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• 4v-sexpr-purebool-p

4v-sexpr-purebool-list-check

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

Signature

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

Arguments

x — The sexpr list 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 — Do these sexprs always evaluate to purely Boolean?.
    Type (booleanp purebool).

alist — When these sexprs are not purely Boolean: an example environment for 4v-sexpr-eval-list that drives some SEXPR to X or Z.

Definitions and Theorems

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

(defun 4v-sexpr-purebool-list-check-fn (x config)
  (declare (xargs :guard (satlink::config-p config)))
  (let ((__function__ '4v-sexpr-purebool-list-check))
    (declare (ignorable __function__))
    (faig-purebool-list-check (sfaiglist x)
                              :config config)))

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

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

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

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

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

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