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Semantics

Write-var

Write a variable's value to the environment.

Signature
(write-var var val env) → new-env
Arguments: var — Guard (stringp var).; val — Guard (integerp val).; env — Guard (envp env).
Returns: new-env — Type (envp new-env).

We add/overwrite a/the pair for the variable in the omap. We do this even if the value is 0; in this case, we could instead just remove the pair, since read-var treats an absent variable the same way as one with value 0. But we prefer to always add/overwrite the pair, avoiding any ``normalization'' of the environment (i.e. avoiding insisting that no variable in the environment has value 0). Treating an absent variable as one with value 0 is a mere convenience for having a total read-var.

Definitions and Theorems

Function: write-var

(defun write-var (var val env)
  (declare (xargs :guard (and (stringp var)
                              (integerp val)
                              (envp env))))
  (omap::update (str-fix var)
                (ifix val)
                (env-fix env)))

Theorem: envp-of-write-var

(defthm envp-of-write-var
  (b* ((new-env (write-var var val env)))
    (envp new-env))
  :rule-classes :rewrite)

Theorem: write-var-of-str-fix-var

(defthm write-var-of-str-fix-var
  (equal (write-var (str-fix var) val env)
         (write-var var val env)))

Theorem: write-var-streqv-congruence-on-var

(defthm write-var-streqv-congruence-on-var
  (implies (acl2::streqv var var-equiv)
           (equal (write-var var val env)
                  (write-var var-equiv val env)))
  :rule-classes :congruence)

Theorem: write-var-of-ifix-val

(defthm write-var-of-ifix-val
  (equal (write-var var (ifix val) env)
         (write-var var val env)))

Theorem: write-var-int-equiv-congruence-on-val

(defthm write-var-int-equiv-congruence-on-val
  (implies (acl2::int-equiv val val-equiv)
           (equal (write-var var val env)
                  (write-var var val-equiv env)))
  :rule-classes :congruence)

Theorem: write-var-of-env-fix-env

(defthm write-var-of-env-fix-env
  (equal (write-var var val (env-fix env))
         (write-var var val env)))

Theorem: write-var-env-equiv-congruence-on-env

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