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Lhs-eval

Signature
(lhs-eval 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

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

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

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

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

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

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

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

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

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

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

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