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• Grammar-parser-implementation

Parse-alternation

Parse an alternation.

Signature

(parse-alternation input) → (mv error? tree? rest-input)

Arguments

input — Guard (nat-listp input).

Returns

error? — Type (maybe-msgp error?).

tree? — Type (and (tree-optionp tree?) (implies (not error?) (treep tree?)) (implies error? (not tree?))) .

rest-input — Type (nat-listp rest-input).

The linear rules below are used in the guard verification proof.

Function: parse-alternation

(defun parse-alternation (input)
 (declare (xargs :guard (nat-listp input)))
 (seq
   input
   (tree :s= (parse-concatenation input))
   (trees := (parse-alt-rest input))
   (return (make-tree-nonleaf :rulename? *alternation*
                              :branches (list (list tree) trees)))))

Theorem: len-of-parse-alternation-linear-1

(defthm len-of-parse-alternation-linear-1
  (<= (len (mv-nth 2 (parse-alternation input)))
      (len input))
  :rule-classes :linear)

Theorem: len-of-parse-alternation-linear-2

(defthm len-of-parse-alternation-linear-2
  (implies (not (mv-nth 0 (parse-alternation input)))
           (< (len (mv-nth 2 (parse-alternation input)))
              (len input)))
  :rule-classes :linear)