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• Svex-env

Svex-env-lookup

(Slow) Look up a variable's value in an svex-env.

Signature

(svex-env-lookup var env) → val

Arguments

var — Guard (svar-p var).

env — Guard (svex-env-p env).

Returns

val — Type (4vec-p val).

We treat any unbound variables as being bound to infinite Xes.

Definitions and Theorems

Function: svex-env-lookup

(defun svex-env-lookup (var env)
  (declare (xargs :guard (and (svar-p var) (svex-env-p env))))
  (let ((__function__ 'svex-env-lookup))
    (declare (ignorable __function__))
    (mbe :logic
         (4vec-fix (cdr (hons-get (svar-fix var) env)))
         :exec
         (let ((look (hons-get var env)))
           (if look (cdr look) (4vec-x))))))

Theorem: 4vec-p-of-svex-env-lookup

(defthm 4vec-p-of-svex-env-lookup
  (b* ((val (svex-env-lookup var env)))
    (4vec-p val))
  :rule-classes :rewrite)

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

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

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

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

Theorem: svex-env-lookup-of-svex-env-fix-env

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

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

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

Theorem: svex-env-lookup-in-empty

(defthm svex-env-lookup-in-empty
  (equal (svex-env-lookup var nil)
         (4vec-x)))

Theorem: svex-env-lookup-in-svex-env-acons

(defthm svex-env-lookup-in-svex-env-acons
  (equal (svex-env-lookup var1 (svex-env-acons var2 val env))
         (if (svar-equiv var1 var2)
             (4vec-fix val)
           (svex-env-lookup var1 env))))