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• Env

Envp

Recognizer for env.

Signature

(envp x) → *

Definitions and Theorems

Function: envp

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

Theorem: booleanp-of-envp

(defthm booleanp-of-envp
  (booleanp (envp x)))

Theorem: mapp-when-envp

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

Theorem: envp-of-tail

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

Theorem: stringp-of-head-key-when-envp

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

Theorem: integerp-of-head-val-when-envp

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

Theorem: envp-of-update

(defthm envp-of-update
  (implies (and (envp x) (stringp k) (integerp v))
           (envp (omap::update k v x))))

Theorem: envp-of-update*

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

Theorem: envp-of-delete

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

Theorem: envp-of-delete*

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

Theorem: stringp-when-assoc-envp-binds-free-x

(defthm stringp-when-assoc-envp-binds-free-x
  (implies (and (omap::assoc k x) (envp x))
           (stringp k)))

Theorem: stringp-of-car-of-assoc-envp

(defthm stringp-of-car-of-assoc-envp
  (implies (and (envp x) (omap::assoc k x))
           (stringp (car (omap::assoc k x)))))

Theorem: integerp-of-cdr-of-assoc-envp

(defthm integerp-of-cdr-of-assoc-envp
  (implies (and (envp x) (omap::assoc k x))
           (integerp (cdr (omap::assoc k x)))))

Theorem: integerp-of-lookup-when-envp

(defthm integerp-of-lookup-when-envp
  (implies (and (envp x) (omap::assoc k x))
           (integerp (omap::lookup k x))))