• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • 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
      • Soft
      • C
        • Syntax-for-tools
        • Atc
        • Language
          • Abstract-syntax
          • Integer-ranges
          • Implementation-environments
          • Dynamic-semantics
          • Static-semantics
          • Grammar
          • Integer-formats
          • Types
          • Portable-ascii-identifiers
          • Values
          • Integer-operations
          • Computation-states
            • Write-object
            • Objdesign-of-var
            • Compustate-scopes-numbers
            • Create-var
            • Read-object
            • Compustate
            • Frame
            • Enter-scope
            • Compustate-scopes-numbers-aux
            • Compustate-option
            • Push-frame
            • Exit-scope
            • Compustate-frames-number
            • Compustate-option-result
            • Scope-list-result
            • Pop-frame
            • Compustate-result
            • Scope-result
            • Compustate-top-frame-scopes-number
            • Top-frame
            • Heap
            • Scope
            • Scope-list
            • Frame-list
          • Object-designators
          • Operations
          • Errors
          • Tag-environments
          • Function-environments
          • Character-sets
          • Flexible-array-member-removal
          • Arithmetic-operations
          • Pointer-operations
          • Bytes
          • Keywords
          • Real-operations
          • Array-operations
          • Scalar-operations
          • Structure-operations
        • Representation
        • Transformation-tools
        • Insertion-sort
        • Pack
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Lists-light
      • Axe
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Computation-states

Compustate-scopes-numbers

Ordered list of the numbers of scopes in the call stack frames.

Signature

(compustate-scopes-numbers compst) → ns

Arguments

compst — Guard (compustatep compst).

Returns

ns — Type (pos-listp ns).

Each frame in the call stack has a number of scopes. This function returns these numbers, in the same order as the frames in the stack.

Definitions and Theorems

Function: compustate-scopes-numbers-aux

(defun compustate-scopes-numbers-aux (frames)
  (declare (xargs :guard (frame-listp frames)))
  (let ((__function__ 'compustate-scopes-numbers-aux))
    (declare (ignorable __function__))
    (cond ((endp frames) nil)
          (t (cons (len (frame->scopes (car frames)))
                   (compustate-scopes-numbers-aux (cdr frames)))))))

Theorem: pos-listp-of-compustate-scopes-numbers-aux

(defthm pos-listp-of-compustate-scopes-numbers-aux
  (b* ((ns (compustate-scopes-numbers-aux frames)))
    (pos-listp ns))
  :rule-classes :rewrite)

Theorem: len-of-compustate-scopes-numbers-aux

(defthm len-of-compustate-scopes-numbers-aux
  (b* ((?ns (compustate-scopes-numbers-aux frames)))
    (equal (len ns) (len frames))))

Theorem: consp-of-compustate-scopes-numbers-aux

(defthm consp-of-compustate-scopes-numbers-aux
  (b* ((?ns (compustate-scopes-numbers-aux frames)))
    (equal (consp ns) (consp frames))))

Theorem: car-of-compustate-scopes-numbers-aux

(defthm car-of-compustate-scopes-numbers-aux
  (b* ((?ns (compustate-scopes-numbers-aux frames)))
    (implies (> (len frames) 0)
             (equal (car ns)
                    (len (frame->scopes (car frames)))))))

Theorem: compustate-scopes-numbers-aux-of-append

(defthm compustate-scopes-numbers-aux-of-append
  (equal (compustate-scopes-numbers-aux (append frames1 frames2))
         (append (compustate-scopes-numbers-aux frames1)
                 (compustate-scopes-numbers-aux frames2))))

Theorem: compustate-scopes-numbers-aux-of-rev

(defthm compustate-scopes-numbers-aux-of-rev
  (equal (compustate-scopes-numbers-aux (rev frames))
         (rev (compustate-scopes-numbers-aux frames))))

Theorem: compustate-scopes-numbers-aux-of-update-nth

(defthm compustate-scopes-numbers-aux-of-update-nth
 (implies
  (< (nfix i) (len frames))
  (equal (compustate-scopes-numbers-aux (update-nth i frame frames))
         (update-nth i (len (frame->scopes frame))
                     (compustate-scopes-numbers-aux frames)))))

Theorem: update-nth-of-nth-and-compustate-scopes-numbers-aux

(defthm update-nth-of-nth-and-compustate-scopes-numbers-aux
 (implies
  (< (nfix i)
     (len (compustate->frames compst)))
  (equal
   (update-nth
        i
        (len (frame->scopes (nth i (compustate->frames compst))))
        (compustate-scopes-numbers-aux (compustate->frames compst)))
   (compustate-scopes-numbers-aux (compustate->frames compst)))))

Theorem: compustate-scopes-numbers-aux-of-frame-list-fix-frames

(defthm compustate-scopes-numbers-aux-of-frame-list-fix-frames
  (equal (compustate-scopes-numbers-aux (frame-list-fix frames))
         (compustate-scopes-numbers-aux frames)))

Theorem: compustate-scopes-numbers-aux-frame-list-equiv-congruence-on-frames

(defthm
 compustate-scopes-numbers-aux-frame-list-equiv-congruence-on-frames
 (implies (frame-list-equiv frames frames-equiv)
          (equal (compustate-scopes-numbers-aux frames)
                 (compustate-scopes-numbers-aux frames-equiv)))
 :rule-classes :congruence)

Function: compustate-scopes-numbers

(defun compustate-scopes-numbers (compst)
  (declare (xargs :guard (compustatep compst)))
  (let ((__function__ 'compustate-scopes-numbers))
    (declare (ignorable __function__))
    (compustate-scopes-numbers-aux (compustate->frames compst))))

Theorem: pos-listp-of-compustate-scopes-numbers

(defthm pos-listp-of-compustate-scopes-numbers
  (b* ((ns (compustate-scopes-numbers compst)))
    (pos-listp ns))
  :rule-classes :rewrite)

Theorem: len-of-compustate-scopes-numbers

(defthm len-of-compustate-scopes-numbers
  (b* ((?ns (compustate-scopes-numbers compst)))
    (equal (len ns)
           (len (compustate->frames compst)))))

Theorem: consp-of-compustate-scopes-numbers

(defthm consp-of-compustate-scopes-numbers
  (implies (> (compustate-frames-number compst) 0)
           (b* ((?ns (compustate-scopes-numbers compst)))
             (consp ns)))
  :rule-classes :type-prescription)

Theorem: posp-of-car-of-compustate-scopes-numbers

(defthm posp-of-car-of-compustate-scopes-numbers
  (implies (> (compustate-frames-number compst) 0)
           (b* ((?ns (compustate-scopes-numbers compst)))
             (posp (car ns))))
  :rule-classes :type-prescription)

Theorem: car-of-compustate-scopes-numbers-lower-bound

(defthm car-of-compustate-scopes-numbers-lower-bound
  (implies (> (compustate-frames-number compst) 0)
           (b* ((?ns (compustate-scopes-numbers compst)))
             (> (car ns) 0)))
  :rule-classes :linear)

Theorem: car-of-compustate-scopes-numbers

(defthm car-of-compustate-scopes-numbers
 (b* ((?ns (compustate-scopes-numbers compst)))
  (implies
    (> (compustate-frames-number compst) 0)
    (equal
         (car ns)
         (len (frame->scopes (car (compustate->frames compst))))))))

Theorem: compustate-scopes-numbers-of-push-frame

(defthm compustate-scopes-numbers-of-push-frame
  (equal (compustate-scopes-numbers (push-frame frame compst))
         (cons (len (frame->scopes frame))
               (compustate-scopes-numbers compst))))

Theorem: compustate-scopes-numbers-of-pop-frame

(defthm compustate-scopes-numbers-of-pop-frame
  (equal (compustate-scopes-numbers (pop-frame compst))
         (cdr (compustate-scopes-numbers compst))))

Theorem: compustate-scopes-numbers-of-compustate-fix-compst

(defthm compustate-scopes-numbers-of-compustate-fix-compst
  (equal (compustate-scopes-numbers (compustate-fix compst))
         (compustate-scopes-numbers compst)))

Theorem: compustate-scopes-numbers-compustate-equiv-congruence-on-compst

(defthm
    compustate-scopes-numbers-compustate-equiv-congruence-on-compst
  (implies (compustate-equiv compst compst-equiv)
           (equal (compustate-scopes-numbers compst)
                  (compustate-scopes-numbers compst-equiv)))
  :rule-classes :congruence)