• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
      • Deftreeops
      • Defdefparse
      • Defgrammar
      • Tree-utilities
      • Notation
      • Grammar-parser
      • Meta-circular-validation
      • Parsing-primitives-defresult
        • Parse-schars
        • Parse-ichars
        • Parse-direct
        • Parse-range
        • Parse-next
      • 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

• Parsing-primitives-defresult

Parse-direct

Parse a direct numeric value consisting of given natural numbers.

Signature

(parse-direct nats input) → (mv tree rest-input)

Arguments

nats — Guard (nat-listp nats).

input — Guard (nat-listp input).

Returns

tree — Type (tree-resultp tree).

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

Definitions and Theorems

Function: parse-direct-aux

(defun parse-direct-aux (nats input)
  (declare (xargs :guard (and (nat-listp nats)
                              (nat-listp input))))
  (let ((__function__ 'parse-direct-aux))
    (declare (ignorable __function__))
    (b* (((when (endp nats))
          (mv nil (nat-list-fix input)))
         ((mv nat? input1) (parse-next input))
         ((when (reserrp nat?))
          (mv (reserrf-push nat?)
              (nat-list-fix input)))
         (nat nat?)
         ((unless (equal nat (lnfix (car nats))))
          (mv (reserrf (list :found nat
                             :required (lnfix (car nats))))
              (nat-list-fix input)))
         ((mv nats? input2)
          (parse-direct-aux (cdr nats) input1))
         ((when (reserrp nats?))
          (mv (reserrf-push nats?) input1))
         (nats nats?))
      (mv (cons nat nats) input2))))

Theorem: nat-list-resultp-of-parse-direct-aux.nats1

(defthm nat-list-resultp-of-parse-direct-aux.nats1
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (nat-list-resultp nats1))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-direct-aux.rest-input

(defthm nat-listp-of-parse-direct-aux.rest-input
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-direct-aux-<=

(defthm len-of-parse-direct-aux-<=
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: len-of-parse-direct-aux-<

(defthm len-of-parse-direct-aux-<
  (b* (((mv ?nats1 ?rest-input)
        (parse-direct-aux nats input)))
    (implies (and (not (reserrp nats1)) (consp nats))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: parse-direct-aux-of-nat-list-fix-nats

(defthm parse-direct-aux-of-nat-list-fix-nats
  (equal (parse-direct-aux (nat-list-fix nats)
                           input)
         (parse-direct-aux nats input)))

Theorem: parse-direct-aux-nat-list-equiv-congruence-on-nats

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

Theorem: parse-direct-aux-of-nat-list-fix-input

(defthm parse-direct-aux-of-nat-list-fix-input
  (equal (parse-direct-aux nats (nat-list-fix input))
         (parse-direct-aux nats input)))

Theorem: parse-direct-aux-nat-list-equiv-congruence-on-input

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

Function: parse-direct

(defun parse-direct (nats input)
  (declare (xargs :guard (and (nat-listp nats)
                              (nat-listp input))))
  (let ((__function__ 'parse-direct))
    (declare (ignorable __function__))
    (b* (((mv nats input)
          (parse-direct-aux nats input))
         ((when (reserrp nats))
          (mv (reserrf-push nats) input)))
      (mv (tree-leafterm nats) input))))

Theorem: tree-resultp-of-parse-direct.tree

(defthm tree-resultp-of-parse-direct.tree
  (b* (((mv ?tree ?rest-input)
        (parse-direct nats input)))
    (tree-resultp tree))
  :rule-classes :rewrite)

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

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

Theorem: len-of-parse-direct-<=

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

Theorem: len-of-parse-direct-<

(defthm len-of-parse-direct-<
  (b* (((mv ?tree ?rest-input)
        (parse-direct nats input)))
    (implies (and (not (reserrp tree)) (consp nats))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: parse-direct-of-nat-list-fix-nats

(defthm parse-direct-of-nat-list-fix-nats
  (equal (parse-direct (nat-list-fix nats) input)
         (parse-direct nats input)))

Theorem: parse-direct-nat-list-equiv-congruence-on-nats

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

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

(defthm parse-direct-of-nat-list-fix-input
  (equal (parse-direct nats (nat-list-fix input))
         (parse-direct nats input)))

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

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