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• No-function-definitions-in-dynamic-semantics

Funinfo+funenv-nofunp

Check that a pair consisting of function information and a function environment has no function definitions in the functions' bodies.

Signature

(funinfo+funenv-nofunp funinfoenv) → yes/no

Arguments

funinfoenv — Guard (funinfo+funenv-p funinfoenv).

Returns

yes/no — Type (booleanp yes/no).

We check each component.

Definitions and Theorems

Function: funinfo+funenv-nofunp

(defun funinfo+funenv-nofunp (funinfoenv)
  (declare (xargs :guard (funinfo+funenv-p funinfoenv)))
  (let ((__function__ 'funinfo+funenv-nofunp))
    (declare (ignorable __function__))
    (and (funinfo-nofunp (funinfo+funenv->info funinfoenv))
         (funenv-nofunp (funinfo+funenv->env funinfoenv)))))

Theorem: booleanp-of-funinfo+funenv-nofunp

(defthm booleanp-of-funinfo+funenv-nofunp
  (b* ((yes/no (funinfo+funenv-nofunp funinfoenv)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: funinfo-nofunp-of-funinfo+funenv->info

(defthm funinfo-nofunp-of-funinfo+funenv->info
  (implies (funinfo+funenv-nofunp funinfoenv)
           (funinfo-nofunp (funinfo+funenv->info funinfoenv))))

Theorem: funenv-nofunp-of-funinfo+funenv->env

(defthm funenv-nofunp-of-funinfo+funenv->env
  (implies (funinfo+funenv-nofunp funinfoenv)
           (funenv-nofunp (funinfo+funenv->env funinfoenv))))

Theorem: funinfo+funenv-nofunp-of-funinfo+funenv-fix-funinfoenv

(defthm funinfo+funenv-nofunp-of-funinfo+funenv-fix-funinfoenv
  (equal (funinfo+funenv-nofunp (funinfo+funenv-fix funinfoenv))
         (funinfo+funenv-nofunp funinfoenv)))

Theorem: funinfo+funenv-nofunp-funinfo+funenv-equiv-congruence-on-funinfoenv

(defthm
 funinfo+funenv-nofunp-funinfo+funenv-equiv-congruence-on-funinfoenv
 (implies (funinfo+funenv-equiv funinfoenv funinfoenv-equiv)
          (equal (funinfo+funenv-nofunp funinfoenv)
                 (funinfo+funenv-nofunp funinfoenv-equiv)))
 :rule-classes :congruence)