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;; Functions used by both defsum and deftuple.
(in-package "ACL2")
(include-book "theory-tools")
(program)
;; A keyword alist is just an alist.
;; Look up the keyword in the alist; return default if it is not present.
(defun kwassoc (x default alist)
(cond ((atom alist) default)
((eq x (caar alist)) (cdar alist))
(t (kwassoc x default (cdr alist)))))
;; Keyword alists are constructed by separating each
;; keyword along with the argument following it from the rest of the input.
(defun strip-keywords (list)
(if (atom list)
;; Return the input in case it is an atom; for situations where a single
;; symbol is acceptible instead of a list
(mv list nil)
(if (keywordp (car list))
(mv-let (slist keyalist)
(strip-keywords (cddr list))
(mv slist (cons (cons (car list) (cadr list)) keyalist)))
(mv-let (slist keyalist)
(strip-keywords (cdr list))
(mv (cons (car list) slist) keyalist)))))
(defun munge-components (components)
(if (atom components)
nil
(cons ;; first component
(mv-let (compo kwalist)
(strip-keywords (car components))
(if (consp compo)
(if (consp (cdr compo))
;; type recognizer first, name second
(list* (cadr compo) (car compo) kwalist)
;; no type recognizer
(list* (car compo) nil kwalist))
;; just an atom, presumably no keywords either
(list* compo nil kwalist)))
(munge-components (cdr components)))))
;; Utility functions for manipulating symbols.
;; Append symbols with dashes in between
(defun appsyms1 (symbols)
(if (atom symbols)
nil
(if (atom (cdr symbols))
symbols
(list* (car symbols) '- (appsyms1 (cdr symbols))))))
(defun packsyms1 (lst)
(cond ((null lst) "")
(t (concatenate 'string (symbol-name (car lst))
(packsyms1 (cdr lst))))))
(defun packsyms (lst)
(intern (packsyms1 lst) "ACL2"))
(defun appsyms (symbols)
(packsyms (appsyms1 symbols)))
;; Each component within a product has a name as well as possibly a type; it
;; may have keywords as well.
(defun component-name (component)
(car component))
(defun component-type (component)
(cadr component))
(defun component-kwalist (component)
(cddr component))
;; Each product has a name, a keyword list, and a list of components.
(defun product-name (product)
(caar product))
(defun product-components (product)
(cdar product))
(defun product-kwalist (product)
(cdr product))
;; just the argument names, given the components of a product
(defun components-names (components)
(if (atom components)
nil
(cons (component-name (car components))
(components-names (cdr components)))))
(defun accessor-name (product component)
(appsyms (list (product-name product) (component-name component))))
;; List of accessor names for a product
(defun accessor-list (product components)
(if (consp components)
(cons (accessor-name product (car components))
(accessor-list product (cdr components)))
nil))
(defun tm-split-list (half rest first)
(if (zp half)
(mv (reverse first) rest)
(tm-split-list (1- half) (cdr rest) (cons (car rest) first))))
(defun argtree (cons args)
(cond ((endp args)
nil)
((endp (cdr args))
(car args))
(t (mv-let (first second)
(tm-split-list (floor (len args) 2) args nil)
`(,cons ,(argtree cons first)
,(argtree cons second))))))
(defun recog-consp-list (nargs obj)
(if (zp nargs)
`((eq ,obj nil))
(if (= nargs 1)
'(t)
(let ((flo (floor nargs 2)))
(cons `(consp ,obj)
(append (recog-consp-list flo `(car ,obj))
(recog-consp-list (- nargs flo)
`(cdr ,obj))))))))
(defun tree-accessor (n total nest opt)
(if (zp total)
nil
(if (= 1 total)
nest
(let ((flo (floor total 2)))
(if (<= n flo)
(tree-accessor n flo `(,(if (eq opt :safe)
'safe-car
'car)
,nest)
opt)
(tree-accessor (- n flo) (- total flo)
`(,(if (eq opt :safe)
'safe-cdr
'cdr)
,nest)
opt))))))
(logic)
;; Theorems needed for proving theorems about defsum and deftuple
;; structures:
(defthmd nth-open
(implies (not (zp n))
(equal (nth n x)
(nth (1- n) (cdr x)))))
;; (defthmd safe-nth-open
;; (implies (and (not (zp n))
;; (true-listp x))
;; (equal (safe-nth n x)
;; (safe-nth (1- n) (cdr x))))
;; :hints (("Goal" :in-theory (enable safe-nth))))
;; (defthmd cancel-+1
;; (implies (and (syntaxp (quotep y))
;; (acl2-numberp y)
;; (acl2-numberp x))
;; (equal (equal (+ 1 x) y)
;; (equal x (+ -1 y)))))
;; (defthmd cancel-+k
;; (implies (and (syntaxp (quotep y))
;; (syntaxp (quotep k))
;; (acl2-numberp k)
;; (acl2-numberp y)
;; (acl2-numberp x))
;; (equal (equal (+ k x) y)
;; (equal x (+ (- k) y)))))
(defthmd true-listp-len-0
(implies (true-listp x)
(equal (equal (len x) 0)
(not x))))
(defthmd acl2-count-car-cdr-of-cons-linear
(implies (consp x)
(and (< (acl2-count (car x)) (acl2-count x))
(< (acl2-count (cdr x)) (acl2-count x))))
:rule-classes :linear)
(defthmd acl2-count-nth-of-cons-linear
(implies (consp x)
(< (acl2-count (nth n x))
(acl2-count x)))
:rule-classes (:rewrite :linear)
:hints (("Goal" :induct (nth n x))))
(defthmd acl2-count-0-len-0
(implies (equal (acl2-count x) 0)
(< (len x) 1))
:rule-classes :linear)
(defthmd acl2-count-nth-of-len-2-or-greater-linear
(and (implies (consp x)
(<= (+ 1 (acl2-count (nth n x)))
(acl2-count x)))
(implies (<= 2 (len x))
(< (+ 1 (acl2-count (nth n x)))
(acl2-count x))))
:hints (("Goal" :induct (nth n x)
:in-theory (enable acl2-count-0-len-0)))
:rule-classes (:rewrite :linear))
(defthmd len-0-true-listp-not-x
(implies (and x (true-listp x))
(not (equal (len x) 0))))
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