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• Parsing-primitives-seq

Parse-exact

Parse a given natural number into a tree that matches a direct numeric value notation that consists of that number.

Signature

(parse-exact nat input) → (mv error? tree? rest-input)

Arguments

nat — Guard (natp nat).

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-exact

(defun parse-exact (nat input)
  (declare (xargs :guard (and (natp nat) (nat-listp input))))
  (b* ((nat (lnfix nat))
       ((mv error? input-nat input)
        (parse-any input))
       ((when error?) (mv error? nil input))
       ((unless (= input-nat nat))
        (mv (msg "Failed to parse ~x0; found ~x1 instead."
                 nat input-nat)
            nil (cons input-nat input))))
    (mv nil (tree-leafterm (list nat))
        input)))

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

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

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

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

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

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

Theorem: len-of-parse-exact-linear-<=

(defthm len-of-parse-exact-linear-<=
  (b* (((mv ?error? ?tree? ?rest-input)
        (parse-exact nat input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: len-of-parse-exact-linear-<

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

Theorem: parse-exact-of-nfix-nat

(defthm parse-exact-of-nfix-nat
  (equal (parse-exact (nfix nat) input)
         (parse-exact nat input)))

Theorem: parse-exact-nat-equiv-congruence-on-nat

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

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

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

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

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