• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-fixpoint-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Moddb
      • Svex-compilation
        • Alias-normalization
        • Svex-design-flatten-and-normalize
        • Svex-design-compile
        • Svex-composition
        • Compile.lisp
          • Svex-normalize-assigns
          • Svex-design-flatten
          • Svex-override-lhrange
          • Svex-override-lhs
          • Svex-compose-assigns/delays
          • Aliases-indexed->named-aux
          • Svex-alist-truncate-by-var-decls
          • Svar-map-truncate-by-var-decls
          • Aliases-to-var-decl-map-aux
          • Aliases-indexed->named
          • Svar-indexed->named-memo
          • Lhs-indexed->named
          • Maybe-svar-p
          • Svar-register-indnamememo
          • Svarlist-indexed->named
          • Maybe-svar-fix
          • Lhs-register-indnamememo
          • Maybe-indname-result
          • Aliases-to-var-decl-map
          • Svar-indexed->named
          • Svex-apply-overrides
          • Aliases-boundedp-aux
          • Indnamememo-to-var-decl-map
          • Indname-result
          • Assigns-compose
          • Delay-svarlist->delays
          • Svex-override-vars
          • Indnamememo
          • Delay-svar->delays
          • Assigns-to-overrides
          • Svarlist-collect-delays
          • Svex-overridelist-vars
          • Svex-overridelist-keys
          • Assigns-to-overrides-nrev
          • Cap-length
          • Var-decl-map
        • Assign->netassigns
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Testing-utilities
  • Math

• Compile.lisp

Lhs-indexed->named

Signature

(lhs-indexed->named x scope moddb indnamememo) 
  → 
(mv xx indnamememo1)

Arguments

x — Guard (lhs-p x).

scope — Guard (modscope-p scope).

moddb — Guard (moddb-ok moddb).

Returns

xx — Type (and (lhs-p xx) (svarlist-addr-p (lhs-vars xx))).

indnamememo1 — Type (equal (len indnamememo1) (len indnamememo)).

Definitions and Theorems

Function: lhs-indexed->named

(defun
 lhs-indexed->named
 (x scope moddb indnamememo)
 (declare (xargs :stobjs (moddb indnamememo)))
 (declare (xargs :guard (and (lhs-p x)
                             (modscope-p scope)
                             (moddb-ok moddb))))
 (declare
  (xargs
      :guard
      (and (modscope-okp scope moddb)
           (svarlist-boundedp (lhs-vars x)
                              (modscope-local-bound scope moddb)))))
 (let
  ((__function__ 'lhs-indexed->named))
  (declare (ignorable __function__))
  (b*
   (((mv first rest) (lhs-decomp x))
    ((unless first) (mv nil indnamememo))
    ((lhrange first) first)
    ((mv repl indnamememo)
     (lhatom-case
          first.atom
          :z (mv first indnamememo)
          :var
          (b* (((mv name indnamememo)
                (svar-indexed->named-memo first.atom.name
                                          scope moddb indnamememo)))
              (mv (lhrange first.w
                           (lhatom-var name first.atom.rsh))
                  indnamememo))))
    ((mv rest indnamememo)
     (lhs-indexed->named rest scope moddb indnamememo)))
   (mv (lhs-cons repl rest) indnamememo))))

Theorem: return-type-of-lhs-indexed->named.xx

(defthm return-type-of-lhs-indexed->named.xx
        (b* (((mv ?xx ?indnamememo1)
              (lhs-indexed->named x scope moddb indnamememo)))
            (and (lhs-p xx)
                 (svarlist-addr-p (lhs-vars xx))))
        :rule-classes :rewrite)

Theorem: return-type-of-lhs-indexed->named.indnamememo1

(defthm return-type-of-lhs-indexed->named.indnamememo1
        (b* (((mv ?xx ?indnamememo1)
              (lhs-indexed->named x scope moddb indnamememo)))
            (equal (len indnamememo1)
                   (len indnamememo)))
        :rule-classes :rewrite)

Theorem: lhs-indexed->named-of-lhs-fix-x

(defthm lhs-indexed->named-of-lhs-fix-x
        (equal (lhs-indexed->named (lhs-fix x)
                                   scope moddb indnamememo)
               (lhs-indexed->named x scope moddb indnamememo)))

Theorem: lhs-indexed->named-lhs-equiv-congruence-on-x

(defthm
  lhs-indexed->named-lhs-equiv-congruence-on-x
  (implies
       (lhs-equiv x x-equiv)
       (equal (lhs-indexed->named x scope moddb indnamememo)
              (lhs-indexed->named x-equiv scope moddb indnamememo)))
  :rule-classes :congruence)

Theorem: lhs-indexed->named-of-modscope-fix-scope

(defthm lhs-indexed->named-of-modscope-fix-scope
        (equal (lhs-indexed->named x (modscope-fix scope)
                                   moddb indnamememo)
               (lhs-indexed->named x scope moddb indnamememo)))

Theorem: lhs-indexed->named-modscope-equiv-congruence-on-scope

(defthm
  lhs-indexed->named-modscope-equiv-congruence-on-scope
  (implies
       (modscope-equiv scope scope-equiv)
       (equal (lhs-indexed->named x scope moddb indnamememo)
              (lhs-indexed->named x scope-equiv moddb indnamememo)))
  :rule-classes :congruence)

Theorem: lhs-indexed->named-of-moddb-fix-moddb

(defthm lhs-indexed->named-of-moddb-fix-moddb
        (equal (lhs-indexed->named x scope (moddb-fix moddb)
                                   indnamememo)
               (lhs-indexed->named x scope moddb indnamememo)))

Theorem: lhs-indexed->named-moddb-equiv-congruence-on-moddb

(defthm
  lhs-indexed->named-moddb-equiv-congruence-on-moddb
  (implies
       (moddb-equiv moddb moddb-equiv)
       (equal (lhs-indexed->named x scope moddb indnamememo)
              (lhs-indexed->named x scope moddb-equiv indnamememo)))
  :rule-classes :congruence)