Theory Compiler1

(*  Title:      JinjaDCI/Compiler/Compiler1.thy
    Author:     Tobias Nipkow, Susannah Mansky
    Copyright   TUM 2003, UIUC 2019-20

    Based on the Jinja theory Compiler/Compiler1.thy by Tobias Nipkow

section ‹ Compilation Stage 1 ›

theory Compiler1 imports PCompiler J1 Hidden begin

text‹ Replacing variable names by indices. ›

primrec compE1  :: "vname list  expr  expr1"
  and compEs1 :: "vname list  expr list  expr1 list" where
  "compE1 Vs (new C) = new C"
| "compE1 Vs (Cast C e) = Cast C (compE1 Vs e)"
| "compE1 Vs (Val v) = Val v"
| "compE1 Vs (e1 «bop» e2) = (compE1 Vs e1) «bop» (compE1 Vs e2)"
| "compE1 Vs (Var V) = Var(last_index Vs V)"
| "compE1 Vs (V:=e) = (last_index Vs V):= (compE1 Vs e)"
| "compE1 Vs (eF{D}) = (compE1 Vs e)F{D}"
| "compE1 Vs (CsF{D}) = CsF{D}"
| "compE1 Vs (e1F{D}:=e2) = (compE1 Vs e1)F{D} := (compE1 Vs e2)"
| "compE1 Vs (CsF{D}:=e2) = CsF{D} := (compE1 Vs e2)"
| "compE1 Vs (eM(es)) = (compE1 Vs e)M(compEs1 Vs es)"
| "compE1 Vs (CsM(es)) = CsM(compEs1 Vs es)"
| "compE1 Vs {V:T; e} = {(size Vs):T; compE1 (Vs@[V]) e}"
| "compE1 Vs (e1;;e2) = (compE1 Vs e1);;(compE1 Vs e2)"
| "compE1 Vs (if (e) e1 else e2) = if (compE1 Vs e) (compE1 Vs e1) else (compE1 Vs e2)"
| "compE1 Vs (while (e) c) = while (compE1 Vs e) (compE1 Vs c)"
| "compE1 Vs (throw e) = throw (compE1 Vs e)"
| "compE1 Vs (try e1 catch(C V) e2) =
    try(compE1 Vs e1) catch(C (size Vs)) (compE1 (Vs@[V]) e2)"
| "compE1 Vs (INIT C (Cs,b)  e) = INIT C (Cs,b)  (compE1 Vs e)"
| "compE1 Vs (RI(C,e);Cs  e') = RI(C,(compE1 Vs e));Cs  (compE1 Vs e')"

| "compEs1 Vs []     = []"
| "compEs1 Vs (e#es) = compE1 Vs e # compEs1 Vs es"

lemma [simp]: "compEs1 Vs es = map (compE1 Vs) es"
(*<*)by(induct es type:list) simp_all(*>*)

lemma [simp]: "Vs. sub_RI (compE1 Vs e) = sub_RI e"
 and [simp]: "Vs. sub_RIs (compEs1 Vs es) = sub_RIs es"
proof(induct rule: sub_RI_sub_RIs_induct) qed(auto)

primrec fin1:: "expr  expr1" where
  "fin1(Val v) = Val v"
| "fin1(throw e) = throw(fin1 e)"

lemma comp_final: "final e  compE1 Vs e = fin1 e"
(*<*)by(erule finalE, simp_all)(*>*)

lemma [simp]:
      "Vs. max_vars (compE1 Vs e) = max_vars e"
and "Vs. max_varss (compEs1 Vs es) = max_varss es"
(*<*)by (induct e and es rule: max_vars.induct max_varss.induct) simp_all(*>*)

text‹ Compiling programs: ›

definition compP1 :: "J_prog  J1_prog"
  "compP1    compP (λb (pns,body). compE1 (case b of NonStatic  this#pns | Static  pns) body)"

declare compP1_def[simp]