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• Svex-env

Svex-env-boundp

(Slow) Check whether a variable is bound in an svex-env.

Signature

(svex-env-boundp var env) → boundp

Arguments

var — Guard (svar-p var).

env — Guard (svex-env-p env).

Definitions and Theorems

Function: svex-env-boundp

(defun svex-env-boundp (var env)
  (declare (xargs :guard (and (svar-p var) (svex-env-p env))))
  (let ((__function__ 'svex-env-boundp))
    (declare (ignorable __function__))
    (mbe :logic (consp (hons-assoc-equal (svar-fix var) env))
         :exec (consp (assoc-equal var env)))))

Theorem: svex-env-boundp-of-nil

(defthm svex-env-boundp-of-nil
  (not (svex-env-boundp k nil)))

Theorem: svex-env-boundp-of-svar-fix-var

(defthm svex-env-boundp-of-svar-fix-var
  (equal (svex-env-boundp (svar-fix var) env)
         (svex-env-boundp var env)))

Theorem: svex-env-boundp-svar-equiv-congruence-on-var

(defthm svex-env-boundp-svar-equiv-congruence-on-var
  (implies (svar-equiv var var-equiv)
           (equal (svex-env-boundp var env)
                  (svex-env-boundp var-equiv env)))
  :rule-classes :congruence)

Theorem: svex-env-boundp-of-svex-env-fix-env

(defthm svex-env-boundp-of-svex-env-fix-env
  (equal (svex-env-boundp var (svex-env-fix env))
         (svex-env-boundp var env)))

Theorem: svex-env-boundp-svex-env-equiv-congruence-on-env

(defthm svex-env-boundp-svex-env-equiv-congruence-on-env
  (implies (svex-env-equiv env env-equiv)
           (equal (svex-env-boundp var env)
                  (svex-env-boundp var env-equiv)))
  :rule-classes :congruence)