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• Grammar-parser-implementation

Parse-bit

Parse a bit.

Signature

(parse-bit 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).

Definitions and Theorems

Function: parse-bit

(defun parse-bit (input)
  (declare (xargs :guard (nat-listp input)))
  (seq-backtrack
       input
       ((tree := (parse-ichar #\0 input))
        (return (make-tree-nonleaf :rulename? *bit*
                                   :branches (list (list tree)))))
       ((tree := (parse-ichar #\1 input))
        (return (make-tree-nonleaf :rulename? *bit*
                                   :branches (list (list tree)))))))

Theorem: maybe-msgp-of-parse-bit.error?

(defthm maybe-msgp-of-parse-bit.error?
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-bit input)))
    (maybe-msgp error?))
  :rule-classes :rewrite)

Theorem: return-type-of-parse-bit.tree?

(defthm return-type-of-parse-bit.tree?
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-bit input)))
    (and (tree-optionp tree?)
         (implies (not error?) (treep tree?))
         (implies error? (not tree?))))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-bit.rest-input

(defthm nat-listp-of-parse-bit.rest-input
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-bit input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-bit-linear

(defthm len-of-parse-bit-linear
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-bit input)))
    (and (<= (len rest-input) (len input))
         (implies (not error?)
                  (< (len rest-input) (len input)))))
  :rule-classes :linear)

Theorem: parse-bit-of-nat-list-fix-input

(defthm parse-bit-of-nat-list-fix-input
  (equal (parse-bit (nat-list-fix input))
         (parse-bit input)))

Theorem: parse-bit-nat-list-equiv-congruence-on-input

(defthm parse-bit-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (parse-bit input)
                  (parse-bit input-equiv)))
  :rule-classes :congruence)