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|
; Defabsstobj Example 5
; Copyright (C) 2018, Regents of the University of Texas
; Written by Matt Kaufmann, Dec., 2018
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
; Here we illustrate building an abstract stobj on top of an abstract stobj,
; concluding with some tests to check proper operation on that top-level stobj.
(in-package "ACL2")
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Concrete stobj
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defstobj st0
fld0
(mem0 :type (array (integer 0 *) (100)) :initially 0))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Abstract stobj based on conventional concrete stobj
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun st1$ap (x)
(declare (xargs :guard t))
(and (true-listp x)
(equal (len x) 2)
(mem0p (nth 1 x))
(equal (len (nth 1 x)) 100)))
(defun lookup1$a (k s)
(declare (xargs :guard (and (st1$ap s)
(natp k)
(< k 100))))
(nth k (nth 1 s)))
(defun update1$a (k v s)
(declare (xargs :guard (and (st1$ap s)
(natp k)
(< k 100)
(natp v))))
(list (car s)
(update-nth k v (nth 1 s))))
(defun fld1$a (s)
(declare (xargs :guard (st1$ap s)))
(car s))
(defun update-fld1$a (v s)
(declare (xargs :guard (st1$ap s)))
(list v (nth 1 s)))
(defun create-st1$a ()
(declare (xargs :guard t))
(list nil (make-list 100 :initial-element 0)))
(defun st1$corr (s0 s1)
(and (st0p s0)
(st1$ap s1)
(equal s0 s1)))
(DEFTHM CREATE-ST1{CORRESPONDENCE}
(ST1$CORR (CREATE-ST0) (CREATE-ST1$A))
:RULE-CLASSES NIL)
(DEFTHM CREATE-ST1{PRESERVED}
(ST1$AP (CREATE-ST1$A))
:RULE-CLASSES NIL)
(DEFTHM LOOKUP1{CORRESPONDENCE}
(IMPLIES (AND (ST1$CORR ST0 ST1)
(ST1$AP ST1)
(NATP I)
(< I 100))
(EQUAL (MEM0I I ST0) (LOOKUP1$A I ST1)))
:RULE-CLASSES NIL)
(DEFTHM LOOKUP1{GUARD-THM}
(IMPLIES (AND (ST1$CORR ST0 ST1)
(ST1$AP ST1)
(NATP I)
(< I 100))
(AND (INTEGERP I)
(<= 0 I)
(< I (MEM0-LENGTH ST0))))
:RULE-CLASSES NIL)
(defthm update-nth-open
(implies (and (syntaxp (quotep n))
(posp n))
(equal (update-nth n v x)
(cons (car x)
(update-nth (1- n) v (cdr x))))))
(defthm equal-plus-len
(implies (and (acl2-numberp k1)
(acl2-numberp k2)
(true-listp x)
(syntaxp (quotep k1))
(syntaxp (quotep k2)))
(equal (equal (+ k1 (len x)) k2)
(equal (len x) (- k2 k1)))))
(defthm mem0p-update-nth
(implies (and (mem0p x)
(natp n)
(< n (len x))
(natp v))
(mem0p (update-nth n v x))))
(defthm equal-len-0
(equal (equal (len x) 0)
(atom x)))
(DEFTHM UPDATE1{CORRESPONDENCE}
(IMPLIES (AND (ST1$CORR ST0 ST1)
(ST1$AP ST1)
(NATP I)
(< I 100)
(NATP V))
(ST1$CORR (UPDATE-MEM0I I V ST0)
(UPDATE1$A I V ST1)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE1{GUARD-THM}
(IMPLIES (AND (ST1$CORR ST0 ST1)
(ST1$AP ST1)
(NATP I)
(< I 100)
(NATP V))
(AND (INTEGERP I)
(<= 0 I)
(< I (MEM0-LENGTH ST0))
(INTEGERP V)
(<= 0 V)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE1{PRESERVED}
(IMPLIES (AND (ST1$AP ST1)
(NATP I)
(< I 100)
(NATP V))
(ST1$AP (UPDATE1$A I V ST1)))
:RULE-CLASSES NIL)
(DEFTHM FLD1{CORRESPONDENCE}
(IMPLIES (AND (ST1$CORR ST0 ST1) (ST1$AP ST1))
(EQUAL (FLD0 ST0) (FLD1$A ST1)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE-FLD1{CORRESPONDENCE}
(IMPLIES (AND (ST1$CORR ST0 ST1) (ST1$AP ST1))
(ST1$CORR (UPDATE-FLD0 V ST0)
(UPDATE-FLD1$A V ST1)))
:otf-flg t
:RULE-CLASSES NIL)
(DEFTHM UPDATE-FLD1{PRESERVED}
(IMPLIES (ST1$AP ST1)
(ST1$AP (UPDATE-FLD1$A V ST1)))
:RULE-CLASSES NIL)
(defabsstobj st1
:foundation st0
:recognizer (st1p :logic st1$ap :exec st0p)
:creator (create-st1 :logic create-st1$a :exec create-st0)
:exports ((lookup1 :exec mem0i)
(update1 :exec update-mem0i)
(fld1 :exec fld0)
(update-fld1 :exec update-fld0)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Abstract stobj based on abstract stobj
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun st2$ap (x)
(declare (xargs :guard t))
(st1$ap x))
(defun lookup2$a (k s)
(declare (xargs :guard (and (st2$ap s)
(natp k)
(< k 100))))
(lookup1$a k s))
(defun update2$a (k v s)
(declare (xargs :guard (and (st2$ap s)
(natp k)
(< k 100)
(natp v))))
(update1$a k v s))
(defun fld2$a (s)
(declare (xargs :guard (st2$ap s)))
(car s))
(defun update-fld2$a (v s)
(declare (xargs :guard (st2$ap s)))
(update-fld1$a v s))
(defun create-st2$a ()
(declare (xargs :guard t))
(create-st1$a))
(defun st2$corr (s0 s1)
(and (st1p s0)
(st2$ap s1)
(equal s0 s1)))
(DEFTHM CREATE-ST2{CORRESPONDENCE}
(ST2$CORR (CREATE-ST1) (CREATE-ST1$A))
:RULE-CLASSES NIL)
(DEFTHM CREATE-ST2{PRESERVED}
(ST2$AP (CREATE-ST1$A))
:RULE-CLASSES NIL)
(DEFTHM LOOKUP2{CORRESPONDENCE}
(IMPLIES (AND (ST2$CORR ST1 ST2)
(ST2$AP ST2)
(NATP I)
(< I 100))
(EQUAL (LOOKUP1 I ST1)
(LOOKUP2$A I ST2)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE2{CORRESPONDENCE}
(IMPLIES (AND (ST2$CORR ST1 ST2)
(ST2$AP ST2)
(NATP I)
(< I 100)
(NATP V))
(ST2$CORR (UPDATE1 I V ST1)
(UPDATE2$A I V ST2)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE2{PRESERVED}
(IMPLIES (AND (ST2$AP ST2)
(NATP I)
(< I 100)
(NATP V))
(ST2$AP (UPDATE2$A I V ST2)))
:RULE-CLASSES NIL)
(DEFTHM FLD2{CORRESPONDENCE}
(IMPLIES (AND (ST2$CORR ST1 ST2) (ST2$AP ST2))
(EQUAL (FLD1 ST1) (FLD2$A ST2)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE-FLD2{CORRESPONDENCE}
(IMPLIES (AND (ST2$CORR ST1 ST2) (ST2$AP ST2))
(ST2$CORR (UPDATE-FLD1 V ST1)
(UPDATE-FLD2$A V ST2)))
:RULE-CLASSES NIL)
(DEFTHM UPDATE-FLD2{PRESERVED}
(IMPLIES (ST2$AP ST2)
(ST2$AP (UPDATE-FLD2$A V ST2)))
:RULE-CLASSES NIL)
(defabsstobj st2
:foundation st1
:recognizer (st2p :logic st2$ap :exec st1p)
:creator (create-st2 :logic create-st1$a :exec create-st1)
:exports ((lookup2 :exec lookup1)
(update2 :exec update1)
(fld2 :exec fld1)
(update-fld2 :exec update-fld1)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Basic tests
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defmacro my-test (form check &optional aok)
`(local (make-event
(er-progn
(trans-eval ',form '(my-test . ,form) state ,aok)
(value '(assert-event ,check))))))
(set-inhibit-warnings "User-stobjs-modified")
(my-test (update2 3 17 st2)
(and (equal (lookup2 3 st2) 17)
(equal (lookup2 4 st2) 0)))
(my-test (let* ((st2 (update2 3 18 st2))
(val2 (lookup2 3 st2))
(st2 (update2 4 val2 st2)))
st2)
(and (equal (lookup2 4 st2)
18)
; Old stobjs aren't modified:
(equal (lookup1 3 st1)
0)
(equal (mem0i 3 st0)
0)))
(defun update-range (i j v st2)
; Update memory fields of st2 for all indices n with i= < n < j, and increments
; fld2 of st2 by j-i.
(declare (xargs :stobjs st2
:guard (and (natp i)
(natp j)
(<= i j)
(<= j 100)
(natp v))
:measure (nfix (- j i))))
(cond ((mbe :logic (zp (nfix (- j i)))
:exec (int= i j))
st2)
(t (let* ((f2 (nfix (fld2 st2)))
(st2 (update-fld2 (1+ f2) st2))
(j (1- j))
(st2 (update2 j v st2)))
(update-range i j v st2)))))
(my-test (update-range 7 20 23 st2)
(and (equal (lookup2 3 st2) 18)
(equal (lookup2 4 st2) 18)
(equal (lookup2 5 st2) 0)
(equal (lookup2 7 st2) 23)
(equal (lookup2 8 st2) 23)
(equal (lookup2 15 st2) 23)
(equal (lookup2 19 st2) 23)
(equal (lookup2 20 st2) 0)
(equal (fld2 st2) 13)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Tests involving memoization
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun fld2-fn (st2)
(declare (xargs :stobjs st2))
(fld2 st2))
(memoize 'fld2-fn)
(my-test (update-fld2 5 st2)
(equal (fld2-fn st2) 5))
(my-test t
(equal (fld2-fn st2) 5))
(my-test (update-fld2 7 st2)
; Make sure the memoize table was flushed.
(equal (fld2-fn st2) 7))
(defun lookup2-fn (i st2)
(declare (xargs :stobjs st2
:guard (and (natp i)
(< i 100))))
(lookup2 i st2))
(my-test (update2 3 12 st2)
(equal (lookup2-fn 3 st2) 12))
(my-test (update2 3 13 st2)
; Make sure the memoize table was flushed.
(equal (lookup2-fn 3 st2) 13))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Congruent stobjs
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defabsstobj st3
:congruent-to st2
:foundation st1
:recognizer (st3p :logic st2$ap :exec st1p)
:creator (create-st3 :logic create-st1$a :exec create-st1)
:exports ((lookup3 :logic lookup2$a :exec lookup1)
(update3 :logic update2$a :exec update1)
(fld3 :logic fld2$a :exec fld1)
(update-fld3 :logic update-fld2$a :exec update-fld1)))
(my-test (update3 33 17 st3)
(and (equal (lookup3 33 st3) 17)
(equal (lookup3 34 st3) 0)))
(memoize 'lookup2-fn)
(my-test (let* ((st3 (update2 33 50 st3))
(val3 (lookup2-fn 33 st3))
(st3 (update-fld3 val3 st3))
(st3 (update3 33 60 st3)))
st3)
(and (equal (fld3 st3)
50)
; Memoization is flushed:
(equal (lookup2-fn 33 st3)
60)
; Old stobjs aren't modified:
(equal (lookup2-fn 33 st2)
0)
(equal (lookup2 33 st2)
0)
(equal (lookup1 33 st1)
0)
(equal (mem0i 33 st0)
0)))
|
