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|
; See the top-level arithmetic-3 LICENSE file for authorship,
; copyright, and license information.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;;; integerp-meta.lisp
;;;
;;;
;;; This book contains a meta rule about when a sum or
;;; product is or is not an integer.
;;;
;;; Pseudo-Example: (See code for an explanation)
;;; (integerp (+ a (+ b (+ c d))))
;;; ===>
;;; (integerp (intp-+ (+ a c) (+ b d)))
;;;
;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-package "ACL2")
(local
(include-book "../pass1/top"))
(include-book "default-hint")
(set-default-hints '((nonlinearp-default-hint stable-under-simplificationp
hist pspv)))
(table acl2-defaults-table :state-ok t)
(table acl2-defaults-table :verify-guards-eagerness 0)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun intp-+ (x y)
(declare (xargs :guard (and (acl2-numberp x)
(acl2-numberp y))))
(+ x y))
(defun intp-* (x y)
(declare (xargs :guard (and (acl2-numberp x)
(acl2-numberp y))))
(* x y))
(defevaluator intp-eva intp-eva-lst ((intp-+ x y)
(intp-* x y)
(binary-+ x y)
(binary-* x y)
(integerp x)
(hide x)
(if x y z)
(equal x y)
(fix x)))
; Our meta rule will, hopefully, massage the terms into a form such that
; these rules can do their work.
(defthm intp-1
(implies (and (integerp x)
(integerp y))
(integerp (intp-* x y))))
(defthm intp-2
(implies (and (integerp x)
(integerp y))
(integerp (intp-+ x y))))
(defthm nintp-1
(implies (and (acl2-numberp x)
(not (integerp x))
(integerp y))
(not (integerp (intp-+ x y)))))
(defthm nintp-2
(implies (and (integerp x)
(acl2-numberp y)
(not (integerp y)))
(not (integerp (intp-+ x y)))))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun leaves (term bin-op)
(declare (xargs :guard (and (pseudo-termp term)
(symbolp bin-op))))
(cond ((atom term)
(if (eq bin-op 'BINARY-+)
(list ''0)
(list ''1)))
((eq (fn-symb term) bin-op)
(if (eq (fn-symb (fargn term 2)) bin-op)
(cons (fargn term 1)
(leaves (fargn term 2) bin-op))
(list (fargn term 1)
(fargn term 2))))
(t
(list term))))
(defun tree (leaves bin-op)
(declare (xargs :guard (and (pseudo-term-listp leaves)
(symbolp bin-op))))
(cond ((endp leaves)
(if (eq bin-op 'BINARY-+)
''0
''1))
((endp (cdr leaves))
(list 'fix (car leaves)))
((endp (cddr leaves))
(list bin-op (car leaves) (cadr leaves)))
(t
(list bin-op (car leaves) (tree (cdr leaves) bin-op)))))
(defun big-tree (bags big-bin-op bin-op)
(declare (xargs :guard (and (pseudo-term-list-listp bags)
(symbolp big-bin-op)
(symbolp bin-op))))
; We form a big-bin-op tree whose 'leaves' are bin-op trees of the
; bagged leaves.
; Pseudo-example:
; (big-tree '((a b) (c d e) (f)) 'big-bin-op 'bin-op)
; ==> (big-bin-op (bin-op a b)
; (big-bin-op (bin-op c (bin-op d e))
; (fix f)))
(cond ((endp bags)
(if (eq bin-op 'BINARY-+)
''0
''1))
((endp (cdr bags))
(tree (car bags) bin-op))
((endp (cddr bags))
(list big-bin-op
(tree (car bags) bin-op)
(tree (cadr bags) bin-op)))
(t
(list big-bin-op
(tree (car bags) bin-op)
(big-tree (cdr bags) big-bin-op bin-op)))))
;;; I leave the following two defuns here in case we ever want to go
;;; back to them. At present, we use mfc-rw to determine whether an
;;; addend is an integer or not. The following code would allow us to
;;; use mfc-ts instead.
#|
(defun ts-fix (x)
(declare (xargs :guard t))
(let ((int-x (ifix x)))
(if (and (<= *min-type-set* int-x)
(<= int-x *max-type-set*))
int-x
0)))
(defun bag-leaves (leaves mfc state
intp-bags non-intp-bags)
(declare (xargs :guard (and (pseudo-term-listp leaves)
(pseudo-term-list-listp intp-bags)
(pseudo-term-list-listp non-intp-bags))))
; Leaves is a list of leaves from a sum or product; intp-bags and
; non-intp-bags are initially nil. We scan through the leaves,
; getting their type from mfc-ts, and accumulate the known integers
; (non-integers) into intp-bags (non-intp-bags). Note that we "bag"
; each leaf individually, and so return two lists of lists of leaves.
(if (endp leaves)
(mv intp-bags non-intp-bags)
(let ((leaf-type (ts-fix (mfc-ts (car leaves) mfc state))))
(cond ((ts-subsetp leaf-type *ts-integer*)
(bag-leaves (cdr leaves) mfc state
(cons (list (car leaves)) intp-bags)
non-intp-bags))
((and (ts-subsetp leaf-type *ts-rational-acl2-number*)
(ts-subsetp leaf-type
(ts-complement *ts-integer*)))
(bag-leaves (cdr leaves) mfc state
intp-bags
(cons (list (car leaves)) non-intp-bags)))
(t
(bag-leaves (cdr leaves) mfc state
intp-bags non-intp-bags))))))
|#
(defun bag-leaves (leaves mfc state
intp-bags non-intp-bags)
(declare (xargs :guard (and (pseudo-term-listp leaves)
(pseudo-term-list-listp intp-bags)
(pseudo-term-list-listp non-intp-bags))))
; Leaves is a list of leaves from a sum or product; intp-bags and
; non-intp-bags are initially nil. We scan through the leaves,
; getting their type from mfc-ts, and accumulate the known integers
; (non-integers) into intp-bags (non-intp-bags). Note that we "bag"
; each leaf individually, and so return two lists of lists of leaves.
(if (endp leaves)
(mv intp-bags non-intp-bags)
(let ((rewriting-result (mfc-rw `(INTEGERP ,(car leaves)) t t mfc state)))
(cond ((equal rewriting-result *t*)
(bag-leaves (cdr leaves) mfc state
(cons (list (car leaves)) intp-bags)
non-intp-bags))
((equal rewriting-result *nil*)
(bag-leaves (cdr leaves) mfc state
intp-bags
(cons (list (car leaves)) non-intp-bags)))
(t
(bag-leaves (cdr leaves) mfc state
intp-bags non-intp-bags))))))
(defun bag-terms (type-alist bin-op intp-bags non-intp-bags)
(declare (xargs :guard (and (type-alistp type-alist)
(or (equal bin-op 'BINARY-+)
(equal bin-op 'BINARY-*))
(pseudo-term-list-listp intp-bags)
(pseudo-term-list-listp non-intp-bags))))
; We scan through the type-alist and "bag" those terms known to be an
; integer or a non-integer, accumulating the result into intp-bags
; and non-intp-bags.
(cond ((endp type-alist)
(mv intp-bags non-intp-bags))
((variablep (caar type-alist))
(bag-terms (cdr type-alist) bin-op
intp-bags non-intp-bags))
((ts-subsetp (cadr (car type-alist))
*ts-integer*)
(bag-terms (cdr type-alist) bin-op
(cons (leaves (caar type-alist) bin-op)
intp-bags)
non-intp-bags))
((and (ts-subsetp (cadr (car type-alist))
*ts-rational-acl2-number*)
(ts-subsetp (cadr (car type-alist))
(ts-complement *ts-integer*)))
(bag-terms (cdr type-alist) bin-op
intp-bags
(cons (leaves (caar type-alist) bin-op)
non-intp-bags)))
(t
(bag-terms (cdr type-alist) bin-op
intp-bags non-intp-bags))))
(defun subtract-leaf (leaf leaves)
(declare (xargs :guard (true-listp leaves)))
(cond ((endp leaves)
(mv nil nil))
((equal leaf (car leaves))
(mv t (cdr leaves)))
(t
(mv-let (flag new-leaves)
(subtract-leaf leaf (cdr leaves))
(if flag
(mv t (cons (car leaves)
new-leaves))
(mv nil leaves))))))
(defun subtract-bag (bag leaves)
(declare (xargs :guard (and (true-listp bag)
(true-listp leaves))))
(cond ((endp bag)
(mv t leaves))
((endp (cdr bag))
(subtract-leaf (car bag) leaves))
(t
(mv-let (flag new-leaves)
(subtract-bag (cdr bag) leaves)
(if flag
(subtract-leaf (car bag) new-leaves)
(mv nil nil))))))
(defun collect-bags-intp (leaves intp-bags)
(declare (xargs :guard (and (true-listp leaves)
(true-list-listp intp-bags))))
; We try to partition leaves such that each part is an intp-bag.
(cond ((endp leaves)
(mv t nil))
((endp intp-bags)
(mv nil nil))
(t
(mv-let (flag new-leaves)
(subtract-bag (car intp-bags) leaves)
(if flag
(mv-let (flag new-bags)
(collect-bags-intp new-leaves (cdr intp-bags))
(if flag
(mv t (cons (car intp-bags)
new-bags))
(collect-bags-intp leaves (cdr intp-bags))))
(collect-bags-intp leaves (cdr intp-bags)))))))
(defun collect-bags-non-intp (leaves intp-bags non-intp-bags)
(declare (xargs :guard (and (true-listp leaves)
(true-list-listp intp-bags)
(true-list-listp non-intp-bags))))
; We try to partition leaves such that exactly one part is a non-intp-bag
; and all the rest are each an intp-bag.
(cond ((endp non-intp-bags)
(mv nil nil))
(t
(mv-let (flag new-leaves)
(subtract-bag (car non-intp-bags) leaves)
(if (and flag
(consp new-leaves))
(mv-let (flag bag-list)
(collect-bags-intp new-leaves intp-bags)
(if flag
(mv t
(cons (car non-intp-bags)
bag-list))
(collect-bags-non-intp leaves
intp-bags
(cdr non-intp-bags))))
(collect-bags-non-intp leaves
intp-bags
(cdr non-intp-bags)))))))
(defun collect-bags (leaves intp-bags non-intp-bags bin-op)
(declare (xargs :guard (and (true-listp leaves)
(true-list-listp intp-bags)
(true-list-listp non-intp-bags))))
; We try to partition leaves in a way that lets us determine that the
; original term is or is not an integerp.
(mv-let (flag bag-list)
(if (eq bin-op 'BINARY-+)
(collect-bags-non-intp leaves intp-bags non-intp-bags)
(mv nil nil))
(if flag
(mv flag bag-list) ;; non-intp
(collect-bags-intp leaves intp-bags))))
(defun meta-integerp (term mfc state)
(declare (xargs :guard (pseudo-termp term)))
; Assumptions: 1. Term is right-associated. 2. Not all leaves
; are known to be integers by type-set.
;
; Pseudo-Example:
; (integerp (+ a (+ b (+ c d))))
; ==> (integerp (intp-+ (+ a c) (+ b d)))
(if (eq (fn-symb term) 'INTEGERP)
(let ((bin-op (fn-symb (fargn term 1))))
(if (and (member-eq bin-op '(BINARY-+ BINARY-*))
(eq (fn-symb (fargn (fargn term 1) 2)) bin-op))
;; We have a term of the form:
;; (integerp (bin-op x (bin-op y z))).
(let ((leaves (leaves (fargn term 1) bin-op)))
(mv-let (intp-leaves non-intp-leaves)
(bag-leaves leaves mfc state nil nil)
(mv-let (intp-bags non-intp-bags)
(bag-terms (mfc-type-alist mfc) bin-op
intp-leaves non-intp-leaves)
(mv-let (flag bag-list)
(collect-bags leaves intp-bags non-intp-bags bin-op)
(if flag
`(INTEGERP ,(big-tree bag-list
(if (eq bin-op 'BINARY-+)
'INTP-+
'INTP-*)
bin-op))
term)))))
term))
term))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(encapsulate
()
(local
(encapsulate
()
(local
(defthm niq-bounds
(implies (and (integerp i)
(<= 0 i)
(integerp j)
(< 0 j))
(and (<= (nonnegative-integer-quotient i j)
(/ i j))
(< (+ (/ i j) -1)
(nonnegative-integer-quotient i j))))
:rule-classes ((:linear
:trigger-terms ((nonnegative-integer-quotient i j))))))
(local
(defthm floor-bounds-1
(implies (and (rationalp x)
(rationalp y))
(and (< (+ (/ x y) -1)
(floor x y))
(<= (floor x y)
(/ x y))))
:rule-classes ((:generalize)
(:linear :trigger-terms ((floor x y))))))
(local
(defthm floor-bounds-2
(implies (and (rationalp x)
(rationalp y)
(integerp (/ x y)))
(equal (floor x y)
(/ x y)))
:rule-classes ((:generalize)
(:linear :trigger-terms ((floor x y))))))
(local
(defthm floor-bounds-3
(implies (and (rationalp x)
(rationalp y)
(not (integerp (/ x y))))
(< (floor x y)
(/ x y)))
:rule-classes ((:generalize)
(:linear :trigger-terms ((floor x y))))))
(local
(in-theory (disable floor)))
(local
(defun ind-hint (x y n)
(declare (xargs :measure (abs (ifix x))))
(cond ((or (zip x) (zip y) (zp n))
t)
((equal x -1)
t)
(t
(ind-hint (floor x 2) (floor y 2) (+ -1 n))))))
(local
(defthm one
(implies (and (integerp x)
(integerp n)
(< 0 n)
(<= (- (EXPT 2 N)) X))
(equal (< (FLOOR X 2) (- (* 1/2 (EXPT 2 N))))
nil))))
(local
(defthm two-x
(implies (and (< x 4)
(<= -4 x)
(integerp x))
(or (equal x -4)
(equal x -3)
(equal x -2)
(equal x -1)
(equal x 0)
(equal x 1)
(equal x 2)
(equal x 3)))
:rule-classes nil))
(local
(defthm two-y
(implies (and (< y 4)
(<= -4 y)
(integerp y))
(or (equal y -4)
(equal y -3)
(equal y -2)
(equal y -1)
(equal y 0)
(equal y 1)
(equal y 2)
(equal y 3)))
:rule-classes nil))
(local
(defthm foo
(implies (and (integerp x)
(integerp n)
(< 1 n)
(< x (* 1/2 (EXPT 2 N))))
(< (+ 1 (* 2 x)) (expt 2 n)))))
(local
(defthm logand-bounds
(implies (and (integerp x)
(<= (- (expt 2 n)) x)
(< x (expt 2 n))
(integerp y)
(<= (- (expt 2 n)) y)
(< y (expt 2 n))
(integerp n)
(< 1 n))
(and (<= (- (expt 2 n)) (logand x y))
(< (logand x y) (expt 2 n))))
:hints (("Goal" :in-theory (disable floor expt)
:induct (ind-hint x y n)
:do-not '(generalize))
("Subgoal *1/3.18" :use (two-x two-y))
("Subgoal *1/3.17" :use (two-x two-y))
("Subgoal *1/3.16" :use (two-x two-y))
("Subgoal *1/3.15" :use (two-x two-y))
("Subgoal *1/3.14" :use (two-x two-y))
("Subgoal *1/3.13" :use (two-x two-y))
)))
(defthm logand-thm
(implies (and (integerp x)
(<= *min-type-set* x)
(<= x *max-type-set*)
(integerp y)
(<= *min-type-set* y)
(<= y *max-type-set*))
(and (<= *min-type-set* (logand x y))
(<= (logand x y) *max-type-set*)))
:hints (("Goal" :use ((:instance logand-bounds
(n (length *actual-primitive-types*)))))))
))
#|
(local
(encapsulate
()
(local
(include-book
"../../ihs/logops-lemmas"))
(defthm logand-thm
(implies (and (integerp x)
(<= *min-type-set* x)
(<= x *max-type-set*)
(integerp y)
(<= *min-type-set* y)
(<= y *max-type-set*))
(and (<= *min-type-set* (logand x y))
(<= (logand x y) *max-type-set*)))
:hints (("Goal" :use ((:instance signed-byte-p-logops
(size (1+ (length *actual-primitive-types*))
(i x)
(j y)))
:in-theory (disable logand signed-byte-p-logops))))
))|#
(verify-guards intp-+)
(verify-guards intp-*)
(verify-guards leaves)
(local
(defthm pseudo-term-listp-leaves
(implies (and (pseudo-termp x)
(or (equal bin-op 'binary-+)
(equal bin-op 'binary-*)))
(pseudo-term-listp (leaves x bin-op)))))
(verify-guards tree)
(verify-guards big-tree)
(verify-guards bag-leaves)
(local
(defthm pseudo-term-list-listp-bag-leaves
(implies (and (pseudo-term-listp x)
(pseudo-term-list-listp y)
(pseudo-term-list-listp z))
(and (pseudo-term-list-listp
(car (bag-leaves x mfc state y z)))
(pseudo-term-list-listp
(mv-nth 1 (bag-leaves x mfc state y z)))))))
(verify-guards bag-terms)
(local
(defthm pseudo-term-list-listp-bag-terms
(implies (and (type-alistp type-alist)
(or (equal bin-op 'binary-+)
(equal bin-op 'binary-*))
(pseudo-term-list-listp intp-bags)
(pseudo-term-list-listp non-intp-bags))
(and (pseudo-term-list-listp
(car (bag-terms type-alist bin-op
intp-bags non-intp-bags)))
(pseudo-term-list-listp
(mv-nth 1 (bag-terms type-alist bin-op
intp-bags non-intp-bags)))))))
(verify-guards subtract-leaf)
(local
(defthm true-listp-subtract-leaf
(implies (true-listp leaves)
(true-listp (mv-nth 1 (subtract-leaf leaf leaves))))))
;; It is odd that I did not need this hint when I was verifying guards
;; as I introduced the functions.
(verify-guards subtract-bag
:otf-flg t)
(local
(defthm true-listp-subtract-bag
(implies (true-listp leaves)
(true-listp (mv-nth 1 (subtract-bag leaf leaves))))))
(verify-guards collect-bags-intp)
(verify-guards collect-bags-non-intp)
(verify-guards collect-bags)
(local
(encapsulate
()
(local
(defthm pseudo-term-list-listp-collect-bags-intp
(implies (and (true-listp leaves)
(pseudo-term-list-listp intp-bags))
(pseudo-term-list-listp
(mv-nth 1 (collect-bags-intp leaves intp-bags))))))
(local
(defthm pseudo-term-list-listp-collect-bags-non-intp
(implies (and (true-listp leaves)
(pseudo-term-list-listp intp-bags)
(pseudo-term-list-listp non-intp-bags))
(pseudo-term-list-listp
(mv-nth 1 (collect-bags-non-intp leaves intp-bags non-intp-bags))))))
(defthm pseudo-term-list-listp-collect-bags
(implies (and (true-listp leaves)
(pseudo-term-list-listp intp-bags)
(pseudo-term-list-listp non-intp-bags)
(or (equal bin-op 'binary-+)
(equal bin-op 'binary-*)))
(pseudo-term-list-listp
(mv-nth 1 (collect-bags leaves intp-bags non-intp-bags bin-op)))))
))
(local
(defthm pseudo-term-list-listp-implies-true-list-listp
(implies (pseudo-term-list-listp x)
(true-list-listp x))))
(verify-guards meta-integerp
:hints (("Goal" :in-theory (disable bag-leaves
bag-terms
collect-bags))))
)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(encapsulate
()
(local
(defun tree-2 (leaves bin-op)
(cond ((endp leaves)
(if (eq bin-op 'BINARY-+)
''0
''1))
(t
(list bin-op (car leaves) (tree-2 (cdr leaves) bin-op))))))
(local
(defthm trees
(implies (or (eq bin-op 'BINARY-+)
(eq bin-op 'BINARY-*))
(equal (intp-eva (tree leaves bin-op) a)
(intp-eva (tree-2 leaves bin-op) a)))))
(local
(in-theory (disable tree)))
(local
(defun big-tree-2 (bags big-bin-op bin-op)
(cond ((endp bags)
(if (eq bin-op 'BINARY-+)
''0
''1))
(t
(list big-bin-op
(tree (car bags) bin-op)
(big-tree-2 (cdr bags) big-bin-op bin-op))))))
(local
(defthm big-tree-big-tree-2
(and
(equal (intp-eva (big-tree bags 'INTP-+ 'BINARY-+) a)
(intp-eva (big-tree-2 bags 'BINARY-+ 'BINARY-+) a))
(equal (intp-eva (big-tree bags 'INTP-* 'BINARY-*) a)
(intp-eva (big-tree-2 bags 'BINARY-* 'BINARY-*) a)))))
(local
(in-theory (disable big-tree)))
(local
(defthm tree-2-leaves
(implies (and (or (eq bin-op 'BINARY-+)
(eq bin-op 'BINARY-*))
(eq (fn-symb term) bin-op))
(equal (intp-eva (tree-2 (leaves term bin-op) bin-op) a)
(intp-eva term a)))
:hints (("Subgoal 2" :induct t)
("Subgoal 1" :induct t))))
(local
(defthm acl2-numberp-tree-2
(implies (or (eq bin-op 'BINARY-+)
(eq bin-op 'BINARY-*))
(acl2-numberp (intp-eva (tree-2 x bin-op) a)))
:rule-classes :type-prescription))
(local
(defthm subtract-leaf-good-+
(mv-let (flag new-leaves)
(subtract-leaf leaf leaves)
(implies flag
(equal (+ (intp-eva leaf a)
(intp-eva (tree-2 new-leaves 'BINARY-+) a))
(intp-eva (tree-2 leaves 'BINARY-+) a))))))
(local
(defthm subtract-leaf-good-*
(mv-let (flag new-leaves)
(subtract-leaf leaf leaves)
(implies flag
(equal (* (intp-eva leaf a)
(intp-eva (tree-2 new-leaves 'BINARY-*) a))
(intp-eva (tree-2 leaves 'BINARY-*) a))))))
(local
(defthm subtract-bag-good-+
(mv-let (flag new-leaves)
(subtract-bag bag leaves)
(implies flag
(equal (+ (intp-eva (tree-2 bag 'BINARY-+) a)
(intp-eva (tree-2 new-leaves 'BINARY-+) a))
(intp-eva (tree-2 leaves 'BINARY-+) a))))
:hints (("Subgoal *1/3"
:use
((:instance subtract-leaf-good-+
(leaf (CAR BAG))
(leaves (MV-NTH 1 (SUBTRACT-BAG (CDR BAG) LEAVES)))))
:in-theory (disable subtract-leaf-good-+ tree)))))
(local
(defthm subtract-bag-good-*
(mv-let (flag new-leaves)
(subtract-bag bag leaves)
(implies flag
(equal (* (intp-eva (tree-2 bag 'BINARY-*) a)
(intp-eva (tree-2 new-leaves 'BINARY-*) a))
(intp-eva (tree-2 leaves 'BINARY-*) a))))
:hints (("Subgoal *1/3"
:use
((:instance subtract-leaf-good-*
(leaf (CAR BAG))
(leaves (MV-NTH 1 (SUBTRACT-BAG (CDR BAG) LEAVES)))))
:in-theory (disable subtract-leaf-good-* tree)))))
(local
(defthm collect-bags-intp-good-+
(mv-let (flag bags)
(collect-bags-intp leaves intp-bags)
(implies (and flag
(consp leaves))
(equal (intp-eva (big-tree-2 bags 'BINARY-+ 'BINARY-+) a)
(intp-eva (tree-2 leaves 'BINARY-+) a))))
:hints (("Subgoal *1/4'5'" :use ((:instance subtract-bag-good-+
(bag INTP-BAGS1)))
:in-theory (disable subtract-bag-good-+)))))
(local
(defthm collect-bags-intp-good-*
(mv-let (flag bags)
(collect-bags-intp leaves intp-bags)
(implies (and flag
(consp leaves))
(equal (intp-eva (big-tree-2 bags 'BINARY-* 'BINARY-*) a)
(intp-eva (tree-2 leaves 'BINARY-*) a))))
:hints (("Subgoal *1/4'5'" :use ((:instance subtract-bag-good-*
(bag INTP-BAGS1)))
:in-theory (disable subtract-bag-good-*)))))
(local
(defthm collect-bags-good
(mv-let (flag bags)
(collect-bags leaves intp-bags non-intp-bags bin-op)
(implies (and flag
(member-eq bin-op '(BINARY-+ BINARY-*))
(consp leaves))
(equal (intp-eva (big-tree-2 bags bin-op bin-op) a)
(intp-eva (tree-2 leaves bin-op) a))))))
(local
(defthm big-tree-term
(mv-let (flag bags)
(collect-bags (leaves term bin-op)
intp-bags non-intp-bags bin-op)
(implies (and flag
(or (and (eq intp-bin-op 'INTP-+)
(eq bin-op 'BINARY-+))
(and (eq intp-bin-op 'INTP-*)
(eq bin-op 'BINARY-*)))
(eq (fn-symb term) bin-op))
(equal (intp-eva (big-tree bags intp-bin-op bin-op) a)
(intp-eva term a))))
:hints (("Goal" :in-theory (disable leaves collect-bags tree-2)))))
(local
(in-theory (disable leaves bag-leaves bag-terms collect-bags big-tree
intp-+ intp-*)))
; We export only this.
(defthm meta-integerp-correct
(equal (intp-eva term a)
(intp-eva (meta-integerp term mfc state) a))
:rule-classes ((:meta :trigger-fns (INTEGERP))))
)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-theory (disable leaves tree big-tree bag-leaves bag-terms
subtract-leaf subtract-bag
collect-bags-intp collect-bags-non-intp
collect-bags meta-integerp))
(in-theory (disable intp-+ intp-*))
|
