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Syntax-abstraction

Abs-equality-constraint

Abstract an equality-constraint to a constraint.

Signature
(abs-equality-constraint tree) → c
Arguments: tree — Guard (abnf::treep tree).
Returns: c — Type (constraint-resultp c).

Definitions and Theorems

Function: abs-equality-constraint

(defun abs-equality-constraint (tree)
  (declare (xargs :guard (abnf::treep tree)))
  (let ((__function__ 'abs-equality-constraint))
    (declare (ignorable __function__))
    (b* (((okf (abnf::tree-list-tuple3 sub))
          (check-tree-nonleaf-3 tree "equality-constraint"))
         ((okf tree) (check-tree-list-1 sub.1st))
         ((okf lhs) (abs-expression tree))
         ((okf tree) (check-tree-list-1 sub.2nd))
         ((okf &) (check-tree-schars tree "=="))
         ((okf tree) (check-tree-list-1 sub.3rd))
         ((okf rhs) (abs-expression tree)))
      (make-constraint-equal :left lhs
                             :right rhs))))

Theorem: constraint-resultp-of-abs-equality-constraint

(defthm constraint-resultp-of-abs-equality-constraint
  (b* ((c (abs-equality-constraint tree)))
    (constraint-resultp c))
  :rule-classes :rewrite)

Theorem: abs-equality-constraint-of-tree-fix-tree

(defthm abs-equality-constraint-of-tree-fix-tree
  (equal (abs-equality-constraint (abnf::tree-fix tree))
         (abs-equality-constraint tree)))

Theorem: abs-equality-constraint-tree-equiv-congruence-on-tree

(defthm abs-equality-constraint-tree-equiv-congruence-on-tree
  (implies (abnf::tree-equiv tree tree-equiv)
           (equal (abs-equality-constraint tree)
                  (abs-equality-constraint tree-equiv)))
  :rule-classes :congruence)