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• Faig-purebool-list-p

Faig-purebool-list-check

An executable version of faig-purebool-list-p using SAT.

Signature

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

Arguments

x — The FAIG 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-list — Do these FAIGs always evaluate to purely Boolean?.
    Type (booleanp purebool-list).

alist — When these FAIGs are not purely Boolean: an example environment for faig-eval-list that drives some FAIG to X or Z.

Definitions and Theorems

Function: faig-purebool-list-check-fn

(defun faig-purebool-list-check-fn (x config)
  (declare (xargs :guard (satlink::config-p config)))
  (let ((__function__ 'faig-purebool-list-check))
    (declare (ignorable __function__))
    (b* ((aig (faig-purebool-list-aig x))
         ((mv status alist)
          (aig-sat (aig-not aig) :config config))
         ((when (eq status :sat))
          (mv nil nil alist))
         ((when (eq status :unsat))
          (mv nil t nil)))
      (mv t nil nil))))

Theorem: booleanp-of-faig-purebool-list-check.fail

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

Theorem: booleanp-of-faig-purebool-list-check.purebool-list

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

Theorem: faig-purebool-list-check-correct

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