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(in-package "ACL2")
(include-book "std/lists/top" :dir :system)
(include-book "std/alists/top" :dir :system)
(include-book "std/strings/top" :dir :system)
(include-book "acl2s/defdata/records" :dir :system)
(defun cons-size (x)
(declare (xargs :guard t))
(if (consp x)
(+ 1 (cons-size (car x)) (cons-size (cdr x)))
0))
(defmacro tree-size (x)
`(cons-size ,x))
(defthm cons-size-type
(natp (cons-size x))
:rule-classes
((:type-prescription)
(:forward-chaining :trigger-terms ((cons-size x)))))
(defthm acons-cons-size-lemma
(= (cons-size (acons x1 x2 x3))
(+ 2 (cons-size x1)
(cons-size x2)
(cons-size x3)))
:rule-classes ((:linear) (:rewrite)))
(defthm split-list-1-cons-size
(implies (consp x)
(< (cons-size (mv-nth 1 (str::split-list-1 x str::del)))
(cons-size x)))
:hints (("Goal" :in-theory (enable str::split-list-1)))
:rule-classes :linear)
(defthm head-cons-size
(implies (not (set::emptyp x))
(< (cons-size (set::head x))
(cons-size x)))
:hints (("Goal" :in-theory (enable set::emptyp set::head)))
:rule-classes :linear)
(defthm tail-cons-size
(implies (not (set::emptyp x))
(< (cons-size (set::tail x))
(cons-size x)))
:hints (("Goal" :in-theory (enable set::emptyp set::tail)))
:rule-classes :linear)
(defthm cons-size-append
(= (cons-size (append x y))
(+ (cons-size x) (cons-size y)))
:rule-classes ((:linear) (:rewrite)))
(defthm rev-cons-size-lemma
(= (cons-size (rev x))
(cons-size x))
:hints (("Goal" :in-theory (enable rev)))
:rule-classes ((:linear) (:rewrite)))
(defthm cons-size-evens-strong
(implies (and (consp x)
(consp (cdr x)))
(< (cons-size (evens x))
(cons-size x)))
:rule-classes :linear)
(defthm cons-size-evens-weak
(<= (cons-size (evens x))
(cons-size x))
:hints (("Goal" :induct (evens x)))
:rule-classes :linear)
(defthm cons-size-of-remove-assoc-equal-upper-bound
(<= (cons-size (remove-assoc-equal a x))
(cons-size x))
:hints (("Goal" :in-theory (enable remove-assoc-equal)))
:rule-classes :linear)
(defthm cons-size-when-member
(implies (member-equal a x)
(< (cons-size a)
(cons-size x)))
:hints (("Goal" :in-theory (enable member-equal)))
:rule-classes :linear)
(defthm cons-size-of-remove-duplicates
(<= (cons-size (remove-duplicates-equal x))
(cons-size x))
:rule-classes :linear)
(defthm cons-size-of-hons-remove-duplicates
(<= (cons-size (acl2::hons-remove-duplicates x))
(cons-size x))
:hints (("Goal" :in-theory (enable acl2::hons-remove-duplicates)))
:rule-classes :linear)
(defthm cons-size-of-nthcdr-linear
(implies (and (not (zp n)) (consp x))
(< (cons-size (nthcdr n x))
(cons-size x)))
:hints (("Goal" :in-theory (enable nthcdr)))
:rule-classes :linear)
(defthm cons-size-of-nthcdr-linear-weak
(<= (cons-size (nthcdr n x))
(cons-size x))
:hints (("Goal" :in-theory (enable nthcdr)))
:rule-classes :linear)
(defthm cons-size-of-nth-linear-weak
(<= (cons-size (nth i x))
(cons-size x))
:rule-classes :linear)
(defthm cons-size-of-nth-linear
(implies (consp x)
(< (cons-size (nth i x))
(cons-size x)))
:rule-classes :linear)
(defthm cons-size-of-prod-cons1
(<= (cons-size std::y)
(cons-size (std::prod-cons std::x std::y)))
:rule-classes :linear)
(defthm cons-size-of-prod-cons2
(<= (cons-size std::x)
(cons-size (std::prod-cons std::x std::y)))
:rule-classes :linear)
(defthm records-cons-size-linear-arith-<=
(<= (cons-size (mget k r))
(cons-size r))
:hints (("goal" :in-theory
(enable mget recordp no-nil-val-alistp ordered-unique-key-alistp)))
:rule-classes :linear)
(defthm records-cons-size-linear-arith-<
(implies (mget k r)
(< (cons-size (mget k r))
(cons-size r)))
:hints (("goal" :in-theory
(enable mget recordp no-nil-val-alistp ordered-unique-key-alistp)))
:rule-classes :linear)
(defthm records-cons-size
(implies (consp r)
(< (cons-size (mget k r))
(cons-size r)))
:hints (("goal" :in-theory
(enable mget recordp no-nil-val-alistp ordered-unique-key-alistp)))
:rule-classes :linear)
(defthm len-<=-cons-size
(<= (len x) (cons-size x))
:rule-classes :linear)
(defthm cons-size-<=-acl2-count
(<= (cons-size x)
(acl2-count x))
:rule-classes :linear)
; This shows that cons-size can be used to prove termination of
; acl2-count (which is what acl2-size is).
(defun acl2-size (x)
(declare (xargs :guard t
:measure (if (and (not (rationalp x))
(complex/complex-rationalp x))
1
(* 2 (cons-size x)))))
(if (consp x)
(+ 1 (acl2-size (car x))
(acl2-size (cdr x)))
(if (rationalp x)
(if (integerp x)
(integer-abs x)
(+ (integer-abs (numerator x))
(denominator x)))
(if (complex/complex-rationalp x)
(+ 1 (acl2-size (realpart x))
(acl2-size (imagpart x)))
(if (stringp x)
(length x)
0)))))
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