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|
; Arithmetic-5 Library
; Written by Robert Krug
; Copyright/License:
; See the LICENSE file at the top level of the arithmetic-5 library.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;;; top.lisp
;;;
;;;
;;; This book collects all the other books together in one place,
;;; establishes a couple of useful theory collections, and sets up
;;; a default starting point.
;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-package "ACL2")
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Notes: 1 |(integerp (* c x))| in integerp.lisp should not be
;;; nneded after my type-set patch gets in ACL2. Fix comment about
;;; version number. Otherwise, prove some guards for it and uncomment
;;; it.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(deftheory base
(current-theory :here))
;;; marker for determining whether this library is active
(include-book "we-are-here")
;;; We want these to be the last rules seen:
;;; See comments in basic.lisp.
(include-book "distributivity")
;;(include-book "elim-hint")
(include-book "default-hint")
(include-book "building-blocks")
(include-book "common")
(include-book "normalize")
(include-book "simplify")
(deftheory minimal-start-a
(current-theory :here))
; (depends-on "build/ground-zero-theory.certdep" :dir :system)
(deftheory-static arithmetic-5-minimal-start-a
(current-theory :here))
(include-book "mini-theories")
(include-book "numerator-and-denominator")
(deftheory natp-posp-start
(current-theory :here))
(include-book "natp-posp")
(deftheory natp-posp-end
(current-theory :here))
(include-book "integerp-meta")
(include-book "integerp")
(include-book "basic")
(include-book "expt")
(deftheory minimal-end-a
(current-theory :here))
(deftheory-static arithmetic-5-minimal-end-a
(current-theory :here))
(include-book "collect")
(include-book "remove-weak-inequalities")
(include-book "arithmetic-theory")
(include-book "types")
(deftheory minimal-start-b
(current-theory :here))
(deftheory-static arithmetic-5-minimal-start-b
(current-theory :here))
(include-book "simple-equalities-and-inequalities")
;;; We want these to be the first rules seen:
(include-book "if-normalization")
(include-book "forcing-types")
(deftheory minimal-end-b
(current-theory :here))
(deftheory-static arithmetic-5-minimal-end-b
(current-theory :here))
(deftheory full
(current-theory :here))
(deftheory minimal-arithmetic-theory
(union-theories
(theory 'base)
(union-theories (set-difference-theories (theory 'minimal-end-a)
(theory 'minimal-start-a))
(set-difference-theories (theory 'minimal-end-b)
(theory 'minimal-start-b)))))
(deftheory natp-posp-theory
(set-difference-theories (theory 'natp-posp-end)
(theory 'natp-posp-start)))
(defmacro enable-natp-pposp-theory ()
'(progn
(in-theory (enable natp-posp-theory))
(in-theory (disable natp posp))))
(defmacro disable-natp-posp-theory ()
'(progn
(in-theory (disable natp-posp-theory))
(in-theory (enable natp posp))))
(disable-natp-posp-theory)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; There are two basic ways of normalizing terms such as
;;; (expt x (+ m n)) and (* (expt x m) (expt x n)). One can choose the
;;; first of these as the normal form and gather-exponents, or one can
;;; choose the second as the normal form and scatter-exponents.
;;; We here define some macros to make things easier, and recommend
;;; that they be used.
(deftheory gather-exponents-theory
'(normalize-factors-gather-exponents
simplify-products-gather-exponents-equal
simplify-products-gather-exponents-<))
;;; Keep this in sync with arithmetic-default-hint
;;; in default-hint.lisp.
(deftheory scatter-exponents-theory
'(|(expt x (+ m n))|
|(expt x (+ m n)) non-zero (+ m n)|
|(expt x (+ m n)) non-zero x|
;;|(expt x (+ m n)) non-pos m and n|
;;|(expt x (+ m n))) non-neg m and n|
normalize-factors-scatter-exponents
simplify-products-scatter-exponents-equal
simplify-products-scatter-exponents-<))
(deftheory prefer-positive-addends-theory
'(prefer-positive-addends-equal
prefer-positive-addends-<
|(equal (+ (- c) x) y)|
|(< (+ (- c) x) y)|
|(< y (+ (- c) x))|))
;;; Keep this in sync with arithmetic-default-hint
;;; in default-hint.lisp.
(deftheory prefer-positive-exponents-scatter-exponents-theory
'(prefer-positive-exponents-scatter-exponents-equal
prefer-positive-exponents-scatter-exponents-<
PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<-2))
(defmacro gather-exponents ()
'(progn
(in-theory (disable scatter-exponents-theory))
(in-theory (disable prefer-positive-exponents-scatter-exponents-theory))
(in-theory (enable gather-exponents-theory))))
(defmacro scatter-exponents ()
'(progn
(in-theory (disable gather-exponents-theory))
(in-theory (enable scatter-exponents-theory))))
(defmacro prefer-positive-exponents ()
'(progn
(in-theory (disable gather-exponents-theory))
(in-theory (enable prefer-positive-exponents-scatter-exponents-theory))
(in-theory (enable scatter-exponents-theory))))
(defmacro do-not-prefer-positive-exponents ()
'(in-theory (disable prefer-positive-exponents-scatter-exponents-theory)))
(defmacro prefer-positive-addends ()
'(in-theory (enable prefer-positive-addends-theory)))
(defmacro do-not-prefer-positive-addends ()
'(in-theory (disable prefer-positive-addends-theory)))
(gather-exponents)
(prefer-positive-addends)
(theory-invariant
(if (active-runep '(:definition arith-5-active-flag))
(not (and (active-runep '(:rewrite |(expt x (+ m n))|))
(active-runep '(:rewrite normalize-factors-gather-exponents))))
t)
:error nil)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-theory (disable expt))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; We wish to set up the theory that will be used when ACL2 is rewriting
;;; an inequality, prepatory to doing linear and non-linear arithmetic.
;;; The user should not have to change any of this.
(in-theory (disable |arith (expt x c)|
|arith (- (- x))| |arith (- (+ x y))|
|arith (* y x)| |arith (* y (* x z))|
|arith (* (* x y) z)| |arith (* 1 x)|
|arith (* x 1)| |arith (* 0 x)|
|arith (* x 0)| |arith (* -1 x)|
|arith (/ (/ x))| |arith (/ (* x y))|
|arith (* x (+ y z))| |arith (* (+ x y) z)|
|arith (* x (- y))| |arith (* (- x) y)|
|arith (- (* c x))| |arith (/ (- x))|
|arith (expt (+ x y) 2)| |arith (expt (+ x y) 3)|
|arith (expt x 0)|
|arith (expt 0 n)| |arith (expt x 1)|
|arith (expt 1 n)| |arith (expt x -1)|
;|arith (expt (/ x) n)| |arith (expt x (- n))|
;|arith (expt (/ x) (- c))|
;|arith (expt 1/c n)|
|arith (expt (/ x) n)|
|arith (/ (expt x n))|
|arith (expt 1/c n)|
|arith (expt 4 n)| |arith (expt 8 n)|
|arith (expt 16 n)|
|arith (expt (* x y) n)|
|arith (expt (expt x m) n)| |arith (expt x (+ m n))|
;;|arith (expt x (+ m n)) non-pos m and n|
;;|arith (expt x (+ m n))) non-neg m and n|
|arith (expt x (+ m n)) non-zero x|
|arith (fix x)| |arith (* (expt x n) (expt y n))|
|arith (* x x)| |arith (* x (/ x))|
|arith (* x (expt x n))| |arith (* x (expt (- x) n))|
|arith (* x (expt x (- n)))|
|arith (* x (/ (expt x n)))|
|arith (* (numerator x) (/ (denominator x)))|
|arith (* c (* d x))|
|arith (* x (expt (- x) (- n)))|
|arith (* x (/ (expt (- x) n)))|
|arith (* (/ x) (expt x n))| |arith (* (/ x) (expt (- x) n))|
|arith (* (expt x m) (expt x n))|
|arith (* (expt (- x) m) (expt x n))|
|arith (* (expt x m) (expt (- x) n))|
|arith (* (expt x (- m)) (expt x n))|
|arith (* (/ (expt x m)) (expt x n))|
|arith (* (expt x m) (expt x (- n)))|
|arith (* (expt (- x) (- m)) (expt x n))|
|arith (* (/ (expt (- x) m)) (expt x n))|
|arith (* (expt x (- m)) (expt (- x) n))|
|arith (* (/ (expt x m)) (expt (- x) n))|
|arith (* (expt x m) (/ (expt x n)))|
|arith (* (expt (- x) m) (/ (expt x n)))|
|arith (* (expt (- x) m) (expt x (- n)))|
|arith (* (expt x m) (expt (- x) (- n)))|
|arith (* (expt x m) (/ (expt (- x) n)))|
|arith (* (expt c n) (expt d n))|
|arith (+ c (+ d x))|
|arith (+ x x)| |arith (+ x (- x))|
|arith (+ x (* c x))| |arith (+ (- x) (* c x))|
|arith (+ (* c x) (* d x))|
arith-collect-+ arith-collect-+-problem-finder
arith-collect-* arith-collect-*-problem-finder
arith-bubble-down
arith-bubble-down-+-problem-finder
arith-bubble-down-+-bubble-down
arith-bubble-down-+-match-1
arith-bubble-down-+-match-2
arith-bubble-down-+-match-3
arith-bubble-down-*-problem-finder
arith-bubble-down-*-bubble-down
arith-bubble-down-*-match-1
arith-bubble-down-*-match-2
arith-bubble-down-*-match-3
|(arith-collect-* y x)| |(arith-collect-+ y x)|
arith-find-matching-factor-scatter-exponents
arith-normalize-factors-scatter-exponents
arith-normalize-addends
arith-find-matching-addend))
(in-arithmetic-theory '(|arith (expt x c)|
|arith (- (- x))| |arith (- (+ x y))|
|arith (* y x)| |arith (* y (* x z))|
|arith (* (* x y) z)| |arith (* 1 x)|
|arith (* x 1)| |arith (* 0 x)|
|arith (* x 0)| |arith (* -1 x)|
|arith (/ (/ x))| |arith (/ (* x y))|
|arith (* x (+ y z))| |arith (* (+ x y) z)|
|arith (* x (- y))| |arith (* (- x) y)|
|arith (- (* c x))| |arith (/ (- x))|
|arith (expt (+ x y) 2)| |arith (expt (+ x y) 3)|
|arith (expt x 0)|
|arith (expt 0 n)| |arith (expt x 1)|
|arith (expt 1 n)| |arith (expt x -1)|
;|arith (expt (/ x) n)| |arith (expt x (- n))|
;|arith (expt (/ x) (- c))|
;|arith (expt 1/c n)|
|arith (expt (/ x) n)|
|arith (/ (expt x n))|
|arith (expt 1/c n)|
|arith (expt 4 n)| |arith (expt 8 n)|
|arith (expt 16 n)|
|arith (expt (* x y) n)|
|arith (expt (expt x m) n)| |arith (expt x (+ m n))|
;;|arith (expt x (+ m n)) non-pos m and n|
;;|arith (expt x (+ m n))) non-neg m and n|
|arith (expt x (+ m n)) non-zero x|
|arith (fix x)| |arith (* (expt x n) (expt y n))|
|arith (* x x)| |arith (* x (/ x))|
|arith (* x (expt x n))| |arith (* x (expt (- x) n))|
|arith (* x (expt x (- n)))|
|arith (* x (/ (expt x n)))|
|arith (* (numerator x) (/ (denominator x)))|
|arith (* c (* d x))|
|arith (* x (expt (- x) (- n)))|
|arith (* x (/ (expt (- x) n)))|
|arith (* (/ x) (expt x n))| |arith (* (/ x) (expt (- x) n))|
|arith (* (expt x m) (expt x n))|
|arith (* (expt (- x) m) (expt x n))|
|arith (* (expt x m) (expt (- x) n))|
|arith (* (expt x (- m)) (expt x n))|
|arith (* (/ (expt x m)) (expt x n))|
|arith (* (expt x m) (expt x (- n)))|
|arith (* (expt (- x) (- m)) (expt x n))|
|arith (* (/ (expt (- x) m)) (expt x n))|
|arith (* (expt x (- m)) (expt (- x) n))|
|arith (* (/ (expt x m)) (expt (- x) n))|
|arith (* (expt x m) (/ (expt x n)))|
|arith (* (expt (- x) m) (/ (expt x n)))|
|arith (* (expt (- x) m) (expt x (- n)))|
|arith (* (expt x m) (expt (- x) (- n)))|
|arith (* (expt x m) (/ (expt (- x) n)))|
|arith (* (expt c n) (expt d n))|
|arith (+ c (+ d x))|
|arith (+ x x)| |arith (+ x (- x))|
|arith (+ x (* c x))| |arith (+ (- x) (* c x))|
|arith (+ (* c x) (* d x))|
;arith-collect-+
arith-collect-+-problem-finder
;arith-collect-*
arith-collect-*-problem-finder
;arith-bubble-down
arith-bubble-down-+-problem-finder
arith-bubble-down-+-bubble-down
arith-bubble-down-+-match-1
arith-bubble-down-+-match-2
arith-bubble-down-+-match-3
arith-bubble-down-*-problem-finder
arith-bubble-down-*-bubble-down
arith-bubble-down-*-match-1
arith-bubble-down-*-match-2
arith-bubble-down-*-match-3
|(arith-collect-* y x)| |(arith-collect-+ y x)|
;arith-find-matching-factor-scatter-exponents
arith-normalize-factors-scatter-exponents
arith-normalize-addends
;arith-find-matching-addend
))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; These next rules have caused problems at one point or another, or
;;; are superseded by rules in this library. I might want to
;;; reconsider what to do later.
(in-theory (disable Associativity-of-+ Commutativity-of-+
Unicity-of-0 Inverse-of-+ Rationalp-+
Rationalp-unary-- Unicity-of-1
Associativity-of-* Commutativity-of-*
Inverse-of-* Rationalp-*
Rationalp-unary-/
Distributivity
Nonnegative-product
Rationalp-implies-acl2-numberp
Expt-type-prescription-non-zero-base
default-+-1 default-+-2
default-*-1 default-*-2
default-unary-minus default-unary-/
default-<-1 default-<-2
default-denominator default-numerator))
(deftheory default-arithmetic-theory
(current-theory :here))
(defmacro set-default-arithmetic-theory ()
`(in-theory (union-theories (set-difference-theories (current-theory :here)
(theory 'full))
(theory 'default-arithmetic-theory))))
(defmacro set-minimal-arithmetic-theory ()
`(in-theory (union-theories (set-difference-theories (current-theory :here)
(theory 'full))
(theory 'minimal-arithmetic-theory))))
(include-book "banner"
; Avoid printing banner twice:
:load-compiled-file nil)
|
