/usr/share/acl2-4.3/books/cutil/defmapappend.lisp is in acl2-books-source 4.3-3.
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; Copyright (C) 2008-2011 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version. This program is distributed in the hope that it will be useful but
; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
; FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
; more details. You should have received a copy of the GNU General Public
; License along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "CUTIL")
(include-book "defprojection")
(defxdoc defmapappend
:parents (cutil)
:short "Append transformations of list elements."
:long "<p>Defmapappend allows you to quickly introduce a function like</p>
<code>
(loop for elem in x append (f elem))
</code>
<p>and produces some basic theorems about this new function.</p>
<p>General form:</p>
<code>
(defmapappend name formals
transform
&key guard ; t by default
verify-guards ; t by default
transform-exec ; nil by default
transform-true-list-p ; nil by default
mode ; default defun-mode by default
parents ; '(undocumented) by default
short ; nil by default
long ; nil by default
)
</code>
<p>For instance,</p>
<code>
(defmapappend append-square-lists (x)
(square-lists x)
:guard (integer-list-listp x))
</code>
<p>would introduce a new function, <tt>append-square-lists</tt>, that applies
<tt>square-lists</tt> to every element of its argument and appends together
all of the results.</p>
<p>Note that <b>x</b> is treated in a special way: it refers to the whole list
in the formals and guards, but refers to the individual elements of the list in
the <tt>element</tt> portion. This is similar to how other macros like @(see
deflist), @(see defalist), and @(see defprojection) handle <tt>x</tt>.</p>
<h3>Usage and Arguments</h3>
<p>Let <tt>pkg</tt> be the package of <tt>name</tt>. All functions, theorems,
and variables are created in this package. One of the formals must be
<tt>pkg::x</tt>, and this argument represents the list that will be
transformed. Otherwise, the only restriction on formals is that you may not
use the names <tt>pkg::a</tt>, <tt>pkg::y</tt>, and <tt>pkg::acc</tt>, because
we use these variables in the theorems we generate.</p>
<p>The <tt>transform</tt> should indicate an element transforming function that
produces a list of some kind as its output. Adopting an ML-like syntax,
<tt>transform</tt> should have a signature such as the following:</p>
<code>
transform : elem -> A list
</code>
<p>We produce a new function of the given <tt>name</tt>, which has the
signature:</p>
<code>
name : elem list -> A list
</code>
<p>Our new function applies <tt>transform</tt> to every element in its input
list, and appends together all of the results. That is, the logical definition
of the new function we introduce is as follows:</p>
<code>
(defun name (x)
(if (atom x)
nil
(append (transform (car x))
(name (cdr x)))))
</code>
<p>The new function will be more efficient than the above. In particular, we
write a <tt>mappappend-exec</tt> function that builds the answer in reverse
using revappend and reverses it at the end. An even more efficient version is
possible when the <tt>:transform-exec</tt> option is provided; see below for
details.</p>
<p>The optional <tt>:guard</tt> and <tt>:verify-guards</tt> are given to the
<tt>defund</tt> event that we introduce. Often @(see deflist) is convenient
for introducing the necessary guard.</p>
<p>The optional <tt>:mode</tt> keyword can be set to <tt>:logic</tt> or
<tt>:program</tt> to introduce the recognizer in logic or program mode. The
default is whatever the current default defun-mode is for ACL2, i.e., if you
are already in program mode, it will default to program mode, etc.</p>
<p>The optional <tt>:transform-true-list-p</tt> argument can be set to
<tt>t</tt> whenever the transformation is known to unconditionally produce a
true list, and allows us to slightly optimize our function.</p>
<h4>The :transform-exec argument</h4>
<p>When provided, the optional <tt>:transform-exec</tt> argument should be the
name of a function that satisfies the following property:</p>
<code>
(implies (true-listp acc)
(equal (transform-exec x acc)
(append (rev (transform x)) acc)))
</code>
<p>Note that such functions are automatically introduced by @(see
defprojection). For instance,</p>
<code>
(defprojection square-list (x)
(square x))
</code>
<p>generates a suitable function named <tt>square-list-exec</tt>. Amusingly,
suitable functions are also generated by defmapappend, itself.</p>
<p>When such a function is provided, we can use it to generate a more efficient
implementation, which uses the tail-recursive function to build the answer in
reverse, and then reverses it at the very end, avoiding even the intermediate
computation of the lists emitted by <tt>transform</tt>.</p>")
(defun defmapappend-fn (name formals transform
guard verify-guards
transform-exec transform-true-list-p
mode
parents short long
)
(declare (xargs :mode :program))
(b* (((unless (symbolp name))
(er hard? 'defmapappend "Name must be a symbol, but is ~x0." name))
(mksym-package-symbol name)
;; Special variables that are reserved by defmapappend
(x (intern-in-package-of-symbol "X" name))
(a (intern-in-package-of-symbol "A" name))
(n (intern-in-package-of-symbol "N" name))
(y (intern-in-package-of-symbol "Y" name))
(acc (intern-in-package-of-symbol "ACC" name))
((unless (and (symbol-listp formals)
(no-duplicatesp formals)))
(er hard 'defmapappend
"The formals must be a list of unique symbols, but the ~
formals are ~x0." formals))
((unless (member x formals))
(er hard 'defmapappend
"The formals must contain X, but are ~x0.~%" formals))
((unless (and (not (member a formals))
(not (member n formals))
(not (member y formals))
(not (member acc formals))))
(er hard 'defmapappend
"As a special restriction, formals may not mention a, n, ~
or y, but the formals are ~x0." formals))
((unless (and (consp transform)
(symbolp (car transform))))
(er hard 'defmapappend
"The transform must be a function applied to the formals, ~
but is ~x0." transform))
(exec-fn (mksym name '-exec))
(transform-fn (car transform))
(transform-args (cdr transform))
((unless (and (subsetp-equal transform-args formals)
(subsetp-equal formals transform-args)))
(er hard 'defmapappend
"The transform's formals do not agree with the defmapappend ~
function's formals."))
((unless (booleanp verify-guards))
(er hard 'defmapappend
":verify-guards must be a boolean, but is ~x0."
verify-guards))
((unless (booleanp transform-true-list-p))
(er hard 'defmapappend
":transform-true-list-p must be a boolean, but is ~x0."
transform-true-list-p))
((unless (symbolp transform-exec))
(er hard 'defmapappend
":transform-exec must be a symbol, but is ~x0."
transform-exec))
((unless (member mode '(:logic :program)))
(er hard 'defmapappend
":mode must be :logic or :program, but is ~x0."
mode))
(short (or short
(and parents
(str::cat "@(call " (symbol-name name)
") applies @(see " (symbol-name transform-fn)
") to every member of the list <tt>x</tt>, "
"and appends together all the resulting lists."))))
(long (or long
(and parents
(str::cat "<p>This is an ordinary @(see defmapappend).</p>"
"@(def " (symbol-name name) ")"))))
(doc (if (or parents short long)
`((defxdoc ,name :parents ,parents :short ,short :long ,long))
nil)))
`(encapsulate
()
,(if (eq mode :program)
'(program)
'(logic))
,@doc
(defund ,exec-fn (,@formals ,acc)
(declare (xargs :guard ,guard
:verify-guards nil))
(if (consp ,x)
(,exec-fn ,@(subst `(cdr ,x) x formals)
,(if transform-exec
`(,transform-exec ,@(subst `(car ,x) x transform-args) ,acc)
`(,(if transform-true-list-p
'revappend
'revappend-without-guard)
(,transform-fn . ,(subst `(car ,x) x transform-args))
,acc)))
,acc))
(defund ,name (,@formals)
(declare (xargs :guard ,guard
:verify-guards nil))
(mbe :logic (if (consp ,x)
(append (,transform-fn . ,(subst `(car ,x) x transform-args))
(,name . ,(subst `(cdr ,x) x formals)))
nil)
:exec (reverse (,exec-fn ,@formals nil))))
,@(and
(eq mode :logic)
`((defthm ,(mksym name '-when-not-consp)
(implies (not (consp ,x))
(equal (,name . ,formals)
nil))
:hints(("Goal" :in-theory (enable ,name))))
(defthm ,(mksym name '-of-cons)
(equal (,name . ,(subst `(cons ,a ,x) x formals))
(append (,transform-fn . ,(subst a x transform-args))
(,name . ,formals)))
:hints(("Goal" :in-theory (enable ,name))))
(local (defthm lemma
(implies (true-listp ,acc)
(true-listp (,exec-fn ,@formals ,acc)))
:hints(("Goal" :in-theory (enable ,exec-fn)))))
(defthm ,(mksym exec-fn '-removal)
(equal (,exec-fn ,@formals ,acc)
(append (rev (,name ,@formals)) ,acc))
:hints(("Goal" :in-theory (enable ,exec-fn))))
,@(if verify-guards
`((verify-guards ,exec-fn)
(verify-guards ,name))
nil)
(defthm ,(mksym name '-of-list-fix)
(equal (,name . ,(subst `(list-fix ,x) x formals))
(,name . ,formals))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym name '-of-append)
(equal (,name . ,(subst `(append ,x ,y) x formals))
(append (,name . ,formals)
(,name . ,(subst y x formals))))
:hints(("Goal" :induct (len ,x))))
)))))
(defmacro defmapappend (name formals transform
&key
transform-exec
(transform-true-list-p 't)
(guard 't)
(verify-guards 't)
mode
(parents '(acl2::undocumented))
(short 'nil)
(long 'nil))
`(make-event (let ((mode (or ',mode (default-defun-mode (w state)))))
(defmapappend-fn ',name ',formals ',transform
',guard ',verify-guards
',transform-exec ',transform-true-list-p
mode
',parents ',short ',long))))
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