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; VL Verilog Toolkit
; 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/
;
; 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@centtech.com>
(in-package "DEPGRAPH")
(include-book "std/util/define" :dir :system)
(include-book "std/alists/alist-defuns" :dir :system)
(include-book "std/osets/top" :dir :system)
(local (include-book "std/alists/top" :dir :system))
(define mergesort-alist-values (x)
:parents (depgraph)
:short "Sort all of the values bound in an alist."
(b* (((when (atom x))
nil)
((when (atom (car x)))
;; Bad alist convention
(mergesort-alist-values (cdr x))))
(cons (cons (caar x)
(mergesort (cdar x)))
(mergesort-alist-values (cdr x))))
///
(defthm mergesort-alist-values-when-atom
(implies (atom x)
(equal (mergesort-alist-values x)
nil)))
(defthm mergesort-alist-values-of-cons
(equal (mergesort-alist-values (cons a x))
(if (atom a)
(mergesort-alist-values x)
(cons (cons (car a)
(mergesort (cdr a)))
(mergesort-alist-values x)))))
(defthm alistp-of-mergesort-alist-values
(alistp (mergesort-alist-values x)))
(defthm hons-assoc-equal-of-mergesort-alist-values
(equal (hons-assoc-equal key (mergesort-alist-values x))
(let ((look (hons-assoc-equal key x)))
(and look
(cons (car look) (mergesort (cdr look)))))))
(defthm alist-keys-of-mergesort-alist-values
(equal (alist-keys (mergesort-alist-values x))
(alist-keys x)))
(encapsulate
()
(local (defthm l0
(equal (mergesort-alist-values (acl2::list-fix x))
(mergesort-alist-values x))
:hints(("Goal" :induct (len x)))))
(defcong acl2::list-equiv equal (mergesort-alist-values x) 1
:hints(("Goal"
:in-theory (e/d (acl2::list-equiv) (l0))
:use ((:instance l0 (x x))
(:instance l0 (x x-equiv)))))))
(encapsulate
()
(local (defthm l0
(implies (acl2::alists-agree keys x y)
(acl2::alists-agree keys
(mergesort-alist-values x)
(mergesort-alist-values y)))
:hints(("Goal" :in-theory (enable acl2::alists-agree)))))
(local (defthm l1
(implies (acl2::sub-alistp x y)
(acl2::sub-alistp (mergesort-alist-values x)
(mergesort-alist-values y)))
:hints(("Goal" :in-theory (enable acl2::sub-alistp)))))
(defcong acl2::alist-equiv acl2::alist-equiv (mergesort-alist-values x) 1
:hints(("Goal" :in-theory (enable acl2::alist-equiv))))))
(define alist-values-are-sets-p (x)
:parents (depgraph)
:short "Recognizer for alists whose every value is an ordered set."
(b* (((when (atom x))
t)
((when (atom (car x)))
;; Non-alist convention
(alist-values-are-sets-p (cdr x))))
(and (setp (cdar x))
(alist-values-are-sets-p (cdr x))))
///
(defthm alist-values-are-sets-p-when-atom
(implies (not (consp x))
(equal (alist-values-are-sets-p x)
t)))
(defthm alist-values-are-sets-p-of-cons
(equal (alist-values-are-sets-p (cons a x))
;; Goofy, don't need to check consp because if it's an atom, then
;; its cdr is NIL, which is a fine set.
(and (setp (cdr a))
(alist-values-are-sets-p x))))
(defthm setp-of-lookup-when-alist-values-are-sets-p
(implies (alist-values-are-sets-p x)
(setp (cdr (hons-assoc-equal a x)))))
(defthm alist-values-are-sets-p-of-hons-shrink-alist
(implies (and (alist-values-are-sets-p x)
(alist-values-are-sets-p ans))
(alist-values-are-sets-p (hons-shrink-alist x ans))))
(defthm alist-values-are-sets-p-of-mergesort-alist-values
(alist-values-are-sets-p (mergesort-alist-values x))
:hints(("Goal" :induct (len x))))
(encapsulate
()
(local (defthm l0
(equal (alist-values-are-sets-p (acl2::list-fix x))
(alist-values-are-sets-p x))
:hints(("Goal" :induct (len x)))))
(defcong acl2::list-equiv equal (alist-values-are-sets-p x) 1
:hints(("Goal"
:in-theory (e/d (acl2::list-equiv) (l0))
:use ((:instance l0 (x x))
(:instance l0 (x x-equiv)))))))
;; BOZO prove alist-equiv congruence
)
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