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|
#|$ACL2s-Preamble$;
(include-book ;; Newline to fool ACL2/cert.pl dependency scanner
"portcullis")
(begin-book t :ttags :all);$ACL2s-Preamble$|#
;; Author: Pete Manolios
(in-package "ACL2S")
(include-book "acl2s/custom" :dir :system :ttags :all)
(set-termination-method :ccg)
;(acl2s-defaults :set testing-enabled nil)
;; Examples from the documentation
(definec int-class (x :int) :pos
(match x
(:pos 1)
(:even 2)
(:neg 3)))
(definec int-class2 (x :int) :pos
(match x
(:pos
(:even 1)
(:odd 2))
(:neg
(:even 3)
(:odd 4))
(0 5)))
(definec int-class3 (x :int) :pos
(match x
(:pos
(:even 1)
(& 2))
(:neg
(:even 3)
(& 4))
(& 5)))
(property (x :int)
(== (int-class2 x) (int-class3 x)))
(must-fail
(definec int-class4 (x :int) :pos
(match x
(:pos
(:even 1)
(& 2))
(:neg
(:even 3)
(:nat 4))
(& 5))))
(definec fact (n :nat) :pos
(match n
(0 1)
(& (* n (fact (1- n))))))
(definec fact1 (n :nat) :pos
(match n
((:t (< n 2)) 1)
(& (* n (fact1 (1- n))))))
(property (n :nat)
(== (fact1 n) (fact n)))
(definec fib (n :nat) :pos
:skip-tests t
(match n
((:or 0 1) 1)
(& (+ (fib (1- n)) (fib (- n 2))))))
(definec fib2 (n :nat) :pos
:skip-tests t
(match n
(0 1)
(1 1)
(& (+ (fib2 (1- n)) (fib2 (- n 2))))))
(definec fib3 (n :nat) :pos
:skip-tests t
(match n
((:t (< n 2)) 1)
(& (+ (fib3 (1- n)) (fib3 (- n 2))))))
(property (n :nat)
:testing? nil
(and (== (fib3 n) (fib n))
(== (fib2 n) (fib n))))
(definec pascal (i :nat j :nat) :pos
:skip-tests t
(match (list i j)
((:or (0 &) (& 0) (& !i)) 1)
(& (+ (pascal (1- i) (1- j))
(pascal (1- i) j)))))
(definec pascal2 (i :nat j :nat) :pos
:skip-tests t
(match (list i j)
((0 &) 1)
((& 0) 1)
((!i !i) 1)
(& (+ (pascal2 (1- i) (1- j))
(pascal2 (1- i) j)))))
(property (i :nat j :nat)
:testing? nil
(== (pascal i j) (pascal2 i j)))
(definec mem (e :all x :tl) :bool
(match x
(nil nil)
((!e . &) t)
((& . r) (mem e r))))
(definec subset (x :tl y :tl) :bool
(match x
(nil t)
((f . r) (and (mem f y) (subset r y)))))
#|
Have to use acl2::x to redefine, but here is the definition.
(defun acl2-count (x)
(declare (xargs :guard t :mode :program))
(if (consp x)
(+ 1 (acl2-count (car x))
(acl2-count (cdr x)))
(if (rationalp x)
(if (integerp x)
(integer-abs x)
(+ (integer-abs (numerator x))
(denominator x)))
(if (complex/complex-rationalp x)
(+ 1 (acl2-count (realpart x))
(acl2-count (imagpart x)))
(if (stringp x)
(length x)
0)))))
|#
(definec acl2-count2 (x :all) :nat
(match x
((a . b) (+ 1 (acl2-count2 a) (acl2-count2 b)))
(:rational
(:integer (integer-abs x))
(& (+ (integer-abs (numerator x))
(denominator x))))
((:r complex/complex-rationalp)
(+ 1 (acl2-count2 (realpart x))
(acl2-count2 (imagpart x))))
(:string (length x))
(& 0)))
(property (x :all)
(== (acl2-count2 x) (acl2-count x)))
#|
(defun acl2s-size (x)
(declare (xargs :guard t))
(cond ((consp x)
(+ 1 (acl2s-size (car x))
(acl2s-size (cdr x))))
((rationalp x)
(integer-abs (numerator x)))
((stringp x) (length x))
(t 0)))
|#
(definec acl2s-size2 (x :all) :nat
(match x
((a . b) (+ 1 (acl2s-size2 a) (acl2s-size2 b)))
(:rational (integer-abs (numerator x)))
((:r stringp) (length x))
(& 0)))
(property (x :all)
(== (acl2s-size2 x) (acl2s-size x)))
;; Example due to Andrew Walter
(defdata Foo (record (x . nat)))
(defdata Bar (record (y . nat)))
(definec baz (a :all) :boolean
(match a
((:or :Foo :Bar) t)
(& nil)))
(property (a :Foo) (baz a))
(property (a :Bar) (baz a))
(property (a :int) (! (baz a)))
(property (a :all) (iff (baz a)
(or (foop a) (barp a))))
(definec nested (x :all) :all
(match x
((:int :int) 1)
(((:int :nat) :int) 2)
((:or ((:bool :bool)) :bool) 3)
(& 4)))
(check= (nested '(1 2)) 1)
(check= (nested '((1 2) 3)) 2)
(check= (nested t) 3)
(check= (nested '((t nil))) 3)
(check= (nested '(t nil)) 4)
#|
Note that something like this does not work, as we do not
allow :or and :t patterns to be nested
(b* ((x '(1 2 3)))
(match x
((:int :int) 1)
((:or ((:or :int :int) :nat) (:int)) 2)
(& 3)))
|#
|
