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Variable-g-bindings

Signature

(variable-g-bindings vars) → bindings

Arguments

vars — Guard (pseudo-var-list-p vars).

Returns

bindings — Type (fgl-object-bindings-p bindings).

Definitions and Theorems

Function: variable-g-bindings

(defun variable-g-bindings (vars)
  (declare (xargs :guard (pseudo-var-list-p vars)))
  (let ((__function__ 'variable-g-bindings))
    (declare (ignorable __function__))
    (if (atom vars)
        nil
      (cons (cons (pseudo-var-fix (car vars))
                  (g-var (car vars)))
            (variable-g-bindings (cdr vars))))))

Theorem: fgl-object-bindings-p-of-variable-g-bindings

(defthm fgl-object-bindings-p-of-variable-g-bindings
  (b* ((bindings (variable-g-bindings vars)))
    (fgl-object-bindings-p bindings))
  :rule-classes :rewrite)

Theorem: fgl-object-bindings-bfrlist-of-variable-g-bindings

(defthm fgl-object-bindings-bfrlist-of-variable-g-bindings
  (b* ((?bindings (variable-g-bindings vars)))
    (equal (fgl-object-bindings-bfrlist bindings)
           nil)))

Theorem: alist-keys-of-variable-g-bindings

(defthm alist-keys-of-variable-g-bindings
  (b* ((?bindings (variable-g-bindings vars)))
    (equal (alist-keys bindings)
           (pseudo-var-list-fix vars))))

Theorem: lookup-in-variable-g-bindings

(defthm lookup-in-variable-g-bindings
  (b* ((?bindings (variable-g-bindings vars)))
    (equal (hons-assoc-equal k bindings)
           (and (member k (pseudo-var-list-fix vars))
                (cons k (g-var k))))))

Theorem: variable-g-bindings-of-pseudo-var-list-fix-vars

(defthm variable-g-bindings-of-pseudo-var-list-fix-vars
  (equal (variable-g-bindings (pseudo-var-list-fix vars))
         (variable-g-bindings vars)))

Theorem: variable-g-bindings-pseudo-var-list-equiv-congruence-on-vars

(defthm variable-g-bindings-pseudo-var-list-equiv-congruence-on-vars
  (implies (pseudo-var-list-equiv vars vars-equiv)
           (equal (variable-g-bindings vars)
                  (variable-g-bindings vars-equiv)))
  :rule-classes :congruence)