• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Acre
    • Milawa
    • Smtlink
    • Aleobft
    • Abnf
      • Deftreeops
      • Defdefparse
      • Defgrammar
      • Abnf-tree-utilities
      • Notation
        • Syntax-abstraction
        • Semantics
          • Tree-terminatedp
          • Tree->string
          • String-has-finite-parse-trees-p
          • Parse-trees-of-string-p
          • Tree-match-element-p
          • Parse-treep
          • Symbol
          • Nat-match-insensitive-char-p
          • String-unambiguousp
          • Tree-match-num-val-p
          • Nats-match-insensitive-chars-p
          • Tree-option
          • String-parsablep
          • Lookup-rulename
          • Nats-match-sensitive-chars-p
          • Numrep-match-repeat-range-p
          • Tree-match-char-val-p
          • Tree-list-match-repetition-p
          • String-ambiguousp
          • Nat-match-sensitive-char-p
          • Parse
          • Tree-match-prose-val-p
          • Theorems-about-terminated-trees-matching-elements
          • Tree-option-result
          • Tree-list-result
          • Tree-list-list-result
          • Tree-result
          • Tree-list-list-match-concatenation-p
          • Languagep
          • Terminal-string-for-rules-p
          • Tree-list-list-match-alternation-p
          • Tree-list-match-element-p
          • Parse!
          • String
          • Tree-set
          • Trees
        • Abstract-syntax
        • Core-rules
        • Concrete-syntax
      • Grammar-parser
      • Meta-circular-validation
      • Parsing-primitives-defresult
      • Parsing-primitives-seq
      • Operations
      • Examples
      • Differences-with-paper
      • Grammar-printer
      • Parsing-tools
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • C
    • Java
    • Taspi
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Riscv
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Bigmems
    • Builtins
    • Axe
    • Execloader
    • Solidity
    • Leo
    • Paco
    • Concurrent-programs
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Semantics

String-unambiguousp

Notion of unambiguous string.

Signature

(string-unambiguousp string rulename rules) → yes/no

Arguments

string — Guard (stringp string).

rulename — Guard (rulenamep rulename).

rules — Guard (rulelistp rules).

Returns

yes/no — Type (booleanp yes/no).

A string is unambiguous iff it has exactly one parse tree.

Definitions and Theorems

Function: string-unambiguousp

(defun string-unambiguousp (string rulename rules)
  (declare (xargs :guard (and (stringp string)
                              (rulenamep rulename)
                              (rulelistp rules))))
  (and (string-parsablep string rulename rules)
       (not (string-ambiguousp string rulename rules))))

Theorem: booleanp-of-string-unambiguousp

(defthm booleanp-of-string-unambiguousp
  (b* ((yes/no (string-unambiguousp string rulename rules)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: parse-treep-when-string-unambiguousp

(defthm parse-treep-when-string-unambiguousp
 (implies
  (string-unambiguousp string rulename rules)
  (equal (parse-treep tree string rulename rules)
         (equal tree
                (string-parsablep-witness string rulename rules)))))

Theorem: treep-of-string-parsablep-witness-when-string-unambiguousp

(defthm treep-of-string-parsablep-witness-when-string-unambiguousp
 (implies (string-unambiguousp string rulename rules)
          (treep (string-parsablep-witness string rulename rules))))

Theorem: string-unambiguousp-of-string-fix-string

(defthm string-unambiguousp-of-string-fix-string
  (equal (string-unambiguousp (string-fix string)
                              rulename rules)
         (string-unambiguousp string rulename rules)))

Theorem: string-unambiguousp-string-equiv-congruence-on-string

(defthm string-unambiguousp-string-equiv-congruence-on-string
 (implies (string-equiv string string-equiv)
          (equal (string-unambiguousp string rulename rules)
                 (string-unambiguousp string-equiv rulename rules)))
 :rule-classes :congruence)

Theorem: string-unambiguousp-of-rulename-fix-rulename

(defthm string-unambiguousp-of-rulename-fix-rulename
  (equal (string-unambiguousp string (rulename-fix rulename)
                              rules)
         (string-unambiguousp string rulename rules)))

Theorem: string-unambiguousp-rulename-equiv-congruence-on-rulename

(defthm string-unambiguousp-rulename-equiv-congruence-on-rulename
 (implies (rulename-equiv rulename rulename-equiv)
          (equal (string-unambiguousp string rulename rules)
                 (string-unambiguousp string rulename-equiv rules)))
 :rule-classes :congruence)

Theorem: string-unambiguousp-of-rulelist-fix-rules

(defthm string-unambiguousp-of-rulelist-fix-rules
  (equal (string-unambiguousp string rulename (rulelist-fix rules))
         (string-unambiguousp string rulename rules)))

Theorem: string-unambiguousp-rulelist-equiv-congruence-on-rules

(defthm string-unambiguousp-rulelist-equiv-congruence-on-rules
 (implies (rulelist-equiv rules rules-equiv)
          (equal (string-unambiguousp string rulename rules)
                 (string-unambiguousp string rulename rules-equiv)))
 :rule-classes :congruence)