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• Semantics

Tree-match-prose-val-p

Semantics of prose value notations.

Signature

(tree-match-prose-val-p tree prose-val) → yes/no

Arguments

tree — Guard (treep tree).

prose-val — Guard (prose-val-p prose-val).

Returns

yes/no — Type (booleanp yes/no).

Formally speaking, any tree matches prose, because prose has no formal semantics. When a rule includes prose, its meaning can be formalized via external predicates on trees.

Definitions and Theorems

Function: tree-match-prose-val-p

(defun tree-match-prose-val-p (tree prose-val)
  (declare (xargs :guard (and (treep tree)
                              (prose-val-p prose-val))))
  t)

Theorem: booleanp-of-tree-match-prose-val-p

(defthm booleanp-of-tree-match-prose-val-p
  (b* ((yes/no (tree-match-prose-val-p tree prose-val)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: tree-match-prose-val-p-of-tree-fix-tree

(defthm tree-match-prose-val-p-of-tree-fix-tree
  (equal (tree-match-prose-val-p (tree-fix tree)
                                 prose-val)
         (tree-match-prose-val-p tree prose-val)))

Theorem: tree-match-prose-val-p-tree-equiv-congruence-on-tree

(defthm tree-match-prose-val-p-tree-equiv-congruence-on-tree
  (implies (tree-equiv tree tree-equiv)
           (equal (tree-match-prose-val-p tree prose-val)
                  (tree-match-prose-val-p tree-equiv prose-val)))
  :rule-classes :congruence)

Theorem: tree-match-prose-val-p-of-prose-val-fix-prose-val

(defthm tree-match-prose-val-p-of-prose-val-fix-prose-val
  (equal (tree-match-prose-val-p tree (prose-val-fix prose-val))
         (tree-match-prose-val-p tree prose-val)))

Theorem: tree-match-prose-val-p-prose-val-equiv-congruence-on-prose-val

(defthm
     tree-match-prose-val-p-prose-val-equiv-congruence-on-prose-val
  (implies (prose-val-equiv prose-val prose-val-equiv)
           (equal (tree-match-prose-val-p tree prose-val)
                  (tree-match-prose-val-p tree prose-val-equiv)))
  :rule-classes :congruence)