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Funscope

Funscopep

Recognizer for funscope.

Signature
(funscopep x) → *

Definitions and Theorems

Function: funscopep

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

Theorem: booleanp-of-funscopep

(defthm booleanp-of-funscopep
  (booleanp (funscopep x)))

Theorem: mapp-when-funscopep

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

Theorem: funscopep-of-tail

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

Theorem: identifierp-of-head-key-when-funscopep

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

Theorem: funinfop-of-head-val-when-funscopep

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

Theorem: funscopep-of-update

(defthm funscopep-of-update
  (implies (and (funscopep x)
                (identifierp k)
                (funinfop v))
           (funscopep (omap::update k v x))))

Theorem: funscopep-of-update*

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

Theorem: funscopep-of-delete

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

Theorem: funscopep-of-delete*

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

Theorem: identifierp-when-assoc-funscopep-binds-free-x

(defthm identifierp-when-assoc-funscopep-binds-free-x
  (implies (and (omap::assoc k x) (funscopep x))
           (identifierp k)))

Theorem: identifierp-of-car-of-assoc-funscopep

(defthm identifierp-of-car-of-assoc-funscopep
  (implies (and (funscopep x) (omap::assoc k x))
           (identifierp (car (omap::assoc k x)))))

Theorem: funinfop-of-cdr-of-assoc-funscopep

(defthm funinfop-of-cdr-of-assoc-funscopep
  (implies (and (funscopep x) (omap::assoc k x))
           (funinfop (cdr (omap::assoc k x)))))

Theorem: funinfop-of-lookup-when-funscopep

(defthm funinfop-of-lookup-when-funscopep
  (implies (and (funscopep x) (omap::assoc k x))
           (funinfop (omap::lookup k x))))