Theory DefsComp (Isabelle2005: October 2005)

# Theory DefsComp

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theory DefsComp
imports JVMExec
begin

    (*  Title:      HOL/MicroJava/Comp/DefsComp.thy
        ID:         $Id: DefsComp.thy,v 1.4 2005/02/01 17:02:05 paulson Exp $
        Author:     Martin Strecker
    *)

    (* Definitions for accessing parts of methods, states etc. *)

    theory DefsComp
    imports "../JVM/JVMExec"
    begin

    constdefs
      method_rT :: "cname × ty × 'c => ty"
      "method_rT mtd == (fst (snd mtd))"

    constdefs
    (* g = get *)
      gx :: "xstate => val option"  "gx ≡ fst"
      gs :: "xstate => state"  "gs ≡ snd"
      gh :: "xstate => aheap"        "gh ≡ fstosnd"
      gl :: "xstate => State.locals" "gl ≡ sndosnd"

      gmb :: "'a prog => cname => sig => 'a"
        "gmb G cn si ≡ snd(snd(the(method (G,cn) si)))"
      gis :: "jvm_method => bytecode"
        "gis ≡ fst o snd o snd"

    (* jmb = aus einem JavaMaethodBody *)
      gjmb_pns  :: "java_mb => vname list"     "gjmb_pns ≡ fst"
      gjmb_lvs  :: "java_mb => (vname×ty)list" "gjmb_lvs ≡ fstosnd"
      gjmb_blk  :: "java_mb => stmt"           "gjmb_blk ≡ fstosndosnd"
      gjmb_res  :: "java_mb => expr"           "gjmb_res ≡ sndosndosnd"
      gjmb_plns :: "java_mb => vname list"
        "gjmb_plns ≡ λjmb. gjmb_pns jmb @ map fst (gjmb_lvs jmb)"

      glvs :: "java_mb => State.locals => locvars"
        "glvs jmb loc ≡ map (theoloc) (gjmb_plns jmb)"

    lemmas gdefs = gx_def gh_def gl_def gmb_def gis_def glvs_def
    lemmas gjmbdefs = gjmb_pns_def gjmb_lvs_def gjmb_blk_def gjmb_res_def gjmb_plns_def

    lemmas galldefs = gdefs gjmbdefs

    constdefs
      locvars_locals :: "java_mb prog => cname => sig => State.locals => locvars"
      "locvars_locals G C S lvs == the (lvs This) # glvs (gmb G C S) lvs"

      locals_locvars :: "java_mb prog => cname => sig => locvars => State.locals"
      "locals_locvars G C S lvs ==
      empty ((gjmb_plns (gmb G C S))[\<mapsto>](tl lvs)) (This\<mapsto>(hd lvs))"

      locvars_xstate :: "java_mb prog => cname => sig => xstate => locvars"
      "locvars_xstate G C S xs == locvars_locals G C S (gl xs)"

    lemma locvars_xstate_par_dep:
      "lv1 = lv2 ==>
      locvars_xstate G C S (xcpt1, hp1, lv1) = locvars_xstate G C S (xcpt2, hp2, lv2)"
    by (simp add: locvars_xstate_def gl_def)

    (**********************************************************************)
    (* Conversions *)

    lemma gx_conv [simp]: "gx (xcpt, s) = xcpt" by (simp add: gx_def)

    lemma gh_conv [simp]: "gh (xcpt, h, l) = h" by (simp add: gh_def)

    end

lemmas gdefs:

      gx == fst

      gh == fst o snd

      gl == snd o snd

      gmb G cn si == snd (snd (the (method (G, cn) si)))

      gis == fst o snd o snd

      glvs jmb loc == map (the o loc) (gjmb_plns jmb)

lemmas gdefs:

      gx == fst

      gh == fst o snd

      gl == snd o snd

      gmb G cn si == snd (snd (the (method (G, cn) si)))

      gis == fst o snd o snd

      glvs jmb loc == map (the o loc) (gjmb_plns jmb)

lemmas gjmbdefs:

      gjmb_pns == fst

      gjmb_lvs == fst o snd

      gjmb_blk == fst o snd o snd

      gjmb_res == snd o snd o snd

      gjmb_plns == %jmb. gjmb_pns jmb @ map fst (gjmb_lvs jmb)

lemmas gjmbdefs:

      gjmb_pns == fst

      gjmb_lvs == fst o snd

      gjmb_blk == fst o snd o snd

      gjmb_res == snd o snd o snd

      gjmb_plns == %jmb. gjmb_pns jmb @ map fst (gjmb_lvs jmb)

lemmas galldefs:

      gx == fst

      gh == fst o snd

      gl == snd o snd

      gmb G cn si == snd (snd (the (method (G, cn) si)))

      gis == fst o snd o snd

      glvs jmb loc == map (the o loc) (gjmb_plns jmb)

      gjmb_pns == fst

      gjmb_lvs == fst o snd

      gjmb_blk == fst o snd o snd

      gjmb_res == snd o snd o snd

      gjmb_plns == %jmb. gjmb_pns jmb @ map fst (gjmb_lvs jmb)

lemmas galldefs:

      gx == fst

      gh == fst o snd

      gl == snd o snd

      gmb G cn si == snd (snd (the (method (G, cn) si)))

      gis == fst o snd o snd

      glvs jmb loc == map (the o loc) (gjmb_plns jmb)

      gjmb_pns == fst

      gjmb_lvs == fst o snd

      gjmb_blk == fst o snd o snd

      gjmb_res == snd o snd o snd

      gjmb_plns == %jmb. gjmb_pns jmb @ map fst (gjmb_lvs jmb)

lemma locvars_xstate_par_dep:

      lv1.0 = lv2.0
      ==> locvars_xstate G C S (xcpt1.0, hp1.0, lv1.0) =
          locvars_xstate G C S (xcpt2.0, hp2.0, lv2.0)

lemma gx_conv:

      gx (xcpt, s) = xcpt

lemma gh_conv:

      gh (xcpt, h, l) = h