
<a name="line-359"></a><a name="rewriteOnOf"></a><span class='hs-comment'>-- | Rewrite recursively over part of a larger structure using a specified 'Setter'.</span>
<a name="line-360"></a><span class='hs-comment'>--</span>
<a name="line-361"></a><span class='hs-comment'>-- @</span>
<a name="line-362"></a><span class='hs-comment'>-- 'rewriteOnOf' :: 'Control.Lens.Iso.Iso'' s a       -&gt; 'Control.Lens.Iso.Iso'' a a       -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-363"></a><span class='hs-comment'>-- 'rewriteOnOf' :: 'Lens'' s a      -&gt; 'Lens'' a a      -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-364"></a><span class='hs-comment'>-- 'rewriteOnOf' :: 'Traversal'' s a -&gt; 'Traversal'' a a -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-365"></a><span class='hs-comment'>-- 'rewriteOnOf' :: 'Setter'' s a    -&gt; 'Setter'' a a    -&gt; (a -&gt; 'Maybe' a) -&gt; s -&gt; s</span>
<a name="line-366"></a><span class='hs-comment'>-- @</span>
<a name="line-367"></a><span class='hs-definition'>rewriteOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span>
<a name="line-368"></a><span class='hs-definition'>rewriteOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>over</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rewriteOf</span> <span class='hs-varid'>l</span>
<a name="line-369"></a><span class='hs-comment'>{-# INLINE rewriteOnOf #-}</span>
<a name="line-370"></a>
<a name="line-371"></a><a name="rewriteM"></a><span class='hs-comment'>-- | Rewrite by applying a monadic rule everywhere you can. Ensures that the rule cannot</span>
<a name="line-372"></a><span class='hs-comment'>-- be applied anywhere in the result.</span>
<a name="line-373"></a><span class='hs-definition'>rewriteM</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-374"></a><span class='hs-definition'>rewriteM</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rewriteMOf</span> <span class='hs-varid'>plate</span>
<a name="line-375"></a><span class='hs-comment'>{-# INLINE rewriteM #-}</span>
<a name="line-376"></a>
<a name="line-377"></a><a name="rewriteMOf"></a><span class='hs-comment'>-- | Rewrite by applying a monadic rule everywhere you recursing with a user-specified 'Traversal'.</span>
<a name="line-378"></a><span class='hs-comment'>-- Ensures that the rule cannot be applied anywhere in the result.</span>
<a name="line-379"></a><span class='hs-definition'>rewriteMOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span>
<a name="line-380"></a><span class='hs-definition'>rewriteMOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-381"></a>  <span class='hs-varid'>go</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transformMOf</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'>&gt;&gt;=</span> <span class='hs-varid'>maybe</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>go</span><span class='hs-layout'>)</span>
<a name="line-382"></a><span class='hs-comment'>{-# INLINE rewriteMOf #-}</span>
<a name="line-383"></a>
<a name="line-384"></a><a name="rewriteMOn"></a><span class='hs-comment'>-- | Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified 'Traversal'.</span>
<a name="line-385"></a><span class='hs-comment'>-- Ensures that the rule cannot be applied anywhere in the result.</span>
<a name="line-386"></a><span class='hs-definition'>rewriteMOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>t</span>
<a name="line-387"></a><span class='hs-definition'>rewriteMOn</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapMOf</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rewriteM</span>
<a name="line-388"></a><span class='hs-comment'>{-# INLINE rewriteMOn #-}</span>
<a name="line-389"></a>
<a name="line-390"></a><a name="rewriteMOnOf"></a><span class='hs-comment'>-- | Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified 'Traversal',</span>
<a name="line-391"></a><span class='hs-comment'>-- using a user-specified 'Traversal' for recursion. Ensures that the rule cannot be applied anywhere in the result.</span>
<a name="line-392"></a><span class='hs-definition'>rewriteMOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>t</span>
<a name="line-393"></a><span class='hs-definition'>rewriteMOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapMOf</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rewriteMOf</span> <span class='hs-varid'>l</span>
<a name="line-394"></a><span class='hs-comment'>{-# INLINE rewriteMOnOf #-}</span>
<a name="line-395"></a>
<a name="line-396"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-397"></a><span class='hs-comment'>-- Universe</span>
<a name="line-398"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-399"></a>
<a name="line-400"></a><a name="universe"></a><span class='hs-comment'>-- | Retrieve all of the transitive descendants of a 'Plated' container, including itself.</span>
<a name="line-401"></a><span class='hs-definition'>universe</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-402"></a><span class='hs-definition'>universe</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>universeOf</span> <span class='hs-varid'>plate</span>
<a name="line-403"></a><span class='hs-comment'>{-# INLINE universe #-}</span>
<a name="line-404"></a>
<a name="line-405"></a><a name="universeOf"></a><span class='hs-comment'>-- | Given a 'Fold' that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself.</span>
<a name="line-406"></a><span class='hs-comment'>--</span>
<a name="line-407"></a><span class='hs-comment'>-- @</span>
<a name="line-408"></a><span class='hs-comment'>-- 'universeOf' :: 'Fold' a a -&gt; a -&gt; [a]</span>
<a name="line-409"></a><span class='hs-comment'>-- @</span>
<a name="line-410"></a><span class='hs-definition'>universeOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Getting</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-411"></a><span class='hs-definition'>universeOf</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-412"></a>  <span class='hs-varid'>go</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span> <span class='hs-conop'>:</span> <span class='hs-varid'>foldMapOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>go</span> <span class='hs-varid'>a</span>
<a name="line-413"></a><span class='hs-comment'>{-# INLINE universeOf #-}</span>
<a name="line-414"></a>
<a name="line-415"></a><a name="universeOn"></a><span class='hs-comment'>-- | Given a 'Fold' that knows how to find 'Plated' parts of a container retrieve them and all of their descendants, recursively.</span>
<a name="line-416"></a><span class='hs-definition'>universeOn</span> <span class='hs-keyglyph'>::</span>  <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Getting</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-417"></a><span class='hs-definition'>universeOn</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>universeOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>plate</span>
<a name="line-418"></a><span class='hs-comment'>{-# INLINE universeOn #-}</span>
<a name="line-419"></a>
<a name="line-420"></a><a name="universeOnOf"></a><span class='hs-comment'>-- | Given a 'Fold' that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself that lie</span>
<a name="line-421"></a><span class='hs-comment'>-- in a region indicated by another 'Fold'.</span>
<a name="line-422"></a><span class='hs-comment'>--</span>
<a name="line-423"></a><span class='hs-comment'>-- @</span>
<a name="line-424"></a><span class='hs-comment'>-- 'toListOf' l ≡ 'universeOnOf' l 'ignored'</span>
<a name="line-425"></a><span class='hs-comment'>-- @</span>
<a name="line-426"></a><span class='hs-definition'>universeOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Getting</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Getting</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-427"></a><span class='hs-definition'>universeOnOf</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldMapOf</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>universeOf</span>
<a name="line-428"></a><span class='hs-comment'>{-# INLINE universeOnOf #-}</span>
<a name="line-429"></a>
<a name="line-430"></a><a name="cosmos"></a><span class='hs-comment'>-- | Fold over all transitive descendants of a 'Plated' container, including itself.</span>
<a name="line-431"></a><span class='hs-definition'>cosmos</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Fold</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-432"></a><span class='hs-definition'>cosmos</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cosmosOf</span> <span class='hs-varid'>plate</span>
<a name="line-433"></a><span class='hs-comment'>{-# INLINE cosmos #-}</span>
<a name="line-434"></a>
<a name="line-435"></a><a name="cosmosOf"></a><span class='hs-comment'>-- | Given a 'Fold' that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself.</span>
<a name="line-436"></a><span class='hs-comment'>--</span>
<a name="line-437"></a><span class='hs-comment'>-- @</span>
<a name="line-438"></a><span class='hs-comment'>-- 'cosmosOf' :: 'Fold' a a -&gt; 'Fold' a a</span>
<a name="line-439"></a><span class='hs-comment'>-- @</span>
<a name="line-440"></a><span class='hs-definition'>cosmosOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-441"></a><span class='hs-definition'>cosmosOf</span> <span class='hs-varid'>d</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varop'>*&gt;</span> <span class='hs-varid'>d</span> <span class='hs-layout'>(</span><span class='hs-varid'>cosmosOf</span> <span class='hs-varid'>d</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-442"></a><span class='hs-comment'>{-# INLINE cosmosOf #-}</span>
<a name="line-443"></a>
<a name="line-444"></a><a name="cosmosOn"></a><span class='hs-comment'>-- | Given a 'Fold' that knows how to find 'Plated' parts of a container fold them and all of their descendants, recursively.</span>
<a name="line-445"></a><span class='hs-comment'>--</span>
<a name="line-446"></a><span class='hs-comment'>-- @</span>
<a name="line-447"></a><span class='hs-comment'>-- 'cosmosOn' :: 'Plated' a =&gt; 'Fold' s a -&gt; 'Fold' s a</span>
<a name="line-448"></a><span class='hs-comment'>-- @</span>
<a name="line-449"></a><span class='hs-definition'>cosmosOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-450"></a><span class='hs-definition'>cosmosOn</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cosmosOnOf</span> <span class='hs-varid'>d</span> <span class='hs-varid'>plate</span>
<a name="line-451"></a><span class='hs-comment'>{-# INLINE cosmosOn #-}</span>
<a name="line-452"></a>
<a name="line-453"></a><a name="cosmosOnOf"></a><span class='hs-comment'>-- | Given a 'Fold' that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself that lie</span>
<a name="line-454"></a><span class='hs-comment'>-- in a region indicated by another 'Fold'.</span>
<a name="line-455"></a><span class='hs-comment'>--</span>
<a name="line-456"></a><span class='hs-comment'>-- @</span>
<a name="line-457"></a><span class='hs-comment'>-- 'cosmosOnOf' :: 'Fold' s a -&gt; 'Fold' a a -&gt; 'Fold' s a</span>
<a name="line-458"></a><span class='hs-comment'>-- @</span>
<a name="line-459"></a><span class='hs-definition'>cosmosOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LensLike'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-460"></a><span class='hs-definition'>cosmosOnOf</span> <span class='hs-varid'>d</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>d</span> <span class='hs-varop'>.</span> <span class='hs-varid'>cosmosOf</span> <span class='hs-varid'>p</span>
<a name="line-461"></a><span class='hs-comment'>{-# INLINE cosmosOnOf #-}</span>
<a name="line-462"></a>
<a name="line-463"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-464"></a><span class='hs-comment'>-- Transformation</span>
<a name="line-465"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-466"></a>
<a name="line-467"></a><a name="transform"></a><span class='hs-comment'>-- | Transform every element in the tree, in a bottom-up manner.</span>
<a name="line-468"></a><span class='hs-comment'>--</span>
<a name="line-469"></a><span class='hs-comment'>-- For example, replacing negative literals with literals:</span>
<a name="line-470"></a><span class='hs-comment'>--</span>
<a name="line-471"></a><span class='hs-comment'>-- @</span>
<a name="line-472"></a><span class='hs-comment'>-- negLits = 'transform' $ \\x -&gt; case x of</span>
<a name="line-473"></a><span class='hs-comment'>--   Neg (Lit i) -&gt; Lit ('negate' i)</span>
<a name="line-474"></a><span class='hs-comment'>--   _           -&gt; x</span>
<a name="line-475"></a><span class='hs-comment'>-- @</span>
<a name="line-476"></a><span class='hs-definition'>transform</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-477"></a><span class='hs-definition'>transform</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transformOf</span> <span class='hs-varid'>plate</span>
<a name="line-478"></a><span class='hs-comment'>{-# INLINE transform #-}</span>
<a name="line-479"></a>
<a name="line-480"></a><a name="transformOn"></a><span class='hs-comment'>-- | Transform every element in the tree in a bottom-up manner over a region indicated by a 'Setter'.</span>
<a name="line-481"></a><span class='hs-comment'>--</span>
<a name="line-482"></a><span class='hs-comment'>-- @</span>
<a name="line-483"></a><span class='hs-comment'>-- 'transformOn' :: 'Plated' a =&gt; 'Traversal'' s a -&gt; (a -&gt; a) -&gt; s -&gt; s</span>
<a name="line-484"></a><span class='hs-comment'>-- 'transformOn' :: 'Plated' a =&gt; 'Setter'' s a    -&gt; (a -&gt; a) -&gt; s -&gt; s</span>
<a name="line-485"></a><span class='hs-comment'>-- @</span>
<a name="line-486"></a><span class='hs-definition'>transformOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span>
<a name="line-487"></a><span class='hs-definition'>transformOn</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>over</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>transform</span>
<a name="line-488"></a><span class='hs-comment'>{-# INLINE transformOn #-}</span>
<a name="line-489"></a>
<a name="line-490"></a><a name="transformOf"></a><span class='hs-comment'>-- | Transform every element by recursively applying a given 'Setter' in a bottom-up manner.</span>
<a name="line-491"></a><span class='hs-comment'>--</span>
<a name="line-492"></a><span class='hs-comment'>-- @</span>
<a name="line-493"></a><span class='hs-comment'>-- 'transformOf' :: 'Traversal'' a a -&gt; (a -&gt; a) -&gt; a -&gt; a</span>
<a name="line-494"></a><span class='hs-comment'>-- 'transformOf' :: 'Setter'' a a    -&gt; (a -&gt; a) -&gt; a -&gt; a</span>
<a name="line-495"></a><span class='hs-comment'>-- @</span>
<a name="line-496"></a><span class='hs-definition'>transformOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span>
<a name="line-497"></a><span class='hs-definition'>transformOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-498"></a>  <span class='hs-varid'>go</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>over</span> <span class='hs-varid'>l</span> <span class='hs-varid'>go</span>
<a name="line-499"></a><span class='hs-comment'>{-# INLINE transformOf #-}</span>
<a name="line-500"></a>
<a name="line-501"></a><a name="transformOnOf"></a><span class='hs-comment'>-- | Transform every element in a region indicated by a 'Setter' by recursively applying another 'Setter'</span>
<a name="line-502"></a><span class='hs-comment'>-- in a bottom-up manner.</span>
<a name="line-503"></a><span class='hs-comment'>--</span>
<a name="line-504"></a><span class='hs-comment'>-- @</span>
<a name="line-505"></a><span class='hs-comment'>-- 'transformOnOf' :: 'Setter'' s a -&gt; 'Traversal'' a a -&gt; (a -&gt; a) -&gt; s -&gt; s</span>
<a name="line-506"></a><span class='hs-comment'>-- 'transformOnOf' :: 'Setter'' s a -&gt; 'Setter'' a a    -&gt; (a -&gt; a) -&gt; s -&gt; s</span>
<a name="line-507"></a><span class='hs-comment'>-- @</span>
<a name="line-508"></a><span class='hs-definition'>transformOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>ASetter</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span>
<a name="line-509"></a><span class='hs-definition'>transformOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>over</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>transformOf</span> <span class='hs-varid'>l</span>
<a name="line-510"></a><span class='hs-comment'>{-# INLINE transformOnOf #-}</span>
<a name="line-511"></a>
<a name="line-512"></a><a name="transformM"></a><span class='hs-comment'>-- | Transform every element in the tree, in a bottom-up manner, monadically.</span>
<a name="line-513"></a><span class='hs-definition'>transformM</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-514"></a><span class='hs-definition'>transformM</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transformMOf</span> <span class='hs-varid'>plate</span>
<a name="line-515"></a><span class='hs-comment'>{-# INLINE transformM #-}</span>
<a name="line-516"></a>
<a name="line-517"></a><a name="transformMOn"></a><span class='hs-comment'>-- | Transform every element in the tree in a region indicated by a supplied 'Traversal', in a bottom-up manner, monadically.</span>
<a name="line-518"></a><span class='hs-comment'>--</span>
<a name="line-519"></a><span class='hs-comment'>-- @</span>
<a name="line-520"></a><span class='hs-comment'>-- 'transformMOn' :: ('Monad' m, 'Plated' a) =&gt; 'Traversal'' s a -&gt; (a -&gt; m a) -&gt; s -&gt; m s</span>
<a name="line-521"></a><span class='hs-comment'>-- @</span>
<a name="line-522"></a><span class='hs-definition'>transformMOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>t</span>
<a name="line-523"></a><span class='hs-definition'>transformMOn</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapMOf</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>transformM</span>
<a name="line-524"></a><span class='hs-comment'>{-# INLINE transformMOn #-}</span>
<a name="line-525"></a>
<a name="line-526"></a><a name="transformMOf"></a><span class='hs-comment'>-- | Transform every element in a tree using a user supplied 'Traversal' in a bottom-up manner with a monadic effect.</span>
<a name="line-527"></a><span class='hs-comment'>--</span>
<a name="line-528"></a><span class='hs-comment'>-- @</span>
<a name="line-529"></a><span class='hs-comment'>-- 'transformMOf' :: 'Monad' m =&gt; 'Traversal'' a a -&gt; (a -&gt; m a) -&gt; a -&gt; m a</span>
<a name="line-530"></a><span class='hs-comment'>-- @</span>
<a name="line-531"></a><span class='hs-definition'>transformMOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span>
<a name="line-532"></a><span class='hs-definition'>transformMOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-533"></a>  <span class='hs-varid'>go</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapMOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>go</span> <span class='hs-varid'>t</span> <span class='hs-varop'>&gt;&gt;=</span> <span class='hs-varid'>f</span>
<a name="line-534"></a><span class='hs-comment'>{-# INLINE transformMOf #-}</span>
<a name="line-535"></a>
<a name="line-536"></a><a name="transformMOnOf"></a><span class='hs-comment'>-- | Transform every element in a tree that lies in a region indicated by a supplied 'Traversal', walking with a user supplied 'Traversal' in</span>
<a name="line-537"></a><span class='hs-comment'>-- a bottom-up manner with a monadic effect.</span>
<a name="line-538"></a><span class='hs-comment'>--</span>
<a name="line-539"></a><span class='hs-comment'>-- @</span>
<a name="line-540"></a><span class='hs-comment'>-- 'transformMOnOf' :: 'Monad' m =&gt; 'Traversal'' s a -&gt; 'Traversal'' a a -&gt; (a -&gt; m a) -&gt; s -&gt; m s</span>
<a name="line-541"></a><span class='hs-comment'>-- @</span>
<a name="line-542"></a><span class='hs-definition'>transformMOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span> <span class='hs-varid'>t</span>
<a name="line-543"></a><span class='hs-definition'>transformMOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapMOf</span> <span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>transformMOf</span> <span class='hs-varid'>l</span>
<a name="line-544"></a><span class='hs-comment'>{-# INLINE transformMOnOf #-}</span>
<a name="line-545"></a>
<a name="line-546"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-547"></a><span class='hs-comment'>-- Holes and Contexts</span>
<a name="line-548"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-549"></a>
<a name="line-550"></a><a name="contexts"></a><span class='hs-comment'>-- | Return a list of all of the editable contexts for every location in the structure, recursively.</span>
<a name="line-551"></a><span class='hs-comment'>--</span>
<a name="line-552"></a><span class='hs-comment'>-- @</span>
<a name="line-553"></a><span class='hs-comment'>-- propUniverse x = 'universe' x '==' 'map' 'Control.Comonad.Store.Class.pos' ('contexts' x)</span>
<a name="line-554"></a><span class='hs-comment'>-- propId x = 'all' ('==' x) ['Control.Lens.Internal.Context.extract' w | w &lt;- 'contexts' x]</span>
<a name="line-555"></a><span class='hs-comment'>-- @</span>
<a name="line-556"></a><span class='hs-comment'>--</span>
<a name="line-557"></a><span class='hs-comment'>-- @</span>
<a name="line-558"></a><span class='hs-comment'>-- 'contexts' ≡ 'contextsOf' 'plate'</span>
<a name="line-559"></a><span class='hs-comment'>-- @</span>
<a name="line-560"></a><span class='hs-definition'>contexts</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Context</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-561"></a><span class='hs-definition'>contexts</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>contextsOf</span> <span class='hs-varid'>plate</span>
<a name="line-562"></a><span class='hs-comment'>{-# INLINE contexts #-}</span>
<a name="line-563"></a>
<a name="line-564"></a><a name="contextsOf"></a><span class='hs-comment'>-- | Return a list of all of the editable contexts for every location in the structure, recursively, using a user-specified 'Traversal' to walk each layer.</span>
<a name="line-565"></a><span class='hs-comment'>--</span>
<a name="line-566"></a><span class='hs-comment'>-- @</span>
<a name="line-567"></a><span class='hs-comment'>-- propUniverse l x = 'universeOf' l x '==' 'map' 'Control.Comonad.Store.Class.pos' ('contextsOf' l x)</span>
<a name="line-568"></a><span class='hs-comment'>-- propId l x = 'all' ('==' x) ['Control.Lens.Internal.Context.extract' w | w &lt;- 'contextsOf' l x]</span>
<a name="line-569"></a><span class='hs-comment'>-- @</span>
<a name="line-570"></a><span class='hs-comment'>--</span>
<a name="line-571"></a><span class='hs-comment'>-- @</span>
<a name="line-572"></a><span class='hs-comment'>-- 'contextsOf' :: 'Traversal'' a a -&gt; a -&gt; ['Context' a a a]</span>
<a name="line-573"></a><span class='hs-comment'>-- @</span>
<a name="line-574"></a><span class='hs-definition'>contextsOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ATraversal'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Context</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-575"></a><span class='hs-definition'>contextsOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sell</span> <span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>context</span> <span class='hs-layout'>(</span><span class='hs-varid'>holesOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-576"></a>  <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-577"></a>    <span class='hs-conid'>Context</span> <span class='hs-varid'>ctx</span> <span class='hs-varid'>child</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-varid'>xs</span>
<a name="line-578"></a>    <span class='hs-conid'>Context</span> <span class='hs-varid'>cont</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-varid'>contextsOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>child</span>
<a name="line-579"></a>    <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Context</span> <span class='hs-layout'>(</span><span class='hs-varid'>ctx</span> <span class='hs-varop'>.</span> <span class='hs-varid'>cont</span><span class='hs-layout'>)</span> <span class='hs-varid'>y</span>
<a name="line-580"></a><span class='hs-comment'>{-# INLINE contextsOf #-}</span>
<a name="line-581"></a>
<a name="line-582"></a><a name="contextsOn"></a><span class='hs-comment'>-- | Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied 'Traversal', recursively using 'plate'.</span>
<a name="line-583"></a><span class='hs-comment'>--</span>
<a name="line-584"></a><span class='hs-comment'>-- @</span>
<a name="line-585"></a><span class='hs-comment'>-- 'contextsOn' b ≡ 'contextsOnOf' b 'plate'</span>
<a name="line-586"></a><span class='hs-comment'>-- @</span>
<a name="line-587"></a><span class='hs-comment'>--</span>
<a name="line-588"></a><span class='hs-comment'>-- @</span>
<a name="line-589"></a><span class='hs-comment'>-- 'contextsOn' :: 'Plated' a =&gt; 'Traversal'' s a -&gt; s -&gt; ['Context' a a s]</span>
<a name="line-590"></a><span class='hs-comment'>-- @</span>
<a name="line-591"></a><span class='hs-definition'>contextsOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>ATraversal</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Context</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span>
<a name="line-592"></a><span class='hs-definition'>contextsOn</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>contextsOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>plate</span>
<a name="line-593"></a><span class='hs-comment'>{-# INLINE contextsOn #-}</span>
<a name="line-594"></a>
<a name="line-595"></a><a name="contextsOnOf"></a><span class='hs-comment'>-- | Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied 'Traversal', recursively using</span>
<a name="line-596"></a><span class='hs-comment'>-- another user-supplied 'Traversal' to walk each layer.</span>
<a name="line-597"></a><span class='hs-comment'>--</span>
<a name="line-598"></a><span class='hs-comment'>-- @</span>
<a name="line-599"></a><span class='hs-comment'>-- 'contextsOnOf' :: 'Traversal'' s a -&gt; 'Traversal'' a a -&gt; s -&gt; ['Context' a a s]</span>
<a name="line-600"></a><span class='hs-comment'>-- @</span>
<a name="line-601"></a><span class='hs-definition'>contextsOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ATraversal</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>ATraversal'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Context</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span>
<a name="line-602"></a><span class='hs-definition'>contextsOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>map</span> <span class='hs-varid'>context</span> <span class='hs-varop'>.</span> <span class='hs-varid'>holesOf</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>where</span>
<a name="line-603"></a>  <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-604"></a>    <span class='hs-conid'>Context</span> <span class='hs-varid'>ctx</span> <span class='hs-varid'>child</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-varid'>xs</span>
<a name="line-605"></a>    <span class='hs-conid'>Context</span> <span class='hs-varid'>cont</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-varid'>contextsOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>child</span>
<a name="line-606"></a>    <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Context</span> <span class='hs-layout'>(</span><span class='hs-varid'>ctx</span> <span class='hs-varop'>.</span> <span class='hs-varid'>cont</span><span class='hs-layout'>)</span> <span class='hs-varid'>y</span>
<a name="line-607"></a><span class='hs-comment'>{-# INLINE contextsOnOf #-}</span>
<a name="line-608"></a>
<a name="line-609"></a><a name="holes"></a><span class='hs-comment'>-- | The one-level version of 'context'. This extracts a list of the immediate children as editable contexts.</span>
<a name="line-610"></a><span class='hs-comment'>--</span>
<a name="line-611"></a><span class='hs-comment'>-- Given a context you can use 'Control.Comonad.Store.Class.pos' to see the values, 'Control.Comonad.Store.Class.peek' at what the structure would be like with an edited result, or simply 'Control.Lens.Internal.Context.extract' the original structure.</span>
<a name="line-612"></a><span class='hs-comment'>--</span>
<a name="line-613"></a><span class='hs-comment'>-- @</span>
<a name="line-614"></a><span class='hs-comment'>-- propChildren x = 'children' l x '==' 'map' 'Control.Comonad.Store.Class.pos' ('holes' l x)</span>
<a name="line-615"></a><span class='hs-comment'>-- propId x = 'all' ('==' x) ['Control.Lens.Internal.Context.extract' w | w &lt;- 'holes' l x]</span>
<a name="line-616"></a><span class='hs-comment'>-- @</span>
<a name="line-617"></a><span class='hs-comment'>--</span>
<a name="line-618"></a><span class='hs-comment'>-- @</span>
<a name="line-619"></a><span class='hs-comment'>-- 'holes' = 'holesOf' 'plate'</span>
<a name="line-620"></a><span class='hs-comment'>-- @</span>
<a name="line-621"></a><span class='hs-definition'>holes</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Pretext</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-&gt;</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-622"></a><span class='hs-definition'>holes</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>holesOf</span> <span class='hs-varid'>plate</span>
<a name="line-623"></a><span class='hs-comment'>{-# INLINE holes #-}</span>
<a name="line-624"></a>
<a name="line-625"></a><a name="holesOn"></a><span class='hs-comment'>-- | An alias for 'holesOf', provided for consistency with the other combinators.</span>
<a name="line-626"></a><span class='hs-comment'>--</span>
<a name="line-627"></a><span class='hs-comment'>-- @</span>
<a name="line-628"></a><span class='hs-comment'>-- 'holesOn' ≡ 'holesOf'</span>
<a name="line-629"></a><span class='hs-comment'>-- @</span>
<a name="line-630"></a><span class='hs-comment'>--</span>
<a name="line-631"></a><span class='hs-comment'>-- @</span>
<a name="line-632"></a><span class='hs-comment'>-- 'holesOn' :: 'Iso'' s a                -&gt; s -&gt; ['Pretext' (-&gt;) a a s]</span>
<a name="line-633"></a><span class='hs-comment'>-- 'holesOn' :: 'Lens'' s a               -&gt; s -&gt; ['Pretext' (-&gt;) a a s]</span>
<a name="line-634"></a><span class='hs-comment'>-- 'holesOn' :: 'Traversal'' s a          -&gt; s -&gt; ['Pretext' (-&gt;) a a s]</span>
<a name="line-635"></a><span class='hs-comment'>-- 'holesOn' :: 'IndexedLens'' i s a      -&gt; s -&gt; ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s]</span>
<a name="line-636"></a><span class='hs-comment'>-- 'holesOn' :: 'IndexedTraversal'' i s a -&gt; s -&gt; ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s]</span>
<a name="line-637"></a><span class='hs-comment'>-- @</span>
<a name="line-638"></a><span class='hs-definition'>holesOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Conjoined</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Over</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bazaar</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Pretext</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span>
<a name="line-639"></a><span class='hs-definition'>holesOn</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>holesOf</span>
<a name="line-640"></a><span class='hs-comment'>{-# INLINE holesOn #-}</span>
<a name="line-641"></a>
<a name="line-642"></a><a name="holesOnOf"></a><span class='hs-comment'>-- | Extract one level of 'holes' from a container in a region specified by one 'Traversal', using another.</span>
<a name="line-643"></a><span class='hs-comment'>--</span>
<a name="line-644"></a><span class='hs-comment'>-- @</span>
<a name="line-645"></a><span class='hs-comment'>-- 'holesOnOf' b l ≡ 'holesOf' (b '.' l)</span>
<a name="line-646"></a><span class='hs-comment'>-- @</span>
<a name="line-647"></a><span class='hs-comment'>--</span>
<a name="line-648"></a><span class='hs-comment'>-- @</span>
<a name="line-649"></a><span class='hs-comment'>-- 'holesOnOf' :: 'Iso'' s a       -&gt; 'Iso'' a a                -&gt; s -&gt; ['Pretext' (-&gt;) a a s]</span>
<a name="line-650"></a><span class='hs-comment'>-- 'holesOnOf' :: 'Lens'' s a      -&gt; 'Lens'' a a               -&gt; s -&gt; ['Pretext' (-&gt;) a a s]</span>
<a name="line-651"></a><span class='hs-comment'>-- 'holesOnOf' :: 'Traversal'' s a -&gt; 'Traversal'' a a          -&gt; s -&gt; ['Pretext' (-&gt;) a a s]</span>
<a name="line-652"></a><span class='hs-comment'>-- 'holesOnOf' :: 'Lens'' s a      -&gt; 'IndexedLens'' i a a      -&gt; s -&gt; ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s]</span>
<a name="line-653"></a><span class='hs-comment'>-- 'holesOnOf' :: 'Traversal'' s a -&gt; 'IndexedTraversal'' i a a -&gt; s -&gt; ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s]</span>
<a name="line-654"></a><span class='hs-comment'>-- @</span>
<a name="line-655"></a><span class='hs-definition'>holesOnOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Conjoined</span> <span class='hs-varid'>p</span>
<a name="line-656"></a>          <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bazaar</span> <span class='hs-varid'>p</span>  <span class='hs-varid'>r</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-657"></a>          <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Over</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bazaar</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>r</span> <span class='hs-varid'>r</span>
<a name="line-658"></a>          <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Pretext</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>r</span> <span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span>
<a name="line-659"></a><span class='hs-definition'>holesOnOf</span> <span class='hs-varid'>b</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>holesOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-varop'>.</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span>
<a name="line-660"></a><span class='hs-comment'>{-# INLINE holesOnOf #-}</span>
<a name="line-661"></a>
<a name="line-662"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-663"></a><span class='hs-comment'>-- Paramorphisms</span>
<a name="line-664"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-665"></a>
<a name="line-666"></a><a name="paraOf"></a><span class='hs-comment'>-- | Perform a fold-like computation on each value, technically a paramorphism.</span>
<a name="line-667"></a><span class='hs-comment'>--</span>
<a name="line-668"></a><span class='hs-comment'>-- @</span>
<a name="line-669"></a><span class='hs-comment'>-- 'paraOf' :: 'Fold' a a -&gt; (a -&gt; [r] -&gt; r) -&gt; a -&gt; r</span>
<a name="line-670"></a><span class='hs-comment'>-- @</span>
<a name="line-671"></a><span class='hs-definition'>paraOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Getting</span> <span class='hs-layout'>(</span><span class='hs-conid'>Endo</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>r</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>r</span>
<a name="line-672"></a><span class='hs-definition'>paraOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-673"></a>  <span class='hs-varid'>go</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>go</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>toListOf</span> <span class='hs-varid'>l</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-674"></a><span class='hs-comment'>{-# INLINE paraOf #-}</span>
<a name="line-675"></a>
<a name="line-676"></a><a name="para"></a><span class='hs-comment'>-- | Perform a fold-like computation on each value, technically a paramorphism.</span>
<a name="line-677"></a><span class='hs-comment'>--</span>
<a name="line-678"></a><span class='hs-comment'>-- @</span>
<a name="line-679"></a><span class='hs-comment'>-- 'para' ≡ 'paraOf' 'plate'</span>
<a name="line-680"></a><span class='hs-comment'>-- @</span>
<a name="line-681"></a><span class='hs-definition'>para</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>r</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>r</span>
<a name="line-682"></a><span class='hs-definition'>para</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>paraOf</span> <span class='hs-varid'>plate</span>
<a name="line-683"></a><span class='hs-comment'>{-# INLINE para #-}</span>
<a name="line-684"></a>
<a name="line-685"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-686"></a><span class='hs-comment'>-- Compos</span>
<a name="line-687"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-688"></a>
<a name="line-689"></a><span class='hs-comment'>-- $compos</span>
<a name="line-690"></a><span class='hs-comment'>--</span>
<a name="line-691"></a><span class='hs-comment'>-- Provided for compatibility with Björn Bringert's @compos@ library.</span>
<a name="line-692"></a><span class='hs-comment'>--</span>
<a name="line-693"></a><span class='hs-comment'>-- Note: Other operations from compos that were inherited by @uniplate@ are /not/ included</span>
<a name="line-694"></a><span class='hs-comment'>-- to avoid having even more redundant names for the same operators. For comparison:</span>
<a name="line-695"></a><span class='hs-comment'>--</span>
<a name="line-696"></a><span class='hs-comment'>-- @</span>
<a name="line-697"></a><span class='hs-comment'>-- 'composOpMonoid' ≡ 'foldMapOf' 'plate'</span>
<a name="line-698"></a><span class='hs-comment'>-- 'composOpMPlus' f ≡ 'msumOf' ('plate' '.' 'to' f)</span>
<a name="line-699"></a><span class='hs-comment'>-- 'composOp' ≡ 'descend' ≡ 'over' 'plate'</span>
<a name="line-700"></a><span class='hs-comment'>-- 'composOpM' ≡ 'descendM' ≡ 'mapMOf' 'plate'</span>
<a name="line-701"></a><span class='hs-comment'>-- 'composOpM_' ≡ 'descendM_' ≡ 'mapMOf_' 'plate'</span>
<a name="line-702"></a><span class='hs-comment'>-- @</span>
<a name="line-703"></a>
<a name="line-704"></a><a name="composOpFold"></a><span class='hs-comment'>-- | Fold the immediate children of a 'Plated' container.</span>
<a name="line-705"></a><span class='hs-comment'>--</span>
<a name="line-706"></a><span class='hs-comment'>-- @</span>
<a name="line-707"></a><span class='hs-comment'>-- 'composOpFold' z c f = 'foldrOf' 'plate' (c '.' f) z</span>
<a name="line-708"></a><span class='hs-comment'>-- @</span>
<a name="line-709"></a><span class='hs-definition'>composOpFold</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span>
<a name="line-710"></a><span class='hs-definition'>composOpFold</span> <span class='hs-varid'>z</span> <span class='hs-varid'>c</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldrOf</span> <span class='hs-varid'>plate</span> <span class='hs-layout'>(</span><span class='hs-varid'>c</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>z</span>
<a name="line-711"></a><span class='hs-comment'>{-# INLINE composOpFold #-}</span>
<a name="line-712"></a>
<a name="line-713"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-714"></a><span class='hs-comment'>-- Parts</span>
<a name="line-715"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-716"></a>
<a name="line-717"></a><a name="parts"></a><span class='hs-comment'>-- | The original @uniplate@ combinator, implemented in terms of 'Plated' as a 'Lens'.</span>
<a name="line-718"></a><span class='hs-comment'>--</span>
<a name="line-719"></a><span class='hs-comment'>-- @</span>
<a name="line-720"></a><span class='hs-comment'>-- 'parts' ≡ 'partsOf' 'plate'</span>
<a name="line-721"></a><span class='hs-comment'>-- @</span>
<a name="line-722"></a><span class='hs-comment'>--</span>
<a name="line-723"></a><span class='hs-comment'>-- The resulting 'Lens' is safer to use as it ignores 'over-application' and deals gracefully with under-application,</span>
<a name="line-724"></a><span class='hs-comment'>-- but it is only a proper 'Lens' if you don't change the list 'length'!</span>
<a name="line-725"></a><span class='hs-definition'>parts</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Plated</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Lens'</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-726"></a><span class='hs-definition'>parts</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>partsOf</span> <span class='hs-varid'>plate</span>
<a name="line-727"></a><span class='hs-comment'>{-# INLINE parts #-}</span>
<a name="line-728"></a>
<a name="line-729"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-730"></a><span class='hs-comment'>-- Generics</span>
<a name="line-731"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-732"></a>
<a name="line-733"></a><a name="gplate"></a><span class='hs-comment'>-- | Implement 'plate' operation for a type using its 'Generic' instance.</span>
<a name="line-734"></a><span class='hs-definition'>gplate</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Generic</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rep</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Traversal'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-735"></a><span class='hs-definition'>gplate</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>GHC</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-varid'>to</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>GHC</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-varid'>from</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-736"></a><span class='hs-comment'>{-# INLINE gplate #-}</span>
<a name="line-737"></a>
<a name="line-738"></a><a name="GPlated"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-varid'>g</span> <span class='hs-keyword'>where</span>
<a name="line-739"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Traversal'</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-740"></a>
<a name="line-741"></a><a name="instance%20GPlated%20a%20(M1%20i%20c%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>c</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-742"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>M1</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-743"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
<a name="line-744"></a>
<a name="line-745"></a><a name="instance%20GPlated%20a%20(f%20:+:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-conop'>:+:</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-746"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>L1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>L1</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-747"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>R1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>R1</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-748"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
<a name="line-749"></a>
<a name="line-750"></a><a name="instance%20GPlated%20a%20(f%20:*:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-751"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conop'>:*:</span><span class='hs-layout'>)</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'>&lt;*&gt;</span> <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>y</span>
<a name="line-752"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
<a name="line-753"></a>
<a name="line-754"></a><a name="instance%20OVERLAPPING_PRAGMA%20GPlated%20a%20(K1%20i%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>OVERLAPPING_PRAGMA</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-755"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>K1</span> <span class='hs-varop'>&lt;$&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-756"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
<a name="line-757"></a>
<a name="line-758"></a><a name="instance%20GPlated%20a%20(K1%20i%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-759"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span>
<a name="line-760"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
<a name="line-761"></a>
<a name="line-762"></a><a name="instance%20GPlated%20a%20U1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-conid'>U1</span> <span class='hs-keyword'>where</span>
<a name="line-763"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span>
<a name="line-764"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
<a name="line-765"></a>
<a name="line-766"></a><a name="instance%20GPlated%20a%20V1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GPlated</span> <span class='hs-varid'>a</span> <span class='hs-conid'>V1</span> <span class='hs-keyword'>where</span>
<a name="line-767"></a>  <span class='hs-varid'>gplate'</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v</span> <span class='hs-varop'>`seq`</span> <span class='hs-varid'>error</span> <span class='hs-str'>"GPlated/V1"</span>
<a name="line-768"></a>  <span class='hs-comment'>{-# INLINE gplate' #-}</span>
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