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;; Cuong Chau <ckc8687@gmail.com>
;; June 2021
(in-package "RTL")
(local (include-book "rtl/rel11/lib/top-alt" :dir :system))
;; ======================================================================
(defmacro arith-5-for-rtl ()
`(progn
(include-book "arithmetic-5/top" :dir :system)
(in-theory
#!acl2(disable |(mod (+ x y) z) where (<= 0 z)|
|(mod (+ x (- (mod a b))) y)|
|(mod (mod x y) z)|
|(mod (+ x (mod a b)) y)|
mod-cancel-*-const
cancel-mod-+
reduce-additive-constant-<
ash-to-floor
|(floor x 2)|
|(equal x (if a b c))|
|(equal (if a b c) x)|
|(logior 1 x)|
mod-theorem-one-b
|(mod (- x) y)|))))
(defmacro bitthm (&rest thm)
(declare (xargs :guard (and (true-listp thm)
(symbolp (car thm)))))
(b* ((body (cadr thm))
(term (cadr body)))
`(defthm ,@thm
:rule-classes ((:type-prescription :corollary (natp ,term))
(:linear :corollary (<= ,term 1))))))
(defmacro bvecthm (&rest thm)
(declare (xargs :guard (and (true-listp thm)
(symbolp (car thm)))))
(b* ((body (cadr thm))
(implies-form? (equal (car body) 'implies))
(term (if implies-form?
(cadr (caddr body))
(cadr body)))
(width (if implies-form?
(caddr (caddr body))
(caddr body))))
(if implies-form?
`(defthm ,@thm
:rule-classes ((:rewrite :corollary ,body)
(:type-prescription
:corollary
(implies ,(cadr body)
(natp ,term)))
(:linear
:corollary
(implies ,(cadr body)
(< ,term (expt 2 ,width))))))
`(defthm ,@thm
:rule-classes ((:rewrite :corollary ,body)
(:type-prescription :corollary (natp ,term))
(:linear :corollary (< ,term (expt 2 ,width))))))))
(defmacro bvecthm-nl (&rest thm)
(declare (xargs :guard (and (true-listp thm)
(symbolp (car thm)))))
(b* ((body (cadr thm))
(implies-form? (equal (car body) 'implies))
(term (if implies-form?
(cadr (caddr body))
(cadr body)))
(width (if implies-form?
(caddr (caddr body))
(caddr body))))
(if implies-form?
`(defthm-nl ,@thm
:rule-classes ((:rewrite :corollary ,body)
(:type-prescription
:corollary
(implies ,(cadr body)
(natp ,term)))
(:linear
:corollary
(implies ,(cadr body)
(< ,term (expt 2 ,width))))))
`(defthm-nl ,@thm
:rule-classes ((:rewrite :corollary ,body)
(:type-prescription :corollary (natp ,term))
(:linear :corollary (< ,term (expt 2 ,width))))))))
(defmacro bvecthm-nl++ (&rest thm)
(declare (xargs :guard (and (true-listp thm)
(symbolp (car thm)))))
(b* ((body (cadr thm))
(implies-form? (equal (car body) 'implies))
(term (if implies-form?
(cadr (caddr body))
(cadr body)))
(width (if implies-form?
(caddr (caddr body))
(caddr body))))
(if implies-form?
`(defthm-nl++ ,@thm
:rule-classes ((:rewrite :corollary ,body)
(:type-prescription
:corollary
(implies ,(cadr body)
(natp ,term)))
(:linear
:corollary
(implies ,(cadr body)
(< ,term (expt 2 ,width))))))
`(defthm-nl++ ,@thm
:rule-classes ((:rewrite :corollary ,body)
(:type-prescription :corollary (natp ,term))
(:linear :corollary (< ,term (expt 2 ,width))))))))
(defund strcat-for-expand-hints-nofree (l param newline)
(declare (xargs :guard (and (symbol-listp l)
(stringp param)
(stringp newline))))
(if (atom l)
newline
(concatenate 'string
newline "(" (symbol-name (car l)) " " param ")"
(strcat-for-expand-hints-nofree (cdr l) param newline))))
(defund strcat-for-expand-hints-free (l param free-str newline)
(declare (xargs :guard (and (symbol-listp l)
(stringp param)
(stringp free-str)
(stringp newline))))
(if (atom l)
newline
(concatenate
'string
newline "(:free " free-str
" (" (symbol-name (car l)) " " param "))"
(strcat-for-expand-hints-free (cdr l) param free-str newline))))
(defund strcat-for-expand-hints (l param free-str)
(declare (xargs :guard (and (symbol-listp l)
(stringp param)
(stringp free-str))))
(if (equal free-str "")
(strcat-for-expand-hints-nofree l param (string '#\Newline))
(strcat-for-expand-hints-free l param free-str (string '#\Newline))))
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