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Scope

Scopep

Recognizer for scope.

Signature
(scopep x) → *

Definitions and Theorems

Function: scopep

(defun scopep (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (identp (caar x))
         (valuep (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (scopep (cdr x)))))))

Theorem: booleanp-of-scopep

(defthm booleanp-of-scopep
  (booleanp (scopep x)))

Theorem: mapp-when-scopep

(defthm mapp-when-scopep
  (implies (scopep x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: scopep-of-tail

(defthm scopep-of-tail
  (implies (scopep x)
           (scopep (omap::tail x))))

Theorem: identp-of-head-key-when-scopep

(defthm identp-of-head-key-when-scopep
  (implies (and (scopep x) (not (omap::emptyp x)))
           (identp (mv-nth 0 (omap::head x)))))

Theorem: valuep-of-head-val-when-scopep

(defthm valuep-of-head-val-when-scopep
  (implies (and (scopep x) (not (omap::emptyp x)))
           (valuep (mv-nth 1 (omap::head x)))))

Theorem: scopep-of-update

(defthm scopep-of-update
  (implies (and (scopep x) (identp k) (valuep v))
           (scopep (omap::update k v x))))

Theorem: scopep-of-update*

(defthm scopep-of-update*
  (implies (and (scopep x) (scopep y))
           (scopep (omap::update* x y))))

Theorem: scopep-of-delete

(defthm scopep-of-delete
  (implies (scopep x)
           (scopep (omap::delete k x))))

Theorem: scopep-of-delete*

(defthm scopep-of-delete*
  (implies (scopep x)
           (scopep (omap::delete* k x))))

Theorem: identp-when-assoc-scopep-binds-free-x

(defthm identp-when-assoc-scopep-binds-free-x
  (implies (and (omap::assoc k x) (scopep x))
           (identp k)))

Theorem: identp-of-car-of-assoc-scopep

(defthm identp-of-car-of-assoc-scopep
  (implies (and (scopep x) (omap::assoc k x))
           (identp (car (omap::assoc k x)))))

Theorem: valuep-of-cdr-of-assoc-scopep

(defthm valuep-of-cdr-of-assoc-scopep
  (implies (and (scopep x) (omap::assoc k x))
           (valuep (cdr (omap::assoc k x)))))

Theorem: valuep-of-lookup-when-scopep

(defthm valuep-of-lookup-when-scopep
  (implies (and (scopep x) (omap::assoc k x))
           (valuep (omap::lookup k x))))