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• Unique-variables

Var-list-unique-vars

Check that all the variables in a list are unique.

Signature

(var-list-unique-vars vars allvars) → new-allvars

Arguments

vars — Guard (identifier-listp vars).

allvars — Guard (identifier-setp allvars).

Returns

new-allvars — Type (identifier-set-resultp new-allvars).

This lifts var-unique-vars to lists.

This is very similar to add-vars, but it has a different purpose.

Definitions and Theorems

Function: var-list-unique-vars

(defun var-list-unique-vars (vars allvars)
  (declare (xargs :guard (and (identifier-listp vars)
                              (identifier-setp allvars))))
  (let ((__function__ 'var-list-unique-vars))
    (declare (ignorable __function__))
    (b* (((when (endp vars))
          (identifier-set-fix allvars))
         ((okf allvars)
          (var-unique-vars (car vars) allvars)))
      (var-list-unique-vars (cdr vars)
                            allvars))))

Theorem: identifier-set-resultp-of-var-list-unique-vars

(defthm identifier-set-resultp-of-var-list-unique-vars
  (b* ((new-allvars (var-list-unique-vars vars allvars)))
    (identifier-set-resultp new-allvars))
  :rule-classes :rewrite)

Theorem: var-list-unique-vars-to-set-list-insert

(defthm var-list-unique-vars-to-set-list-insert
  (b* ((allvars1 (var-list-unique-vars vars allvars)))
    (implies
         (not (reserrp allvars1))
         (equal allvars1
                (set::list-insert (identifier-list-fix vars)
                                  (identifier-set-fix allvars))))))

Theorem: var-list-unique-vars-of-identifier-list-fix-vars

(defthm var-list-unique-vars-of-identifier-list-fix-vars
  (equal (var-list-unique-vars (identifier-list-fix vars)
                               allvars)
         (var-list-unique-vars vars allvars)))

Theorem: var-list-unique-vars-identifier-list-equiv-congruence-on-vars

(defthm
      var-list-unique-vars-identifier-list-equiv-congruence-on-vars
  (implies (identifier-list-equiv vars vars-equiv)
           (equal (var-list-unique-vars vars allvars)
                  (var-list-unique-vars vars-equiv allvars)))
  :rule-classes :congruence)

Theorem: var-list-unique-vars-of-identifier-set-fix-allvars

(defthm var-list-unique-vars-of-identifier-set-fix-allvars
  (equal (var-list-unique-vars vars (identifier-set-fix allvars))
         (var-list-unique-vars vars allvars)))

Theorem: var-list-unique-vars-identifier-set-equiv-congruence-on-allvars

(defthm
    var-list-unique-vars-identifier-set-equiv-congruence-on-allvars
  (implies (identifier-set-equiv allvars allvars-equiv)
           (equal (var-list-unique-vars vars allvars)
                  (var-list-unique-vars vars allvars-equiv)))
  :rule-classes :congruence)