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• 4v-sexpr-purebool-p

4v-sexpr-purebool-check

An executable version of 4v-sexpr-purebool-p using SAT.

Signature

(4v-sexpr-purebool-check sexpr &key 
                         (config 'satlink::*default-config*)) 
 
  → 
(mv fail purebool ctrex)

Arguments

sexpr — The 4v-sexpr to check.

config — Guard (satlink::config-p config).

Returns

fail — If true, calling the SAT solver failed and the other answers are meaningless.
    Type (booleanp fail).

purebool — Does the sexpr always evaluate to purely Boolean?.
    Type (booleanp purebool).

ctrex — NIL when the sexpr is purely Boolean. Otherwise, an example environment (an alist suitable for 4v-sexpr-eval) for which sexpr evaluates to X or Z.

Note: if you want to check whether several sexprs are all purely Boolean valued, 4v-sexpr-purebool-list-check will typically be far more efficient than calling 4v-sexpr-purebool-check repeatedly.

Definitions and Theorems

Function: 4v-sexpr-purebool-check-fn

(defun 4v-sexpr-purebool-check-fn (sexpr config)
  (declare (xargs :guard (satlink::config-p config)))
  (let ((__function__ '4v-sexpr-purebool-check))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((faig (sfaig sexpr))
              ((mv fail purebool faig-env)
               (faig-purebool-check faig
                                    :config config))
              ((when fail) (mv fail nil nil))
              ((when purebool) (mv nil t nil))
              (4v-env (sfaig-recover-4venv sexpr faig-env)))
           (mv nil nil 4v-env))
         :exec
         (b* ((vars (4v-sexpr-vars-1pass sexpr))
              (onoff (num-varmap vars 0))
              (faig (4v-sexpr-to-faig sexpr onoff))
              ((mv fail purebool faig-env)
               (faig-purebool-check faig
                                    :config config))
              ((when fail) (mv fail nil nil))
              ((when purebool) (mv nil t nil))
              (4v-env (faig-const-alist->4v-alist
                           (faig-eval-alist onoff faig-env))))
           (mv nil nil 4v-env)))))

Theorem: booleanp-of-4v-sexpr-purebool-check.fail

(defthm booleanp-of-4v-sexpr-purebool-check.fail
  (b* (((mv ?fail ?purebool ?ctrex)
        (4v-sexpr-purebool-check-fn sexpr config)))
    (booleanp fail))
  :rule-classes :type-prescription)

Theorem: booleanp-of-4v-sexpr-purebool-check.purebool

(defthm booleanp-of-4v-sexpr-purebool-check.purebool
  (b* (((mv ?fail ?purebool ?ctrex)
        (4v-sexpr-purebool-check-fn sexpr config)))
    (booleanp purebool))
  :rule-classes :type-prescription)

Theorem: 4v-sexpr-purebool-check-correct

(defthm 4v-sexpr-purebool-check-correct
  (b* (((mv fail purebool ?alist)
        (4v-sexpr-purebool-check sexpr
                                 :config config)))
    (implies (not fail)
             (equal purebool (4v-sexpr-purebool-p sexpr)))))

Theorem: 4v-sexpr-purebool-check-counterexample-correct

(defthm 4v-sexpr-purebool-check-counterexample-correct
  (b* (((mv fail ?purebool alist)
        (4v-sexpr-purebool-check sexpr
                                 :config config)))
    (implies (and (not fail)
                  (not (4v-sexpr-purebool-p sexpr)))
             (and (not (equal (4v-sexpr-eval sexpr alist)
                              (4vt)))
                  (not (equal (4v-sexpr-eval sexpr alist)
                              (4vf)))))))