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• Grammar-parser-implementation

Parse-ichar2

Parse two natural numbers that encode, case-insensitively, two given characters, into a tree that matches a case-insensitive character value notation that consists of those two characters.

Signature

(parse-ichar2 char1 char2 input) 
  → 
(mv error? tree? rest-input)

Arguments

char1 — Guard (characterp char1).

char2 — Guard (characterp char2).

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-ichar2

(defun parse-ichar2 (char1 char2 input)
  (declare (xargs :guard (and (characterp char1)
                              (characterp char2)
                              (nat-listp input))))
  (b* (((mv error? nat1 input)
        (parse-any input))
       ((when error?) (mv error? nil input))
       ((unless (nat-match-insensitive-char-p nat1 char1))
        (mv *grammar-parser-error-msg*
            nil (cons nat1 input)))
       ((mv error? nat2 input)
        (parse-any input))
       ((when error?) (mv error? nil input))
       ((unless (nat-match-insensitive-char-p nat2 char2))
        (mv *grammar-parser-error-msg*
            nil (cons nat2 input))))
    (mv nil (tree-leafterm (list nat1 nat2))
        input)))

Theorem: maybe-msgp-of-parse-ichar2.error?

(defthm maybe-msgp-of-parse-ichar2.error?
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-ichar2 char1 char2 input)))
    (maybe-msgp error?))
  :rule-classes :rewrite)

Theorem: return-type-of-parse-ichar2.tree?

(defthm return-type-of-parse-ichar2.tree?
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-ichar2 char1 char2 input)))
    (and (tree-optionp tree?)
         (implies (not error?) (treep tree?))
         (implies error? (not tree?))))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-ichar2.rest-input

(defthm nat-listp-of-parse-ichar2.rest-input
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-ichar2 char1 char2 input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-ichar2-linear

(defthm len-of-parse-ichar2-linear
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-ichar2 char1 char2 input)))
    (and (<= (len rest-input) (len input))
         (implies (not error?)
                  (< (len rest-input) (len input)))))
  :rule-classes :linear)

Theorem: parse-ichar2-of-char-fix-char1

(defthm parse-ichar2-of-char-fix-char1
  (equal (parse-ichar2 (char-fix char1)
                       char2 input)
         (parse-ichar2 char1 char2 input)))

Theorem: parse-ichar2-chareqv-congruence-on-char1

(defthm parse-ichar2-chareqv-congruence-on-char1
  (implies (acl2::chareqv char1 char1-equiv)
           (equal (parse-ichar2 char1 char2 input)
                  (parse-ichar2 char1-equiv char2 input)))
  :rule-classes :congruence)

Theorem: parse-ichar2-of-char-fix-char2

(defthm parse-ichar2-of-char-fix-char2
  (equal (parse-ichar2 char1 (char-fix char2)
                       input)
         (parse-ichar2 char1 char2 input)))

Theorem: parse-ichar2-chareqv-congruence-on-char2

(defthm parse-ichar2-chareqv-congruence-on-char2
  (implies (acl2::chareqv char2 char2-equiv)
           (equal (parse-ichar2 char1 char2 input)
                  (parse-ichar2 char1 char2-equiv input)))
  :rule-classes :congruence)

Theorem: parse-ichar2-of-nat-list-fix-input

(defthm parse-ichar2-of-nat-list-fix-input
  (equal (parse-ichar2 char1 char2 (nat-list-fix input))
         (parse-ichar2 char1 char2 input)))

Theorem: parse-ichar2-nat-list-equiv-congruence-on-input

(defthm parse-ichar2-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (parse-ichar2 char1 char2 input)
                  (parse-ichar2 char1 char2 input-equiv)))
  :rule-classes :congruence)