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; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "list-list-fix")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund slow-simple-flatten (x)
;; Computes (simple-flatten x) very inefficiently. There's no reason to ever
;; use this function.
(declare (xargs :guard t))
(if (consp x)
(app (car x)
(slow-simple-flatten (cdr x)))
nil))
(defthm slow-simple-flatten-when-not-consp
(implies (not (consp x))
(equal (slow-simple-flatten x)
nil))
:hints(("Goal" :in-theory (enable slow-simple-flatten))))
(defthm slow-simple-flatten-of-cons
(equal (slow-simple-flatten (cons a x))
(app a (slow-simple-flatten x)))
:hints(("Goal" :in-theory (enable slow-simple-flatten))))
(defund fast-simple-flatten$ (x acc)
;; Computes (revappend (simple-flatten x) acc). This is cheaper than calling
;; simple-flatten, saveing you one "fast-rev" call and the associated
;; consing.
(declare (xargs :guard (true-listp acc)))
(if (consp x)
(fast-simple-flatten$ (cdr x)
(revappend (car x) acc))
acc))
(defund simple-flatten (x)
;; Does one level of list flattening. This won't flatten a whole tree, it'll
;; just condense a two-level "list of lists" into a regular, one-level list.
;; It takes two linear passes of consing.
(declare (xargs :guard t))
(fast-rev (fast-simple-flatten$ x nil)))
(defthmd lemma-for-definition-of-simple-flatten
(implies (true-listp acc)
(equal (fast-simple-flatten$ x acc)
(app (rev (slow-simple-flatten x)) acc)))
:hints(("Goal" :in-theory (enable fast-simple-flatten$))))
(defthmd definition-of-simple-flatten
(equal (simple-flatten x)
(if (consp x)
(app (car x)
(simple-flatten (cdr x)))
nil))
:rule-classes :definition
:hints(("Goal" :in-theory (enable simple-flatten
lemma-for-definition-of-simple-flatten))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition simple-flatten))))
(defthm simple-flatten-when-not-consp
(implies (not (consp x))
(equal (simple-flatten x)
nil))
:hints(("Goal" :in-theory (enable definition-of-simple-flatten))))
(defthm simple-flatten-of-cons
(equal (simple-flatten (cons a x))
(app a (simple-flatten x)))
:hints(("Goal" :in-theory (enable definition-of-simple-flatten))))
(defthm true-listp-of-simple-flatten
(equal (true-listp (simple-flatten x))
t)
:hints(("Goal" :induct (cdr-induction x))))
(defthm simple-flatten-of-list-fix
(equal (simple-flatten (list-fix x))
(simple-flatten x))
:hints(("Goal" :induct (cdr-induction x))))
(defthm simple-flatten-of-app
(equal (simple-flatten (app x y))
(app (simple-flatten x) (simple-flatten y)))
:hints(("Goal" :induct (cdr-induction x))))
(defthm simple-flatten-of-list-list-fix
(equal (simple-flatten (list-list-fix x))
(simple-flatten x))
:hints(("Goal" :induct (cdr-induction x))))
(defthm forcing-fast-simple-flatten$-removal
(implies (force (true-listp acc))
(equal (fast-simple-flatten$ x acc)
(app (rev (simple-flatten x)) acc)))
:hints(("Goal" :in-theory (enable fast-simple-flatten$))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition fast-simple-flatten$))))
(defun fast-simple-flatten-of-domain$ (x acc)
;; Calculates (revappend (simple-flatten (domain x)) acc) in a single,
;; tail-recursive linear pass.
(declare (xargs :guard (and (mapp x)
(true-listp acc))))
(if (consp x)
(fast-simple-flatten-of-domain$ (cdr x)
(revappend (car (car x)) acc))
acc))
(defthm fast-simple-flatten-of-domain$-removal
(implies (force (true-listp acc))
(equal (fast-simple-flatten-of-domain$ x acc)
(app (rev (simple-flatten (domain x))) acc))))
(defun fast-simple-flatten-of-range$ (x acc)
;; Calculates (revappend (simple-flatten (range x)) acc) in a single,
;; tail-recursive linear pass.
(declare (xargs :guard (and (mapp x)
(true-listp acc))))
(if (consp x)
(fast-simple-flatten-of-range$ (cdr x)
(revappend (cdr (car x)) acc))
acc))
(defthm fast-simple-flatten-of-range$-removal
(implies (force (true-listp acc))
(equal (fast-simple-flatten-of-range$ x acc)
(app (rev (simple-flatten (range x))) acc))))
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