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• Svex-env

Svex-env-acons

Extend an svex-env with a new variable binding. Does not expect or preserve fast-alists.

Signature

(svex-env-acons var val env) → new-env

Arguments

var — Guard (svar-p var).

val — Guard (4vec-p val).

env — Guard (svex-env-p env).

Returns

new-env — Type (svex-env-p new-env).

Definitions and Theorems

Function: svex-env-acons

(defun svex-env-acons (var val env)
  (declare (xargs :guard (and (svar-p var)
                              (4vec-p val)
                              (svex-env-p env))))
  (let ((__function__ 'svex-env-acons))
    (declare (ignorable __function__))
    (mbe :logic (cons (cons (svar-fix var) (4vec-fix val))
                      (svex-env-fix env))
         :exec (cons (cons var val) env))))

Theorem: svex-env-p-of-svex-env-acons

(defthm svex-env-p-of-svex-env-acons
  (b* ((new-env (svex-env-acons var val env)))
    (svex-env-p new-env))
  :rule-classes :rewrite)

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

(defthm svex-env-acons-of-svar-fix-var
  (equal (svex-env-acons (svar-fix var) val env)
         (svex-env-acons var val env)))

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

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

Theorem: svex-env-acons-of-4vec-fix-val

(defthm svex-env-acons-of-4vec-fix-val
  (equal (svex-env-acons var (4vec-fix val) env)
         (svex-env-acons var val env)))

Theorem: svex-env-acons-4vec-equiv-congruence-on-val

(defthm svex-env-acons-4vec-equiv-congruence-on-val
  (implies (4vec-equiv val val-equiv)
           (equal (svex-env-acons var val env)
                  (svex-env-acons var val-equiv env)))
  :rule-classes :congruence)

Theorem: svex-env-acons-of-svex-env-fix-env

(defthm svex-env-acons-of-svex-env-fix-env
  (equal (svex-env-acons var val (svex-env-fix env))
         (svex-env-acons var val env)))

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

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