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; Copyright (C) 2015, Regents of the University of Texas
; This version of ACL2 is a descendent of ACL2 Version 1.9, Copyright
; (C) 1997 Computational Logic, Inc. See the documentation topic NOTE-2-0.
; This program is free software; you can redistribute it and/or modify
; it under the terms of the LICENSE file distributed with ACL2.
; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
; LICENSE for more details.
; Written by: Matt Kaufmann and J Strother Moore
; email: Kaufmann@cs.utexas.edu and Moore@cs.utexas.edu
; Department of Computer Science
; University of Texas at Austin
; Austin, TX 78712 U.S.A.
(in-package "ACL2")
;=================================================================
; We here begin the support functions for non-linear arithmetic.
;=================================================================
(defun cleanse-type-alist (type-alist pt)
; This function removes equality facts from the type-alist in
; preparation for the call to rewrite-linear-term-lst in
; add-terms-and-lemmas.
; In order to see why we need this function now, redefine
; cleanse-type-alist to be the identity and trace
; rewrite-linear-term-lst and linearize in the (failed) proof
; of the following lemma:
; (defthm uniqueness-of-+-inverses-lemma
; (implies (and (acl2-numberp x)
; (acl2-numberp y)
; (equal (+ x y)
; 0))
; (equal (- x) y))
; :rule-classes nil)
(cond ((null type-alist)
nil)
((to-be-ignoredp (cddar type-alist) pt)
(cleanse-type-alist (cdr type-alist) pt))
(t
(cons (car type-alist)
(cleanse-type-alist (cdr type-alist) pt)))))
(defun var-with-divisionp (var)
; We test whether var is of the form
; 1. (/ x) or (expt (/ x) n), or [don't change this line without
; 2. (expt x c) or (expt x (* c y)) seeing the Warning below]
; where c is a negative constant.
; Warning: If you change this code, search for other instances of
; ``1. (/ x) or (expt (/ x) n)'' and adjust those comments
; appropriately.
; Warning: Keep this function in sync with invert-var.
(cond ((eq (fn-symb var) 'EXPT)
(let ((base (fargn var 1))
(exponent (fargn var 2)))
(or (and (eq (fn-symb base) 'UNARY-/)
(not (eq (fn-symb (fargn base 1)) 'BINARY-+)))
(and (not (eq (fn-symb base) 'BINARY-+))
(quotep exponent)
(integerp (unquote exponent))
(< (unquote exponent) 0))
(and (not (eq (fn-symb base) 'BINARY-+))
(eq (fn-symb exponent) 'BINARY-*)
(quotep (fargn exponent 1))
(integerp (unquote (fargn exponent 1)))
(< (unquote (fargn exponent 1)) 0)))))
(t
(and (eq (fn-symb var) 'UNARY-/)
(not (eq (fn-symb (fargn var 1)) 'BINARY-+))))))
(defun varify (x)
; We ensure that x is a legitimate pot-label. See invert-var from whence
; this is called.
(cond ((quotep x)
(er hard 'varify
"This should not have happened. The supposed ~
variable, ~x0, is instead a constant."
x))
((equal (fn-symb x) 'BINARY-+)
;;; We have to pick one.
(if (quotep (fargn x 1))
(varify (fargn x 2))
(varify (fargn x 1))))
((and (equal (fn-symb x) 'BINARY-*)
(quotep (fargn x 1)))
(varify (fargn x 2)))
(t
x)))
(defun varify! (x)
(let ((temp (varify x)))
(if (good-pot-varp temp)
temp
(er hard 'varify!
"Varify! is supposed to return a good-pot-varp, but ~
returned ~x0 on ~x1."
temp x))))
(defun varify!-lst1 (lst acc)
(if (null lst)
acc
(varify!-lst1 (cdr lst) (cons (varify! (car lst)) acc))))
(defun varify!-lst (lst)
; This is used in expanded-new-vars-in-pot-lst, and we want to
; reverse the list. Thus the use of an accumulator.
(varify!-lst1 lst nil))
(defun invert-var (var)
; Var is an arithmetic ACL2 term. We return a term suitable for use
; as an unknown in a poly, but that's all we guarantee. The idea is
; that the term is ``relevant'' to the non-linear properties of var
; and we try to return the multiplicative inverse. We expect to go
; find additional polys about this term.
(cond ((eq (fn-symb var) 'EXPT)
(let ((base (fargn var 1))
(exponent (fargn var 2)))
(cond ((eql exponent ''-1)
(varify! base))
((eq (fn-symb base) 'UNARY-/)
(fcons-term* 'EXPT (fargn base 1) exponent))
((eq (fn-symb exponent) 'UNARY--)
(fcons-term* 'EXPT base (fargn exponent 1)))
((and (quotep exponent)
(integerp (unquote exponent))
(< (unquote exponent) 0))
(fcons-term* 'EXPT base (kwote (- (unquote exponent)))))
((and (eq (fn-symb exponent) 'BINARY-*)
(quotep (fargn exponent 1))
(integerp (unquote (fargn exponent 1)))
(< (unquote (fargn exponent 1)) 0))
(fcons-term* 'EXPT
base
(cons-term
'BINARY-*
(list
(kwote (- (unquote (fargn exponent 1))))
(fargn exponent 2)))))
(t
(fcons-term* 'EXPT
(cons-term 'UNARY-/ (list base))
exponent)))))
((eq (fn-symb var) 'UNARY-/)
(varify! (fargn var 1)))
(t
(cons-term 'UNARY-/ (list var)))))
(defun part-of1 (var1 var2)
; NOTE: Note that we are implicitly assuming that var2 is right
; associated. This should be taken care of some day. Perhaps what I
; should do is take the fringe of both vars, and do a simple set
; difference.
(cond ((or (variablep var2)
(fquotep var2))
(if (equal var1 var2)
*1*
nil))
((eq (ffn-symb var2) 'BINARY-*)
(let ((arg1 (fargn var2 1))
(arg2 (fargn var2 2)))
(if (equal var1 arg1)
arg2
(let ((new-var2 (part-of1 var1 arg2)))
(cond ((null new-var2)
nil)
((equal new-var2 ''1)
arg1)
(t
(cons-term 'BINARY-*
(list arg1
new-var2))))))))
(t
(if (equal var1 var2)
*1*
nil))))
(defun part-of (var1 var2)
; We ask whether the factors of var1 are a subset of the factors of
; var2. If so, we return a naive calculation of (/ var2 var1).
(cond ((or (variablep var1)
(fquotep var1))
(part-of1 var1 var2))
((eq (ffn-symb var1) 'BINARY-*)
(let ((new-var2 (part-of (fargn var1 1) var2)))
(cond (new-var2
(part-of (fargn var1 2) new-var2))
(t
nil))))
(t
(part-of1 var1 var2))))
(defun product-already-triedp (var-list products-already-tried)
; Var-list is a list of ACL2 terms, products-already-tried is a
; list of lists of ACL2 terms. If (a permutation of) var-list
; appears in products-already-tried, we return t. Otherwise, we
; return nil.
(cond ((null products-already-tried)
nil)
(t
(or (equal var-list (car products-already-tried))
(product-already-triedp var-list
(cdr products-already-tried))))))
(defun too-many-polysp (var-lst pot-lst counter)
; Var-list is a list of pot-labels from pot-lst, and counter is initially
; 1. We we are about to multiply the polys from the pots in var-lst,
; we first check whether doing so would generate too many polys.
; Note: This function has a magic number, 20, which probably should be
; settable.
(cond
((null var-lst)
(< 20 counter))
(t
(too-many-polysp (cdr var-lst)
pot-lst
(* counter
(length (polys-with-var1 (car var-lst) pot-lst)))))))
(defun expanded-new-vars-in-pot-lst2 (new-var vars-to-skip vars-to-return)
; We explore the term new-var and accumulate into vars-to-skip and
; vars-to-return all the tips of the BINARY-* tree and the inverses of
; vars with division.
(cond
((or (member-equal new-var vars-to-skip)
(quotep new-var)
(eq (fn-symb new-var) 'BINARY-+))
(mv vars-to-skip vars-to-return))
((eq (fn-symb new-var) 'BINARY-*)
(let ((new-factor (fargn new-var 1)))
(if (or (member-equal new-factor vars-to-skip)
(quotep new-factor)
(eq (fn-symb new-factor) 'BINARY-+))
(expanded-new-vars-in-pot-lst2 (fargn new-var 2)
vars-to-skip
vars-to-return)
(expanded-new-vars-in-pot-lst2 (fargn new-var 2)
(cons new-factor vars-to-skip)
(cons new-factor vars-to-return)))))
((var-with-divisionp new-var)
(let ((inverted-var (invert-var new-var)))
(if (member-equal inverted-var vars-to-skip)
(mv (cons new-var vars-to-skip)
(cons new-var vars-to-return))
(mv (cons new-var (cons inverted-var vars-to-skip))
(cons new-var (cons inverted-var vars-to-return))))))
(t
(mv (cons new-var vars-to-skip)
(cons new-var vars-to-return)))))
(defun expanded-new-vars-in-pot-lst1 (new-pot-lst vars-to-skip
vars-to-return)
; We explore all the terms in new-pot-lst and collect all the ``new''
; vars (relative to vars-to-skip) and the inverses of the vars with
; division. We also collect all the factors of the vars we collect
; above, and their inverses. We accumulate onto both vars-to-skip and
; vars-to-return, but only return the latter.
(if (null new-pot-lst)
vars-to-return
(let ((new-var (access linear-pot (car new-pot-lst) :var)))
(cond
((member-equal new-var vars-to-skip)
(expanded-new-vars-in-pot-lst1 (cdr new-pot-lst)
vars-to-skip
vars-to-return))
((var-with-divisionp new-var)
(let* ((inverse-var (invert-var new-var))
; We keep vars-to-skip a superset of vars-to-return.
(new-vars-to-skip (if (member-equal inverse-var vars-to-skip)
(cons new-var vars-to-skip)
(cons new-var (cons inverse-var
vars-to-skip))))
(new-vars-to-return (if (member-equal inverse-var vars-to-skip)
(cons new-var vars-to-return)
(cons new-var (cons inverse-var
vars-to-return)))))
(expanded-new-vars-in-pot-lst1 (cdr new-pot-lst)
new-vars-to-skip
new-vars-to-return)))
((eq (fn-symb new-var) 'BINARY-*)
(mv-let (new-vars-to-skip new-vars-to-return)
(expanded-new-vars-in-pot-lst2 new-var
vars-to-skip
vars-to-return)
(expanded-new-vars-in-pot-lst1 (cdr new-pot-lst)
(cons new-var new-vars-to-skip)
(cons new-var new-vars-to-return))))
(t
(expanded-new-vars-in-pot-lst1 (cdr new-pot-lst)
(cons new-var vars-to-skip)
(cons new-var vars-to-return)))))))
(defun expanded-new-vars-in-pot-lst (new-pot-lst old-pot-lst)
; This is a variant of new-vars-in-pot-lst. See the comments there.
; Here, if a new var is a product, we recursively add all its individual
; factors to the list of new vars as well as the product itself.
; E. g., if a new var is (* x (foo y) (bar z)), we add
; x, (foo y), (bar z), and (* x (foo y) (bar z)) to the new var list.
; In addition, if a var or one of its factors is of the form
; 1. (/ x) or (expt (/ x) n) or
; 2. (expt x c) or (expt x (* c y)), where c is a negative integer,
; we expand the multiplicative inverse.
; We need to generate a list of vars to skip. We expand the vars in
; old-pot-lst.
(let ((vars-to-skip (expanded-new-vars-in-pot-lst1
old-pot-lst
nil ; vars-to-skip
nil)))
(varify!-lst
(expanded-new-vars-in-pot-lst1 new-pot-lst
vars-to-skip
nil))))
(defun extract-bounds (bounds-polys)
; Bounds-polys is a list of bounds-polys as returned by bounds-polys-with-var.
; It is either nil meaning no bounds were found, a list of one element
; which is either an upper or lower bound poly, or a list of length two
; consisting of an upper and lower bound poly. We return six items ---
; any of which may be nil if it was not found --- the lower bound, its
; relation, its ttree, an upper bound, its relation, and its ttree.
(cond ((null bounds-polys)
(mv nil nil nil nil nil nil))
((null (cdr bounds-polys))
;; We have only a lower, or upper bound.
(if (< (first-coefficient (car bounds-polys)) 0)
;; ((var < c)), we have only an upper bound.
(mv nil nil nil
(access poly (car bounds-polys) :constant)
(access poly (car bounds-polys) :relation)
(access poly (car bounds-polys) :ttree))
;; ((c < var)), we have only a lower bound.
(mv (- (access poly (car bounds-polys) :constant))
(access poly (car bounds-polys) :relation)
(access poly (car bounds-polys) :ttree)
nil nil nil)))
(t
;; We have both a lower and upper bound.
(if (< (first-coefficient (car bounds-polys)) 0)
;; ((var < c) (c < var)), upper bound lower bound.
(mv (- (access poly (cadr bounds-polys) :constant))
(access poly (cadr bounds-polys) :relation)
(access poly (cadr bounds-polys) :ttree)
(access poly (car bounds-polys) :constant)
(access poly (car bounds-polys) :relation)
(access poly (car bounds-polys) :ttree))
;; ((c < var) (var < c)), lower bound upper bound.
(mv (- (access poly (car bounds-polys) :constant))
(access poly (car bounds-polys) :relation)
(access poly (car bounds-polys) :ttree)
(access poly (cadr bounds-polys) :constant)
(access poly (cadr bounds-polys) :relation)
(access poly (cadr bounds-polys) :ttree))))))
(defun good-bounds-in-pot (var pot-lst pt)
; Is bds good enough for deal-with-division? That is, can we use
; the information in pot-lst to bound var either away from zero or
; at zero?
; This information is needed in deal-with-division where we may,
; for instance, multiply x and (/ x). If we know that x is non-zero,
; their product will be equal to one. If we know that x is zero, their
; product is equal to zero.
(let ((bounds-polys (bounds-polys-with-var var
pot-lst
pt)))
(mv-let (var-lbd var-lbd-rel var-lbd-ttree
var-ubd var-ubd-rel var-ubd-ttree)
(extract-bounds bounds-polys)
(declare (ignore var-lbd-ttree var-ubd-ttree))
(or (and (eql var-lbd 0)
(eql var-ubd 0))
(and var-lbd
(< 0 var-lbd))
(and (eql var-lbd 0)
(eq var-lbd-rel '<))
(and var-ubd
(< var-ubd 0))
(and (eql var-ubd 0)
(eq var-ubd-rel '<))))))
(defun inverse-polys (var inv-var pot-lst ttree pt)
; Var and inv-var are as in add-inverse-polys. Ttree is the ttree
; from the call to type-set in inverse-polys.
; Bounds-polys-for-var extracts any bounds polys from pot-lst.
; Extract-bounds deconstructs any bounds polys found. This
; information is then used to try to tighten up our knowledge about
; both var and inv-var. We return a list of bounds polys constructed
; using this information.
; A couple of simple examples will help to understand what we are doing:
; 1. If we can determine that (< 4 x), we can add both (< 0 (/ x)) and
; (< (/ x) 1/4).
; 2. If we can determine that (< 0 x) and (< x 4), we can add
; (< 0 (/ x)) and (< (/ x) 1/4).
; 3. If we can only determine that (< -2 x), we cannot add anything about
; (/ x) to the pot-lst.
; We handle the symmetric cases for negative x.
(if (and (good-pot-varp var)
(good-pot-varp inv-var))
(let ((bounds-polys-for-var
(bounds-polys-with-var var pot-lst pt))
(bounds-polys-for-inv-var
(bounds-polys-with-var inv-var pot-lst pt)))
(mv-let (var-lbd var-lbd-rel var-lbd-ttree
var-ubd var-ubd-rel var-ubd-ttree)
(extract-bounds bounds-polys-for-var)
(mv-let (inv-var-lbd inv-var-lbd-rel inv-var-lbd-ttree
inv-var-ubd inv-var-ubd-rel inv-var-ubd-ttree)
(extract-bounds bounds-polys-for-inv-var)
(cond
((and (or (eql var-lbd 0)
(eql inv-var-lbd 0))
(or (eql var-ubd 0)
(eql inv-var-ubd 0)))
; Assume that all four relations are <=. That is a weaker assumption
; than whatever is really the case. From that assumption, we conclude
; that var and inv-var are 0. We make sure that this is recorded in
; the pot-lst. If the actual case is that one of the relations is a
; strict <, then the case is contradictory and we can add any other
; polys we want, including these. Note that at least two of the four
; polys we are about to add are already in the pot-lst.
(list
;; 0 <= var
(add-linear-terms :rhs var
(base-poly (cons-tag-trees
ttree
(cons-tag-trees var-lbd-ttree
inv-var-lbd-ttree))
'<=
t
nil))
;; var <= 0
(add-linear-terms :lhs var
(base-poly (cons-tag-trees
ttree
(cons-tag-trees var-ubd-ttree
inv-var-ubd-ttree))
'<=
t
nil))
;; 0 <= inv-var
(add-linear-terms :rhs inv-var
(base-poly (cons-tag-trees
ttree
(cons-tag-trees var-lbd-ttree
inv-var-lbd-ttree))
'<=
t
nil))
;; inv-var <= 0
(add-linear-terms :lhs inv-var
(base-poly (cons-tag-trees
ttree
(cons-tag-trees var-ubd-ttree
inv-var-ubd-ttree))
'<=
t
nil))))
((or (and var-lbd
(< 0 var-lbd))
(and inv-var-lbd
(< 0 inv-var-lbd)))
; We try to gather bounds polys in four stages --- a lower bound for inv-var,
; a lower bound for var, an upper bound for inv-var, and an upper bound
; for var.
(let* ((ttree1 (cons-tag-trees ttree
(cons-tag-trees var-lbd-ttree
inv-var-lbd-ttree)))
(bounds-polys1
(cond ((and var-ubd
(not (eql var-ubd 0))
(or (null inv-var-lbd)
(< inv-var-lbd (/ var-ubd))))
(list
;; (/ var-ubd) [<,<=] inv-var
(add-linear-terms :lhs (kwote (/ var-ubd))
:rhs inv-var
(base-poly (cons-tag-trees
ttree1
var-ubd-ttree)
var-ubd-rel
t
nil))))
((null inv-var-lbd)
(list
;; 0 < inv-var
(add-linear-terms :rhs inv-var
(base-poly ttree1
'<
t
nil))))
(t
nil)))
(bounds-polys2
(cond ((and inv-var-ubd
(not (eql inv-var-ubd 0))
(or (null var-lbd)
(< var-lbd (/ inv-var-ubd))))
(cons
;; (/ inv-var-ubd) [<,<=] var
(add-linear-terms :lhs (kwote (/ inv-var-ubd))
:rhs var
(base-poly (cons-tag-trees
ttree1
inv-var-ubd-ttree)
inv-var-ubd-rel
t
nil))
bounds-polys1))
((null var-lbd)
;; 0 < var
(cons
(add-linear-terms :rhs var
(base-poly ttree1
'<
t
nil))
bounds-polys1))
(t
bounds-polys1)))
(bounds-polys3
(cond ((and var-lbd
(not (eql var-lbd 0))
(or (null inv-var-ubd)
(< (/ var-lbd) inv-var-ubd)))
(cons
;; inv-var [<,<=] (/ var-lbd)
(add-linear-terms :lhs inv-var
:rhs (kwote (/ var-lbd))
(base-poly ttree1
var-lbd-rel
t
nil))
bounds-polys2))
(t
bounds-polys2)))
(bounds-polys4
(cond ((and inv-var-lbd
(not (eql inv-var-lbd 0))
(or (null var-ubd)
(< (/ inv-var-lbd) var-ubd)))
(cons
;; var [<,<=] (/ inv-var-lbd)
(add-linear-terms :lhs var
:rhs (kwote (/ inv-var-lbd))
(base-poly ttree1
inv-var-lbd-rel
t
nil))
bounds-polys3))
(t
bounds-polys3))))
bounds-polys4))
((or (and var-ubd
(< var-ubd 0))
(and inv-var-ubd
(< inv-var-ubd 0)))
; We try to gather bounds polys in four stages --- a upper bound for inv-var,
; a upper bound for var, an lower bound for inv-var, and an lower bound
; for var.
(let* ((ttree1 (cons-tag-trees ttree
(cons-tag-trees var-ubd-ttree
inv-var-ubd-ttree)))
(bounds-polys1
(cond ((and var-lbd
(not (eql var-lbd 0))
(or (null inv-var-ubd)
(< (/ var-lbd) inv-var-ubd)))
(list
;; inv-var [<,<=] (/ var-lbd)
(add-linear-terms :lhs inv-var
:rhs (kwote (/ var-lbd))
(base-poly (cons-tag-trees
ttree1
var-lbd-ttree)
var-lbd-rel
t
nil))))
((null inv-var-ubd)
(list
;; inv-var < 0
(add-linear-terms :lhs inv-var
(base-poly ttree1
'<
t
nil))))
(t
nil)))
(bounds-polys2
(cond ((and inv-var-lbd
(not (eql inv-var-lbd 0))
(or (null var-ubd)
(< (/ inv-var-lbd) var-ubd)))
(cons
;; var [<,<=] (/ inv-var-lbd)
(add-linear-terms :lhs var
:rhs (kwote (/ inv-var-lbd))
(base-poly (cons-tag-trees
ttree1
inv-var-lbd-ttree)
var-lbd-rel
t
nil))
bounds-polys1))
((null var-ubd)
;; var < 0
(cons
(add-linear-terms :lhs var
(base-poly ttree1
'<
t
nil))
bounds-polys1))
(t
bounds-polys1)))
(bounds-polys3
(cond ((and var-ubd
(not (eql var-ubd 0))
(or (null inv-var-lbd)
(< inv-var-lbd (/ var-ubd))))
(cons
;; (/ var-ubd) [<,<=] inv-var
(add-linear-terms :lhs (kwote (/ var-ubd))
:rhs inv-var
(base-poly ttree1
var-ubd-rel
t
nil))
bounds-polys2))
(t
bounds-polys2)))
(bounds-polys4
(cond ((and inv-var-ubd
(not (eql inv-var-ubd 0))
(or (null var-lbd)
(< var-lbd (/ inv-var-ubd))))
(cons
;; (/ inv-var-ubd) [<,<=] var
(add-linear-terms :lhs (kwote (/ inv-var-ubd))
:rhs var
(base-poly ttree1
inv-var-ubd-rel
t
nil))
bounds-polys3))
(t
bounds-polys3))))
bounds-polys4))
((and (eql var-lbd 0)
(eq var-lbd-rel '<))
;; 0 < inv-var
(list
(add-linear-terms :rhs inv-var
(base-poly (cons-tag-trees
ttree
var-lbd-ttree)
'<
t
nil))))
((and (eql inv-var-lbd 0)
(eq inv-var-lbd-rel '<))
;; 0 < var
(list
(add-linear-terms :rhs var
(base-poly (cons-tag-trees
ttree
inv-var-lbd-ttree)
'<
t
nil))))
((and (eql var-ubd 0)
(eq var-ubd-rel '<))
;; inv-var < 0
(list
(add-linear-terms :lhs inv-var
(base-poly (cons-tag-trees
ttree
var-ubd-ttree)
'<
t
nil))))
((and (eql inv-var-ubd 0)
(eq inv-var-ubd-rel '<))
;; var < 0
(list
(add-linear-terms :lhs var
(base-poly (cons-tag-trees
ttree
inv-var-ubd-ttree)
'<
t
nil))))
(t
nil)))))
(er hard 'inverse-polys
"A presumptive pot-label, ~x0, has turned out to be illegitimate. ~
If possible, please send a script reproducing this error ~
to the authors of ACL2."
(if (good-pot-varp var)
inv-var
var))))
(defun add-inverse-polys (var
type-alist wrld
simplify-clause-pot-lst
force-flg ens pt)
; If var is of the form
; 1. (/ x) or (expt (/ x) n) and x is rational, or
; 2. (expt x c) or (expt x (* c y)), where c is a negative integer
; and x is rational,
; we try to find bounds for either var or its multiplicative inverse and
; then use any bounds found to bound the other. The work of gathering
; the polys is done in inverse-polys.
(if (var-with-divisionp var)
(let ((inverted-var (invert-var var)))
(mv-let (base-ts base-ttree)
(type-set inverted-var
force-flg
nil ; dwp
type-alist
ens
wrld
nil ; ttree
nil ; pot-lst
nil) ; pt
(if (ts-real/rationalp base-ts)
(let ((inverse-polys
(inverse-polys var
inverted-var
simplify-clause-pot-lst
base-ttree
pt)))
(add-polys inverse-polys
simplify-clause-pot-lst
pt
t ; nonlinearp hint
type-alist
ens
force-flg
wrld))
(mv nil simplify-clause-pot-lst))))
(mv nil simplify-clause-pot-lst)))
(defun add-polys-from-type-set (var pot-lst type-alist
pt force-flg ens wrld)
; At the time of this writing, this function is called only from
; add-polys-and-lemmas3. When doing non-linear arithmetic, we
; have found this extra information gathering useful.
; Warning: This function should not be used with any terms that are
; not legitimate pot-vars. See the definition of good-pot-varp.
; Assuming that term is a legitimate pot-label --- meets all the
; invariants --- we do not have to normalize any of the polys below.
; It would, however, not be very expensive to wrap the below in a call
; to normalize-poly-lst.
(if (good-pot-varp var)
(add-polys (polys-from-type-set var
force-flg
nil ; dwp
type-alist
ens
wrld
nil) ; ttree
pot-lst
pt
t ; nonlinearp hint
type-alist
ens
force-flg
wrld)
(mv (er hard 'add-polys-from-type-set
"A presumptive pot-label, ~x0, has turned out to be illegitimate. ~
If possible, please send a script reproducing this error ~
to the authors of ACL2."
var)
nil)))
(defun length-of-shortest-polys-with-var (poly-lst pt n)
; Poly-lst is a list of polys, pt is a parent tree of polys to be
; ignored, and n is the length of the shortest alist found so far, or
; t if we haven't found any yet. We cdr down pot-lst looking for a
; poly whose alist is shorter than n, and return the length of the
; shortest alist found.
(cond ((null poly-lst)
n)
((and (or (eq n t)
(< (length (access poly (car poly-lst) :alist)) n))
(not (ignore-polyp (access poly (car poly-lst) :parents) pt)))
(length-of-shortest-polys-with-var (cdr poly-lst) pt
(length (access poly
(car poly-lst)
:alist))))
(t
(length-of-shortest-polys-with-var (cdr poly-lst) pt n))))
(defun shortest-polys-with-var1 (poly-lst pt n)
(cond ((or (null poly-lst)
(eq n t))
nil)
((and (or (equal (length (access poly (car poly-lst) :alist)) n)
(equal (length (access poly (car poly-lst) :alist)) (+ n 1)))
(not (ignore-polyp (access poly (car poly-lst) :parents) pt)))
(cons (car poly-lst)
(shortest-polys-with-var1 (cdr poly-lst) pt n)))
(t
(shortest-polys-with-var1 (cdr poly-lst) pt n))))
(defun shortest-polys-with-var (var pot-lst pt)
; Var is a pot-label in pot-lst and pt is a parent tree of polys to ignore.
; We return a list of the polys with the shortest alists in the pot
; labeled with var. These polys can be considered as the ``simplest''
; polys about var.
(cond ((null pot-lst)
nil)
((equal var (access linear-pot (car pot-lst) :var))
; We have found the pot we are looking for. We find the length of the
; shortest polys in the pot. We then find all the polys in the pot
; with alists of that length, and return a list of those polys.
(let ((n (length-of-shortest-polys-with-var
(append (access linear-pot
(car pot-lst)
:negatives)
(access linear-pot
(car pot-lst)
:positives))
pt
t)))
(append (shortest-polys-with-var1
(access linear-pot (car pot-lst) :negatives)
pt n)
(shortest-polys-with-var1
(access linear-pot (car pot-lst) :positives)
pt n))))
(t (shortest-polys-with-var var (cdr pot-lst) pt))))
(defun binary-*-leaves (term)
(if (eq (fn-symb term) 'BINARY-*)
(cons (fargn term 1)
(binary-*-leaves (fargn term 2)))
(list term)))
(defun binary-*-tree (leaves)
; Return the BINARY-* term with leaves at its tips. In practice,
; leaves always contains at least two elements.
(cond ((null (cdr leaves))
(car leaves))
((null (cddr leaves))
(cons-term 'BINARY-*
(list
(car leaves)
(cadr leaves))))
(t
(cons-term 'BINARY-*
(list
(car leaves)
(binary-*-tree (cdr leaves)))))))
(defun merge-arith-term-order (l1 l2)
(cond ((null l1) l2)
((null l2) l1)
((arith-term-order (car l2) (car l1))
(cons (car l2) (merge-arith-term-order l1 (cdr l2))))
(t (cons (car l1) (merge-arith-term-order (cdr l1) l2)))))
(defun insert-arith-term-order (item list)
(cond ((null list)
(list item))
((arith-term-order item (car list))
(cons item list))
(t
(cons (car list)
(insert-arith-term-order item (cdr list))))))
(defun sort-arith-term-order (list)
(cond ((null list)
nil)
(t
(insert-arith-term-order (car list)
(sort-arith-term-order (cdr list))))))
(defun multiply-alist-and-const (alist const poly)
(cond ((null alist)
poly)
(t
(let ((temp-poly (add-linear-term (cons-term 'BINARY-*
(list
(kwote (* const
(cdar alist)))
(caar alist)))
'rhs
poly)))
(multiply-alist-and-const (cdr alist)
const
temp-poly)))))
(defun collect-rational-poly-p-lst (poly-lst)
(cond ((endp poly-lst) nil)
((access poly (car poly-lst) :rational-poly-p)
(cons (car poly-lst)
(collect-rational-poly-p-lst (cdr poly-lst))))
(t (collect-rational-poly-p-lst (cdr poly-lst)))))
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