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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>
;
; Additional copyright notice:
;
; This file is adapted from Milawa, which is also released under the GPL.
(in-package "CUTIL")
(include-book "deflist")
(defxdoc defprojection
:parents (cutil)
:short "Project a transformation across a list."
:long "<p>Defprojection allows you to quickly introduce a function like
<tt>map f</tt>. That is, given an element-transforming function, <tt>f</tt>,
it can define a new function that applies <tt>f</tt> to every element in a
list.</p>
<p>General form:</p>
<code>
(defprojection name formals
element
&key guard ; t by default
verify-guards ; t by default
nil-preservingp ; nil by default
result-type ; nil by default
already-definedp ; nil by default
mode ; current defun-mode by default
optimize ; t by default
result-type ; nil by default
parents ; '(acl2::undocumented) by default
short ; nil by default
long ; nil by default
)
</code>
<p>For example,</p>
<code>
(defprojection my-strip-cars (x)
(car x)
:guard (alistp x))
</code>
<p>defines a new function, <tt>my-strip-cars</tt>, that is like the built-in
ACL2 function <tt>strip-cars</tt>.</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 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 defmapappend) 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::n</tt>, <tt>pkg::y</tt>, and
<tt>pkg::acc</tt>, because we use these variables in the theorems we
generate.</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>:nil-preservingp</tt> argument can be set to <tt>t</tt>
when the element transformation satisfies <tt>(element nil ...) = nil</tt>.
This allows <tt>defprojection</tt> to produce slightly better theorems.</p>
<p>The optional <tt>:result-type</tt> keyword defaults to <tt>nil</tt>, and in
this case no additional \"type theorem\" will be inferred. But, if you instead
give the name of a unary predicate like <tt>nat-listp</tt>, then a defthm will
be generated that looks like <tt>(implies (force guard) (nat-listp (name
...)))</tt> while <tt>name</tt> is still enabled. This is not a very general
mechanism, but it is often good enough to save a lot of work.</p>
<p>The optional <tt>:already-definedp</tt> keyword can be set if you have
already defined the function. This can be used to generate all of the ordinary
<tt>defprojection</tt> theorems without generating a <tt>defund</tt> event, and
is useful when you are dealing with mutually recursive transformations.</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>:optimize</tt> keyword can be set to <tt>nil</tt> if you do
not want the projection to be optimized with <tt>nreverse</tt>. This will
result in a slightly slower transformation function, but avoids a ttag.</p>
<p>The optional <tt>:parents</tt>, <tt>:short</tt>, and <tt>:long</tt> keywords
are as in @(see defxdoc). Typically you only need to specify
<tt>:parents</tt>, and suitable documentation will be automatically generated
for <tt>:short</tt> and <tt>:long</tt>. If you don't like this documentation,
you can supply your own <tt>:short</tt> and/or <tt>:long</tt> to override
it.</p>")
(defthmd defprojection-append-of-nil
(implies (true-listp a)
(equal (append a nil) a)))
(defthmd defprojection-associativity-of-append
(equal (append (append x y) z)
(append x (append y z))))
(defun defprojection-fn (name formals element
nil-preservingp already-definedp
guard verify-guards
mode optimize result-type
parents short long)
(declare (xargs :mode :program))
(b* (((unless (symbolp name))
(er hard? 'defprojection "Name must be a symbol, but is ~x0." name))
(mksym-package-symbol name)
;; Special variables that are reserved by defprojection
(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 'defprojection
"The formals must be a list of unique symbols, but the ~
formals are ~x0." formals))
((unless (member x formals))
(er hard 'defprojection
"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 'defprojection
"As a special restriction, formals may not mention a, n, ~
or y, but the formals are ~x0." formals))
((unless (and (consp element)
(symbolp (car element))))
(er hard 'defprojection
"The element transformation must be a function applied ~
to the formals, but is ~x0." element))
(list-fn name)
(list-args formals)
(elem-fn (car element))
(elem-args (cdr element))
(exec-fn (mksym list-fn '-exec))
((unless (and (symbol-listp elem-args)
(no-duplicatesp elem-args)
(subsetp elem-args formals)
(subsetp formals elem-args)))
(er hard 'defprojection
"The element transformation's formals do not agree with ~
the list transformation's formals."))
((unless (or (eq mode :logic)
(eq mode :program)))
(er hard 'defprojection
":mode must be one of :logic or :program, but is ~x0." mode))
((unless (booleanp verify-guards))
(er hard 'defprojection
":verify-guards must be a boolean, but is ~x0."
verify-guards))
((unless (booleanp nil-preservingp))
(er hard 'defprojection
":nil-preservingp must be a boolean, but is ~x0."
nil-preservingp))
((unless (booleanp already-definedp))
(er hard 'defprojection
":already-definedp must be a boolean, but is ~x0."
already-definedp))
((unless (booleanp optimize))
(er hard 'defprojection
":optimize must be a boolean, but is ~x0."
optimize))
((unless (symbolp result-type))
(er hard 'defprojection
":result-type must be a symbol, but is ~x0."
result-type))
(short (or short
(and parents
(str::cat "@(call " (symbol-name list-fn) ") maps "
"@(see " (symbol-name elem-fn) ") across a list."))))
(long (or long
(and parents
(str::cat "<p>This is an ordinary @(see defprojection).</p>"
"@(def " (symbol-name list-fn) ")"))))
(doc (if (or parents short long)
`((defxdoc ,name :parents ,parents :short ,short :long ,long))
nil))
(def (if already-definedp
nil
`((defun ,exec-fn (,@list-args ,acc)
(declare (xargs :guard ,(if (equal guard t)
`(true-listp ,acc)
`(and (true-listp ,acc)
,guard))
:mode ,mode
:verify-guards nil))
(if (consp ,x)
(,exec-fn ,@(subst `(cdr ,x) x list-args)
(cons (,elem-fn ,@(subst `(car ,x) x elem-args))
,acc))
,acc))
(defun ,list-fn (,@list-args)
(declare (xargs :guard ,guard
:mode ,mode
:verify-guards nil))
(mbe :logic
(if (consp ,x)
(cons (,elem-fn ,@(subst `(car ,x) x elem-args))
(,list-fn ,@(subst `(cdr ,x) x list-args)))
nil)
:exec
(reverse (,exec-fn ,@list-args nil)))))))
(ndef `(defun ,list-fn (,@list-args)
(nreverse (,exec-fn ,@list-args nil))))
(opt (if (or already-definedp (not optimize))
nil
`((progn
(make-event
(if (acl2::global-val 'acl2::include-book-path (w state))
;; We're in an include book. Don't print.
(value '(value-triple :invisible))
(value '(value-triple
(cw "~|~%Optimizing definition of ~s0:~% ~p1~%~%"
',list-fn ',ndef)))))
(defttag cutil-optimize)
(progn!
(set-raw-mode t)
(when (boundp 'ACL2::*never-profile-ht*)
;; ACL2(h). Never allow exec function to be
;; memoized, to justify nreverse
(setf (gethash ',exec-fn ACL2::*never-profile-ht*) t))
,ndef)
(defttag nil)))))
((when (eq mode :program))
`(encapsulate
()
(program)
,@doc
,@def
,@opt)))
`(encapsulate
()
(logic)
,@doc
,@def
,@(if already-definedp
nil
`((in-theory (disable ,list-fn ,exec-fn))))
(local (in-theory (enable defprojection-append-of-nil
defprojection-associativity-of-append)))
(defthm ,(mksym list-fn '-when-not-consp)
(implies (not (consp ,x))
(equal (,list-fn ,@list-args)
nil))
:hints(("Goal" :in-theory (enable ,list-fn))))
(defthm ,(mksym list-fn '-of-cons)
(equal (,list-fn ,@(subst `(cons ,a ,x) x list-args))
(cons (,elem-fn ,@(subst a x elem-args))
(,list-fn ,@list-args)))
:hints(("Goal" :in-theory (enable ,list-fn))))
(defthm ,(mksym 'true-listp-of- list-fn)
(equal (true-listp (,list-fn ,@list-args))
t)
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym 'len-of- list-fn)
(equal (len (,list-fn ,@list-args))
(len ,x))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym 'consp-of- list-fn)
(equal (consp (,list-fn ,@list-args))
(consp ,x))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym 'car-of- list-fn)
(equal (car (,list-fn ,@list-args))
,(if nil-preservingp
`(,elem-fn ,@(subst `(car ,x) x elem-args))
`(if (consp ,x)
(,elem-fn ,@(subst `(car ,x) x elem-args))
nil))))
(defthm ,(mksym 'cdr-of- list-fn)
(equal (cdr (,list-fn ,@list-args))
(,list-fn ,@(subst `(cdr ,x) x list-args))))
(defthm ,(mksym list-fn '-under-iff)
(iff (,list-fn ,@list-args)
(consp ,x))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym list-fn '-of-list-fix)
(equal (,list-fn ,@(subst `(list-fix ,x) x list-args))
(,list-fn ,@list-args))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym list-fn '-of-append)
(equal (,list-fn ,@(subst `(append ,x ,y) x list-args))
(append (,list-fn ,@list-args)
(,list-fn ,@(subst y x list-args))))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym list-fn '-of-rev)
(equal (,list-fn ,@(subst `(rev ,x) x list-args))
(rev (,list-fn ,@list-args)))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym list-fn '-of-revappend)
(equal (,list-fn ,@(subst `(revappend ,x ,y) x list-args))
(revappend (,list-fn ,@list-args)
(,list-fn ,@(subst y x list-args)))))
,@(if nil-preservingp
`((defthm ,(mksym 'simpler-take-of- list-fn)
(equal (simpler-take ,n (,list-fn ,@list-args))
(,list-fn ,@(subst `(simpler-take ,n ,x) x list-args)))
:hints(("Goal"
:in-theory (enable simpler-take)
:induct (simpler-take ,n ,x)))))
nil)
(defthm ,(mksym 'nthcdr-of- list-fn)
(equal (nthcdr ,n (,list-fn ,@list-args))
(,list-fn ,@(subst `(nthcdr ,n ,x) x list-args)))
:hints(("Goal"
:in-theory (enable nthcdr)
:induct (nthcdr ,n ,x))))
(defthm ,(mksym 'member-equal-of- elem-fn '-in- list-fn '-when-member-equal)
(implies (member-equal ,a (double-rewrite ,x))
(member-equal (,elem-fn ,@(subst a x elem-args))
(,list-fn ,@list-args)))
:hints(("Goal" :induct (len ,x))))
(defthm ,(mksym 'subsetp-equal-of- list-fn 's-when-subsetp-equal)
(implies (subsetp-equal (double-rewrite ,x)
(double-rewrite ,y))
(subsetp-equal (,list-fn ,@list-args)
(,list-fn ,@(subst y x list-args))))
:hints(("Goal"
;; bleh
:in-theory (enable subsetp-equal)
:induct (len ,x))))
,@(if nil-preservingp
`((defthm ,(mksym 'nth-of- list-fn)
(equal (nth ,n (,list-fn ,@list-args))
(,elem-fn ,@(subst `(nth ,n ,x) x elem-args)))
:hints(("Goal"
:in-theory (enable nth)
:induct (nth ,n ,x)))))
nil)
,@(if already-definedp
nil
`((defthm ,(mksym exec-fn '-removal)
(implies (force (true-listp ,acc))
(equal (,exec-fn ,@list-args ,acc)
(revappend (,list-fn ,@list-args) ,acc)))
:hints(("Goal" :in-theory (enable ,exec-fn))))
,@(if verify-guards
`((verify-guards ,exec-fn)
(verify-guards ,list-fn))
nil)))
,@(and result-type
`((defthm ,(mksym result-type '-of- list-fn)
,(if (eq guard t)
`(,result-type (,list-fn ,@list-args))
`(implies (force ,guard)
(,result-type (,list-fn ,@list-args))))
:hints(("Goal"
:induct (len ,x)
:in-theory (enable (:induction len)))))))
,@opt
)))
(defmacro defprojection (name formals element &key nil-preservingp already-definedp
(optimize 't)
result-type
(guard 't)
(verify-guards 't)
mode
(parents '(acl2::undocumented))
(short 'nil)
(long 'nil))
`(make-event (let ((mode (or ',mode (default-defun-mode (w state)))))
(defprojection-fn ',name ',formals ',element
',nil-preservingp ',already-definedp
',guard ',verify-guards
mode ',optimize ',result-type
',parents ',short ',long))))
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