• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Set
      • C
        • Syntax-for-tools
        • Atc
        • Transformation-tools
        • Language
          • Abstract-syntax
          • Integer-ranges
          • Implementation-environments
          • Dynamic-semantics
            • Exec-expr
            • Exec
            • Exec-arrsub
            • Variable-resolution-preservation
            • Init-value-to-value
            • Apconvert-expr-value
            • Execution-limit-monotonicity
              • Exec-2limits
              • Exec-monotone
              • Exec-2limits-to-exec
            • Exec-memberp
            • Exec-stmt
            • Exec-address
            • Init-scope
            • Exec-unary
            • Exec-member
            • Exec-fun
            • Exec-stmt-while
            • Eval-iconst
            • Exec-binary-strict-pure
            • Variable-visibility-preservation
            • Object-type-preservation
            • Eval-binary-strict-pure
            • Exec-block-item-list
            • Exec-indir
            • Exec-ident
            • Exec-block-item
            • Eval-cast
            • Frame-and-scope-peeling
            • Exec-expr-list
            • Exec-obj-declon
            • Exec-cast
            • Exec-const
            • Eval-unary
            • Exec-stmt-dowhile
            • Exec-initer
            • Eval-const
            • Execution-without-function-calls
          • Static-semantics
          • Grammar
          • Types
          • Integer-formats-definitions
          • Computation-states
          • Portable-ascii-identifiers
          • Values
          • Integer-operations
          • Object-designators
          • Operations
          • Errors
          • Tag-environments
          • Function-environments
          • Character-sets
          • Flexible-array-member-removal
          • Arithmetic-operations
          • Pointer-operations
          • Real-operations
          • Array-operations
          • Scalar-operations
          • Structure-operations
        • Representation
        • Insertion-sort
        • Pack
      • Soft
      • Bv
      • Imp-language
      • Ethereum
      • Event-macros
      • Java
      • Riscv
      • Bitcoin
      • Zcash
      • Yul
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Axe
      • Lists-light
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Execution-limit-monotonicity

Exec-2limits-to-exec

Equivalence of the execution functions with two limits to the normal execution functions.

See execution-limit-monotonicity for motivation.

We leave these enabled so they can be used automatically in exec-monotone.

Definitions and Theorems

Theorem: exec-fun-2limits-to-exec-fun

(defthm exec-fun-2limits-to-exec-fun
  (implies
       (>= (nfix limit1) (nfix limit))
       (equal (exec-fun-2limits fun args compst fenv limit limit1)
              (exec-fun fun args compst fenv limit))))

Theorem: exec-expr-2limits-to-exec-expr

(defthm exec-expr-2limits-to-exec-expr
  (implies (>= (nfix limit1) (nfix limit))
           (equal (exec-expr-2limits e compst fenv limit limit1)
                  (exec-expr e compst fenv limit))))

Theorem: exec-expr-list-2limits-to-exec-expr-list

(defthm exec-expr-list-2limits-to-exec-expr-list
  (implies
       (>= (nfix limit1) (nfix limit))
       (equal (exec-expr-list-2limits es compst fenv limit limit1)
              (exec-expr-list es compst fenv limit))))

Theorem: exec-stmt-2limits-to-exec-stmt

(defthm exec-stmt-2limits-to-exec-stmt
  (implies (>= (nfix limit1) (nfix limit))
           (equal (exec-stmt-2limits s compst fenv limit limit1)
                  (exec-stmt s compst fenv limit))))

Theorem: exec-stmt-while-2limits-to-exec-stmt-while

(defthm exec-stmt-while-2limits-to-exec-stmt-while
 (implies
   (>= (nfix limit1) (nfix limit))
   (equal
        (exec-stmt-while-2limits test body compst fenv limit limit1)
        (exec-stmt-while test body compst fenv limit))))

Theorem: exec-stmt-dowhile-2limits-to-exec-stmt-dowhile

(defthm exec-stmt-dowhile-2limits-to-exec-stmt-dowhile
 (implies
  (>= (nfix limit1) (nfix limit))
  (equal
      (exec-stmt-dowhile-2limits body test compst fenv limit limit1)
      (exec-stmt-dowhile body test compst fenv limit))))

Theorem: exec-initer-2limits-to-exec-initer

(defthm exec-initer-2limits-to-exec-initer
  (implies
       (>= (nfix limit1) (nfix limit))
       (equal (exec-initer-2limits initer compst fenv limit limit1)
              (exec-initer initer compst fenv limit))))

Theorem: exec-obj-declon-2limits-to-exec-obj-declon

(defthm exec-obj-declon-2limits-to-exec-obj-declon
 (implies
    (>= (nfix limit1) (nfix limit))
    (equal (exec-obj-declon-2limits declon compst fenv limit limit1)
           (exec-obj-declon declon compst fenv limit))))

Theorem: exec-block-item-2limits-to-exec-block-item

(defthm exec-block-item-2limits-to-exec-block-item
 (implies
      (>= (nfix limit1) (nfix limit))
      (equal (exec-block-item-2limits item compst fenv limit limit1)
             (exec-block-item item compst fenv limit))))

Theorem: exec-block-item-list-2limits-to-exec-block-item-list

(defthm exec-block-item-list-2limits-to-exec-block-item-list
 (implies
  (>= (nfix limit1) (nfix limit))
  (equal
       (exec-block-item-list-2limits items compst fenv limit limit1)
       (exec-block-item-list items compst fenv limit))))