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Lhs-eval-zx

Signature
(lhs-eval-zx x env) → val
Arguments: x — Guard (lhs-p x).; env — Guard (svex-env-p env).
Returns: val — Type (4vec-p val).

Definitions and Theorems

Function: lhs-eval-zx

(defun lhs-eval-zx (x env)
  (declare (xargs :guard (and (lhs-p x) (svex-env-p env))))
  (let ((__function__ 'lhs-eval-zx))
    (declare (ignorable __function__))
    (if (atom x)
        0
      (4vec-concat (2vec (lhrange->w (car x)))
                   (lhatom-eval-zero (lhrange->atom (car x))
                                     env)
                   (lhs-eval-zx (cdr x) env)))))

Theorem: 4vec-p-of-lhs-eval-zx

(defthm 4vec-p-of-lhs-eval-zx
  (b* ((val (lhs-eval-zx x env)))
    (4vec-p val))
  :rule-classes :rewrite)

Theorem: lhs-eval-zx-of-lhs-fix-x

(defthm lhs-eval-zx-of-lhs-fix-x
  (equal (lhs-eval-zx (lhs-fix x) env)
         (lhs-eval-zx x env)))

Theorem: lhs-eval-zx-lhs-equiv-congruence-on-x

(defthm lhs-eval-zx-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-eval-zx x env)
                  (lhs-eval-zx x-equiv env)))
  :rule-classes :congruence)

Theorem: lhs-eval-zx-of-svex-env-fix-env

(defthm lhs-eval-zx-of-svex-env-fix-env
  (equal (lhs-eval-zx x (svex-env-fix env))
         (lhs-eval-zx x env)))

Theorem: lhs-eval-zx-svex-env-equiv-congruence-on-env

(defthm lhs-eval-zx-svex-env-equiv-congruence-on-env
  (implies (svex-env-equiv env env-equiv)
           (equal (lhs-eval-zx x env)
                  (lhs-eval-zx x env-equiv)))
  :rule-classes :congruence)

Theorem: lhs-eval-zx-of-cons

(defthm lhs-eval-zx-of-cons
  (equal (lhs-eval-zx (cons a x) env)
         (4vec-concat (2vec (lhrange->w a))
                      (lhatom-eval-zero (lhrange->atom a) env)
                      (lhs-eval-zx x env))))

Theorem: lhs-eval-zx-of-nil

(defthm lhs-eval-zx-of-nil
  (equal (lhs-eval-zx nil env) 0))