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• Truth

Truth-eval

Signature

(truth-eval truth env numvars) → *

Arguments

truth — Guard (integerp truth).

env — Guard (natp env).

numvars — Guard (natp numvars).

Definitions and Theorems

Function: truth-eval

(defun
     truth-eval (truth env numvars)
     (declare (xargs :guard (and (integerp truth)
                                 (natp env)
                                 (natp numvars))))
     (declare (xargs :guard (unsigned-byte-p numvars env)))
     (let ((__function__ 'truth-eval))
          (declare (ignorable __function__))
          (b* ((env (mbe :logic (loghead (nfix numvars) (nfix env))
                         :exec env)))
              (logbitp env truth))))

Theorem: truth-eval-of-lognot

(defthm truth-eval-of-lognot
        (equal (truth-eval (lognot truth) env numvars)
               (not (truth-eval truth env numvars))))

Theorem: truth-eval-of-logand

(defthm truth-eval-of-logand
        (equal (truth-eval (logand x y) env numvars)
               (and (truth-eval x env numvars)
                    (truth-eval y env numvars))))

Theorem: truth-eval-of-logior

(defthm truth-eval-of-logior
        (equal (truth-eval (logior x y) env numvars)
               (or (truth-eval x env numvars)
                   (truth-eval y env numvars))))

Theorem: truth-eval-of-logxor

(defthm truth-eval-of-logxor
        (equal (truth-eval (logxor x y) env numvars)
               (xor (truth-eval x env numvars)
                    (truth-eval y env numvars))))

Theorem: truth-eval-of-consts

(defthm truth-eval-of-consts
        (and (equal (truth-eval 0 env numvars) nil)
             (equal (truth-eval -1 env numvars) t)))

Theorem: truth-eval-of-ifix-truth

(defthm truth-eval-of-ifix-truth
        (equal (truth-eval (ifix truth) env numvars)
               (truth-eval truth env numvars)))

Theorem: truth-eval-int-equiv-congruence-on-truth

(defthm truth-eval-int-equiv-congruence-on-truth
        (implies (int-equiv truth truth-equiv)
                 (equal (truth-eval truth env numvars)
                        (truth-eval truth-equiv env numvars)))
        :rule-classes :congruence)

Theorem: truth-eval-of-nfix-env

(defthm truth-eval-of-nfix-env
        (equal (truth-eval truth (nfix env) numvars)
               (truth-eval truth env numvars)))

Theorem: truth-eval-nat-equiv-congruence-on-env

(defthm truth-eval-nat-equiv-congruence-on-env
        (implies (nat-equiv env env-equiv)
                 (equal (truth-eval truth env numvars)
                        (truth-eval truth env-equiv numvars)))
        :rule-classes :congruence)

Theorem: truth-eval-of-nfix-numvars

(defthm truth-eval-of-nfix-numvars
        (equal (truth-eval truth env (nfix numvars))
               (truth-eval truth env numvars)))

Theorem: truth-eval-nat-equiv-congruence-on-numvars

(defthm truth-eval-nat-equiv-congruence-on-numvars
        (implies (nat-equiv numvars numvars-equiv)
                 (equal (truth-eval truth env numvars)
                        (truth-eval truth env numvars-equiv)))
        :rule-classes :congruence)