• 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
          • Simpadd0
          • Proof-generation
            • Xeq-fundef
            • Xeq-expr-cond
            • Xeq-expr-binary
            • Xeq-block-item-list-cons
            • Xeq-stmt-ifelse
            • Xeq-expr-const
            • Gen-param-thms
            • Gen-from-params
            • Xeq-decl-decl
            • Gout
            • Gen-block-item-list-thm
            • Xeq-stmt-while
            • Xeq-stmt-dowhile
            • Gin
            • Xeq-expr-ident
            • Gen-block-item-thm
            • Xeq-stmt-if
            • Xeq-expr-cast
            • Gen-initer-single-thm
            • Gen-init-scope-thm
            • Gen-expr-thm
            • Xeq-expr-unary
            • Gen-decl-thm
            • Gen-stmt-thm
            • Xeq-stmt-return
            • Xeq-stmt-expr
            • Xeq-block-item-decl
            • Xeq-block-item-stmt
            • Xeq-stmt-compound
            • Xeq-initer-single
            • Gen-thm-name
            • Gin-update
            • Gen-var-assertions
            • Tyspecseq-to-type
            • Xeq-block-item-list-empty
            • Gout-no-thm
            • Irr-gout
          • Split-gso
          • Wrap-fn
          • Constant-propagation
          • Specialize
          • Split-fn
          • Split-fn-when
          • Split-all-gso
          • Copy-fn
          • Variables-in-computation-states
          • Rename
          • Utilities
          • Proof-generation-theorems
          • Input-processing
        • Language
        • 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

• Proof-generation

Gen-block-item-thm

Generate a theorem for the transformation of a block item.

Signature

(gen-block-item-thm old new vartys-pre 
                    vartys-post const-new thm-index hints) 
 
  → 
(mv thm-event thm-name updated-thm-index)

Arguments

old — Guard (block-itemp old).

new — Guard (block-itemp new).

vartys-pre — Guard (c::ident-type-mapp vartys-pre).

vartys-post — Guard (c::ident-type-mapp vartys-post).

const-new — Guard (symbolp const-new).

thm-index — Guard (posp thm-index).

hints — Guard (true-listp hints).

Returns

thm-event — Type (pseudo-event-formp thm-event).

thm-name — Type (symbolp thm-name).

updated-thm-index — Type (posp updated-thm-index).

Definitions and Theorems

Function: gen-block-item-thm

(defun gen-block-item-thm
       (old new vartys-pre
            vartys-post const-new thm-index hints)
 (declare (xargs :guard (and (block-itemp old)
                             (block-itemp new)
                             (c::ident-type-mapp vartys-pre)
                             (c::ident-type-mapp vartys-post)
                             (symbolp const-new)
                             (posp thm-index)
                             (true-listp hints))))
 (declare (xargs :guard (and (block-item-unambp old)
                             (block-item-annop old)
                             (block-item-unambp new)
                             (block-item-annop new))))
 (let ((__function__ 'gen-block-item-thm))
  (declare (ignorable __function__))
  (b*
   ((old (block-item-fix old))
    (new (block-item-fix new))
    ((unless (block-item-formalp old))
     (raise "Internal error: ~x0 is not in the formalized subset."
            old)
     (mv '(_) nil 1))
    ((unless (block-item-formalp new))
     (raise "Internal error: ~x0 is not in the formalized subset."
            new)
     (mv '(_) nil 1))
    (types (block-item-types old))
    ((unless (equal (block-item-types new) types))
     (raise
      "Internal error: ~
                the types ~x0 of the new block item ~x1 differ from ~
                the types ~x2 of the old block item ~x3."
      (block-item-types new)
      new types old)
     (mv '(_) nil 1))
    (vars-pre (gen-var-assertions vartys-pre 'compst))
    (vars-post (gen-var-assertions vartys-post 'old-compst))
    ((mv & old-item) (ldm-block-item old))
    ((mv & new-item) (ldm-block-item new))
    ((mv & ctypes)
     (ldm-type-option-set types))
    (formula
     (cons
      'b*
      (cons
       (cons
        (cons 'old-item
              (cons (cons 'quote (cons old-item 'nil))
                    'nil))
        (cons
          (cons 'new-item
                (cons (cons 'quote (cons new-item 'nil))
                      'nil))
          '(((mv old-sval old-compst)
             (c::exec-block-item old-item compst old-fenv limit))
            ((mv new-sval new-compst)
             (c::exec-block-item new-item compst new-fenv limit)))))
       (cons
        (cons
         'implies
         (cons
          (cons 'and
                (cons '(> (c::compustate-frames-number compst)
                          0)
                      (append vars-pre
                              '((not (c::errorp old-sval))))))
          (cons
           (cons
            'and
            (cons
             '(not (c::errorp new-sval))
             (cons
              '(equal old-sval new-sval)
              (cons
               '(equal old-compst new-compst)
               (cons
                (cons 'in
                      (cons '(c::type-option-of-stmt-value old-sval)
                            (cons (cons 'quote (cons ctypes 'nil))
                                  'nil)))
                vars-post)))))
           'nil)))
        'nil))))
    ((mv thm-name thm-index)
     (gen-thm-name const-new thm-index))
    (thm-event
     (cons
      'defrule
      (cons
           thm-name
           (cons formula
                 (cons ':rule-classes
                       (cons 'nil
                             (cons ':hints (cons hints 'nil)))))))))
   (mv thm-event thm-name thm-index))))

Theorem: pseudo-event-formp-of-gen-block-item-thm.thm-event

(defthm pseudo-event-formp-of-gen-block-item-thm.thm-event
  (b* (((mv ?thm-event ?thm-name ?updated-thm-index)
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)))
    (pseudo-event-formp thm-event))
  :rule-classes :rewrite)

Theorem: symbolp-of-gen-block-item-thm.thm-name

(defthm symbolp-of-gen-block-item-thm.thm-name
  (b* (((mv ?thm-event ?thm-name ?updated-thm-index)
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)))
    (symbolp thm-name))
  :rule-classes :rewrite)

Theorem: posp-of-gen-block-item-thm.updated-thm-index

(defthm posp-of-gen-block-item-thm.updated-thm-index
  (b* (((mv ?thm-event ?thm-name ?updated-thm-index)
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)))
    (posp updated-thm-index))
  :rule-classes :rewrite)

Theorem: gen-block-item-thm-of-block-item-fix-old

(defthm gen-block-item-thm-of-block-item-fix-old
 (equal (gen-block-item-thm (block-item-fix old)
                            new vartys-pre
                            vartys-post const-new thm-index hints)
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)))

Theorem: gen-block-item-thm-block-item-equiv-congruence-on-old

(defthm gen-block-item-thm-block-item-equiv-congruence-on-old
 (implies
   (c$::block-item-equiv old old-equiv)
   (equal
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)
        (gen-block-item-thm old-equiv new vartys-pre
                            vartys-post const-new thm-index hints)))
 :rule-classes :congruence)

Theorem: gen-block-item-thm-of-block-item-fix-new

(defthm gen-block-item-thm-of-block-item-fix-new
 (equal (gen-block-item-thm old (block-item-fix new)
                            vartys-pre
                            vartys-post const-new thm-index hints)
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)))

Theorem: gen-block-item-thm-block-item-equiv-congruence-on-new

(defthm gen-block-item-thm-block-item-equiv-congruence-on-new
 (implies
   (c$::block-item-equiv new new-equiv)
   (equal
        (gen-block-item-thm old new vartys-pre
                            vartys-post const-new thm-index hints)
        (gen-block-item-thm old new-equiv vartys-pre
                            vartys-post const-new thm-index hints)))
 :rule-classes :congruence)