• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
      • Deftreeops
      • Defdefparse
      • Defgrammar
      • Tree-utilities
      • Notation
      • Grammar-parser
        • Grammar-parser-implementation
          • Parse-grammar-from-file
          • Parse-ichar2
          • Parse-ichar
          • Parse-in-either-range
          • Parse-*-in-either-range
          • Parse-bit
          • Parse-equal-/-equal-slash
          • Parse-wsp
          • Parse-*digit-star-*digit
          • Parse-hexdig
          • Parse-cwsp
          • Parse-concatenation
          • Parse-case-insensitive-string
          • Parse-alpha
          • Parse-dot-1*bit
          • Parse-case-sensitive-string
          • Parse-bin/dec/hex-val
          • Parse-alpha/digit/dash
          • Parse-rule
          • Parse-repeat
          • Parse-cnl
          • Parse-sp
          • Parse-rule-/-*cwsp-cnl
          • Parse-element
          • Parse-dec-val
          • Parse-bin-val
          • Parse-alternation
          • Parse-*cwsp-cnl
          • Parse-*bit
          • Parse-wsp/vchar
          • Parse-quoted-string
          • Parse-prose-val
          • Parse-hex-val
          • Parse-grammar
          • Parse-elements
          • Parse-defined-as
          • Parse-dash-1*hexdig
          • Parse-comment
          • Parse-char-val
          • Parse-1*bit
          • Parse-rulename
          • Parse-num-val
          • Parse-htab
          • Parse-hex-val-rest
          • Parse-dot-1*hexdig
          • Parse-dot-1*digit
          • Parse-digit
          • Parse-dec-val-rest
          • Parse-dash-1*digit
          • Parse-dash-1*bit
          • Parse-crlf
          • Parse-cr
          • Parse-conc-rest-comp
          • Parse-cnl-wsp
          • Parse-bin-val-rest
          • Parse-alt-rest-comp
          • Parse-*cwsp
          • Parse-vchar
          • Parse-rulelist
          • Parse-option
          • Parse-group
          • Parse-1*-dot-1*hexdig
          • Parse-1*-dot-1*digit
          • Parse-1*-dot-1*bit
          • Parse-*-rule-/-*cwsp-cnl
          • Parse-*-alpha/digit/dash
          • Parse-lf
          • Parse-dquote
          • Parse-1*hexdig
          • Parse-1*cwsp
          • Parse-?repeat
          • Parse-*-dot-1*hexdig
          • Parse-*-dot-1*digit
          • Parse-*-dot-1*bit
          • Parse-repetition
          • Parse-1*digit
          • Parse-?%i
          • Parse-*wsp/vchar
          • Parse-*hexdig
          • Parse-*digit
          • Parse-alt-rest
          • Parse-conc-rest
          • *grammar-parser-error-msg*
        • Grammar-parser-correctness
      • Meta-circular-validation
      • Parsing-primitives-defresult
      • Parsing-primitives-seq
      • Operations
      • Examples
      • Differences-with-paper
      • Constructor-utilities
      • Grammar-printer
      • Parsing-tools
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Bigmems
    • Builtins
    • Execloader
    • Aleo
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• 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)