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; FTY::defprod Example
; Copyright (C) 2014, Oracle and/or its affiliates. All rights reserved.
;
; 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: David L. Rager <david.rager@oracle.com>
(in-package "ACL2")
; WARNING: This file is a work in progress. Hopefully at some point it will
; suffice as a nice working example for defprod's dependent types feature, but
; as of December 2015, it's broken. It is currently intended to be "ld"'d into
; a system, not certified or included as a book.
(include-book "std/util/bstar" :dir :system)
(include-book "centaur/fty/deftypes" :dir :system)
(include-book "ihs/basic-definitions" :dir :system)
(include-book "centaur/fty/basetypes" :dir :system)
(include-book "std/top" :dir :system)
(defxdoc shifting-fifo-model
:short "The start of a FIFO model that looks like a shifting-fifo in its
implementation")
(local (set-default-parents shifting-fifo-model))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Here begins the "defprod" part of this modeling example
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define unsigned4b-p (x)
(declare (xargs :guard t))
(unsigned-byte-p 4 x))
(defun unsigned4b-p-fix (x)
(if (unsigned4b-p x)
x
0))
(fty::deffixtype unsigned4b-p
:pred unsigned4b-p
:fix unsigned4b-p-fix
:equiv equal)
(define unsigned8b-p (x)
(declare (xargs :guard t))
(unsigned-byte-p 8 x))
(defun unsigned8b-p-fix (x)
(if (unsigned8b-p x)
x
0))
(fty::deffixtype unsigned8b-p
:pred unsigned8b-p
:fix unsigned8b-p-fix
:equiv equal)
(fty::deffixtype bitp
:pred bitp
:fix bfix
:equiv equal)
(define boolean-fix (x)
(if (booleanp x) x nil))
(fty::deffixtype boolean
:fix boolean-fix
:pred booleanp
:equiv equal)
(in-theory (enable boolean-fix))
(fty::defprod data-address-valid
((data unsigned8b-p)
(address unsigned4b-p)
(valid booleanp :reqfix (if (booleanp valid) valid nil))))
(defval *default-invalid-data-address*
:short "Default values for invalid address and associated data"
(data-address-valid 0 0 nil))
(define match-address
((buffer data-address-valid-p)
(in data-address-valid-p))
:returns (retval booleanp :rule-classes :type-prescription)
(b* (((data-address-valid buffer))
((data-address-valid in)))
(and buffer.valid in.valid
(equal buffer.address in.address))))
(defrule match-commute
(equal (match-address x y)
(match-address y x))
:enable match-address)
(define buffers-req
((b1 data-address-valid-p)
(b2 data-address-valid-p)
(b3 data-address-valid-p)
(b4 data-address-valid-p))
(and (not (match-address b1 b2))
(not (match-address b1 b3))
(not (match-address b1 b4))
(not (match-address b2 b3))
(not (match-address b2 b4))
(not (match-address b3 b4))))
(define data-address-valid-fix-for-buffers
((x data-address-valid-p)
(b2 data-address-valid-p)
(b3 data-address-valid-p)
(b4 data-address-valid-p))
:returns (retval data-address-valid-p :hyp :fguard)
(if (or (match-address x b2)
(match-address x b3)
(match-address x b4))
*default-invalid-data-address*
x))
(defrule data-address-valid-fix-for-buffers-identities
(and (IMPLIES (AND (BUFFERS-REQ B1 B2 B3 B4)
(DATA-ADDRESS-VALID-P B4)
(DATA-ADDRESS-VALID-P B3)
(DATA-ADDRESS-VALID-P B2)
(DATA-ADDRESS-VALID-P B1))
(EQUAL (DATA-ADDRESS-VALID-FIX-FOR-BUFFERS B2 B1 B3 B4)
B2))
(IMPLIES (AND (BUFFERS-REQ B1 B2 B3 B4)
(DATA-ADDRESS-VALID-P B4)
(DATA-ADDRESS-VALID-P B3)
(DATA-ADDRESS-VALID-P B2)
(DATA-ADDRESS-VALID-P B1))
(EQUAL (DATA-ADDRESS-VALID-FIX-FOR-BUFFERS B4 B1 B2 B3)
B4))
(IMPLIES (AND (BUFFERS-REQ B1 B2 B3 B4)
(DATA-ADDRESS-VALID-P B4)
(DATA-ADDRESS-VALID-P B3)
(DATA-ADDRESS-VALID-P B2)
(DATA-ADDRESS-VALID-P B1))
(EQUAL (DATA-ADDRESS-VALID-FIX-FOR-BUFFERS B1 B2 B3 B4)
B1))
(IMPLIES (AND (BUFFERS-REQ B1 B2 B3 B4)
(DATA-ADDRESS-VALID-P B4)
(DATA-ADDRESS-VALID-P B3)
(DATA-ADDRESS-VALID-P B2)
(DATA-ADDRESS-VALID-P B1))
(EQUAL (DATA-ADDRESS-VALID-FIX-FOR-BUFFERS B3 B1 B2 B4)
B3)))
:enable (buffers-req data-address-valid-fix-for-buffers))
(defrulel match-of-default-is-always-nil
; For subgoal 23.9 in buffers-fix-works and buffers-req-of-fixes, but it's not
; a horrible lemma to have in general. Still, we make it local.
(equal (MATCH-ADDRESS *default-invalid-data-address* xxx)
nil)
:enable match-address)
;; (defrule match-of-default-is-always-nil-2
;; (equal (MATCH-ADDRESS xxx *default-invalid-data-address* )
;; nil)
;; :enable match-address)
(defrule buffers-fix-works
(implies (and (data-address-valid-p b1)
(data-address-valid-p b2)
(data-address-valid-p b3)
(data-address-valid-p b4))
(buffers-req (data-address-valid-fix-for-buffers b1 b2 b3 b4)
(data-address-valid-fix-for-buffers b2 b1 b3 b4)
(data-address-valid-fix-for-buffers b3 b1 b2 b4)
(data-address-valid-fix-for-buffers b4 b1 b1 b2)))
:enable (data-address-valid-fix-for-buffers buffers-req))
(defrule buffers-req-of-fixes
; I don't quite understand why this is necessary, but it is. At least it's
; clear how to duplicate this to one's own work.
(BUFFERS-REQ
(DATA-ADDRESS-VALID-FIX-FOR-BUFFERS (DATA-ADDRESS-VALID-FIX B1)
(DATA-ADDRESS-VALID-FIX B2)
(DATA-ADDRESS-VALID-FIX B3)
(DATA-ADDRESS-VALID-FIX B4))
(DATA-ADDRESS-VALID-FIX-FOR-BUFFERS (DATA-ADDRESS-VALID-FIX B2)
(DATA-ADDRESS-VALID-FIX B1)
(DATA-ADDRESS-VALID-FIX B3)
(DATA-ADDRESS-VALID-FIX B4))
(DATA-ADDRESS-VALID-FIX-FOR-BUFFERS (DATA-ADDRESS-VALID-FIX B3)
(DATA-ADDRESS-VALID-FIX B1)
(DATA-ADDRESS-VALID-FIX B2)
(DATA-ADDRESS-VALID-FIX B4))
(DATA-ADDRESS-VALID-FIX-FOR-BUFFERS (DATA-ADDRESS-VALID-FIX B4)
(DATA-ADDRESS-VALID-FIX B1)
(DATA-ADDRESS-VALID-FIX B2)
(DATA-ADDRESS-VALID-FIX B3)))
:enable (buffers-req DATA-ADDRESS-VALID-FIX-FOR-BUFFERS))
(defrulel obscure-fact
; The rewrite rule has to be structured to rewrite an equality to t, because if
; it's used to rewrite the lhs of the inner equality to the rhs of the inner
; equality, it generates bad checkpoints for other proof obligations (during
; the buffers defprod).
; That being said, why this rule is necessary (and corresponding rules for b2,
; b3, and b4 aren't necessary) is still a mystery.
(equal (EQUAL (DATA-ADDRESS-VALID-FIX-FOR-BUFFERS (DATA-ADDRESS-VALID-FIX B1)
(DATA-ADDRESS-VALID-FIX B2)
(DATA-ADDRESS-VALID-FIX B3)
(DATA-ADDRESS-VALID-FIX B4))
(DATA-ADDRESS-VALID-FIX-FOR-BUFFERS (DATA-ADDRESS-VALID-FIX B1)
B2 B3 B4))
t)
:enable (data-address-valid-fix-for-buffers match-address))
(fty::defprod buffers
((b1 data-address-valid :reqfix (data-address-valid-fix-for-buffers b1 b2 b3 b4))
(b2 data-address-valid :reqfix (data-address-valid-fix-for-buffers b2 b1 b3 b4))
(b3 data-address-valid :reqfix (data-address-valid-fix-for-buffers b3 b1 b2 b4))
(b4 data-address-valid :reqfix (data-address-valid-fix-for-buffers b4 b1 b2 b3))
(out data-address-valid))
:require (buffers-req b1 b2 b3 b4))
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