• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
      • Proof-support
      • Abstract-syntax
      • R1cs-subset
      • Semantics
      • Abstract-syntax-operations
      • Indexed-names
      • Well-formedness
      • Concrete-syntax
        • Lexer
        • Grammar
        • Parser
          • Parse-separator
          • Parse-operator
          • Parse-definition
          • Parse-relation-constraint
          • Parse-equality-constraint
          • Parse-*-comma-identifier
          • Parse-*-comma-expression
          • Parse-*-comma-constraint
          • Parse-system
          • Parse-identifier
          • Parse-pfcs-integer
          • Parse-constraint
          • Parse-*-definition
          • Parse-*-constraint
          • Parsize
          • Check-token-string
          • Check-token-root
          • Parse-token
          • Token-stringp
          • Token-rootp
          • Patbind-pok<
          • Parse-multiplication-expression-rest
          • Parse-addition-expression-rest
          • Parse-primary-expression
          • Parse-multiplication-expression
          • Parse-addition-expression
          • Parse-expression
          • Patbind-pok
          • Perr
        • Tokenizer
      • R1cs-bridge
      • Parser-interface
    • 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

• Parser

Parse-relation-constraint

Parse a relation-constraint.

Signature

(parse-relation-constraint token input) 
  → 
(mv tree next-token rest-input)

Arguments

token — Guard (abnf::tree-optionp token).

input — Guard (abnf::tree-listp input).

Returns

tree — Type (abnf::tree-resultp tree).

next-token — Type (abnf::tree-optionp next-token).

rest-input — Type (abnf::tree-listp rest-input).

Definitions and Theorems

Function: parse-relation-constraint

(defun parse-relation-constraint (token input)
 (declare (xargs :guard (and (abnf::tree-optionp token)
                             (abnf::tree-listp input))))
 (let ((__function__ 'parse-relation-constraint))
  (declare (ignorable __function__))
  (b*
   (((pok tree1)
     (parse-identifier token input))
    ((pok tree2)
     (parse-separator "(" token input))
    ((pok tree3)
     (if (token-stringp ")" token)
         (mv (abnf::make-tree-nonleaf :rulename? nil
                                      :branches nil)
             token input)
      (b* (((pok< tree)
            (parse-expression token input))
           ((pok trees)
            (parse-*-comma-expression token input)))
       (mv
        (abnf::make-tree-nonleaf :rulename? nil
                                 :branches (list (list tree) trees))
        token input))))
    ((pok tree4)
     (parse-separator ")" token input)))
   (mv (abnf::make-tree-nonleaf
            :rulename? (abnf::rulename "relation-constraint")
            :branches (list (list tree1)
                            (list tree2)
                            (list tree3)
                            (list tree4)))
       token input))))

Theorem: tree-resultp-of-parse-relation-constraint.tree

(defthm tree-resultp-of-parse-relation-constraint.tree
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-relation-constraint token input)))
    (abnf::tree-resultp tree))
  :rule-classes :rewrite)

Theorem: tree-optionp-of-parse-relation-constraint.next-token

(defthm tree-optionp-of-parse-relation-constraint.next-token
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-relation-constraint token input)))
    (abnf::tree-optionp next-token))
  :rule-classes :rewrite)

Theorem: tree-listp-of-parse-relation-constraint.rest-input

(defthm tree-listp-of-parse-relation-constraint.rest-input
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-relation-constraint token input)))
    (abnf::tree-listp rest-input))
  :rule-classes :rewrite)

Theorem: parsize-of-parse-relation-constraint-<=

(defthm parsize-of-parse-relation-constraint-<=
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-relation-constraint token input)))
    (<= (parsize next-token rest-input)
        (parsize token input)))
  :rule-classes :linear)

Theorem: parsize-of-parse-relation-constraint-<

(defthm parsize-of-parse-relation-constraint-<
  (b* (((mv ?tree ?next-token ?rest-input)
        (parse-relation-constraint token input)))
    (implies (not (reserrp tree))
             (< (parsize next-token rest-input)
                (parsize token input))))
  :rule-classes :linear)

Theorem: parse-relation-constraint-of-tree-option-fix-token

(defthm parse-relation-constraint-of-tree-option-fix-token
  (equal (parse-relation-constraint (abnf::tree-option-fix token)
                                    input)
         (parse-relation-constraint token input)))

Theorem: parse-relation-constraint-tree-option-equiv-congruence-on-token

(defthm
    parse-relation-constraint-tree-option-equiv-congruence-on-token
  (implies (abnf::tree-option-equiv token token-equiv)
           (equal (parse-relation-constraint token input)
                  (parse-relation-constraint token-equiv input)))
  :rule-classes :congruence)

Theorem: parse-relation-constraint-of-tree-list-fix-input

(defthm parse-relation-constraint-of-tree-list-fix-input
  (equal
       (parse-relation-constraint token (abnf::tree-list-fix input))
       (parse-relation-constraint token input)))

Theorem: parse-relation-constraint-tree-list-equiv-congruence-on-input

(defthm
      parse-relation-constraint-tree-list-equiv-congruence-on-input
  (implies (abnf::tree-list-equiv input input-equiv)
           (equal (parse-relation-constraint token input)
                  (parse-relation-constraint token input-equiv)))
  :rule-classes :congruence)