(* Title: HOL/MicroJava/Comp/TranslCompTp.thy
ID: $Id$
Author: Martin Strecker
Copyright GPL 2002
*)
theory TranslCompTp = JVMType + Index:
(**********************************************************************)
constdefs
comb :: "['a \<Rightarrow> 'b list \<times> 'c, 'c \<Rightarrow> 'b list \<times> 'd, 'a] \<Rightarrow> 'b list \<times> 'd"
"comb == (\<lambda> f1 f2 x0. let (xs1, x1) = f1 x0;
(xs2, x2) = f2 x1
in (xs1 @ xs2, x2))"
comb_nil :: "'a \<Rightarrow> 'b list \<times> 'a"
"comb_nil a == ([], a)"
syntax (xsymbols)
"comb" :: "['a \<Rightarrow> 'b list \<times> 'c, 'c \<Rightarrow> 'b list \<times> 'd, 'a] \<Rightarrow> 'b list \<times> 'd"
(infixr "\<box>" 55)
lemma comb_nil_left [simp]: "comb_nil \<box> f = f"
by (simp add: comb_def comb_nil_def split_beta)
lemma comb_nil_right [simp]: "f \<box> comb_nil = f"
by (simp add: comb_def comb_nil_def split_beta)
lemma comb_assoc [simp]: "(fa \<box> fb) \<box> fc = fa \<box> (fb \<box> fc)"
by (simp add: comb_def split_beta)
lemma comb_inv: "(xs', x') = (f1 \<box> f2) x0 \<Longrightarrow>
\<exists> xs1 x1 xs2 x2. (xs1, x1) = (f1 x0) \<and> (xs2, x2) = f2 x1 \<and> xs'= xs1 @ xs2 \<and> x'=x2"
apply (case_tac "f1 x0")
apply (case_tac "f2 x1")
apply (simp add: comb_def split_beta)
done
(**********************************************************************)
syntax
mt_of :: "method_type \<times> state_type \<Rightarrow> method_type"
sttp_of :: "method_type \<times> state_type \<Rightarrow> state_type"
translations
"mt_of" => "fst"
"sttp_of" => "snd"
consts
compTpExpr :: "java_mb \<Rightarrow> java_mb prog \<Rightarrow> expr
\<Rightarrow> state_type \<Rightarrow> method_type \<times> state_type"
compTpExprs :: "java_mb \<Rightarrow> java_mb prog \<Rightarrow> expr list
\<Rightarrow> state_type \<Rightarrow> method_type \<times> state_type"
compTpStmt :: "java_mb \<Rightarrow> java_mb prog \<Rightarrow> stmt
\<Rightarrow> state_type \<Rightarrow> method_type \<times> state_type"
constdefs
nochangeST :: "state_type \<Rightarrow> method_type \<times> state_type"
"nochangeST sttp == ([Some sttp], sttp)"
pushST :: "[ty list, state_type] \<Rightarrow> method_type \<times> state_type"
"pushST tps == (\<lambda> (ST, LT). ([Some (ST, LT)], (tps @ ST, LT)))"
dupST :: "state_type \<Rightarrow> method_type \<times> state_type"
"dupST == (\<lambda> (ST, LT). ([Some (ST, LT)], (hd ST # ST, LT)))"
dup_x1ST :: "state_type \<Rightarrow> method_type \<times> state_type"
"dup_x1ST == (\<lambda> (ST, LT). ([Some (ST, LT)],
(hd ST # hd (tl ST) # hd ST # (tl (tl ST)), LT)))"
popST :: "[nat, state_type] \<Rightarrow> method_type \<times> state_type"
"popST n == (\<lambda> (ST, LT). ([Some (ST, LT)], (drop n ST, LT)))"
replST :: "[nat, ty, state_type] \<Rightarrow> method_type \<times> state_type"
"replST n tp == (\<lambda> (ST, LT). ([Some (ST, LT)], (tp # (drop n ST), LT)))"
storeST :: "[nat, ty, state_type] \<Rightarrow> method_type \<times> state_type"
"storeST i tp == (\<lambda> (ST, LT). ([Some (ST, LT)], (tl ST, LT [i:= OK tp])))"
(* Expressions *)
primrec
"compTpExpr jmb G (NewC c) = pushST [Class c]"
"compTpExpr jmb G (Cast c e) =
(compTpExpr jmb G e) \<box> (replST 1 (Class c))"
"compTpExpr jmb G (Lit val) = pushST [the (typeof (\<lambda>v. None) val)]"
"compTpExpr jmb G (BinOp bo e1 e2) =
(compTpExpr jmb G e1) \<box> (compTpExpr jmb G e2) \<box>
(case bo of
Eq => popST 2 \<box> pushST [PrimT Boolean] \<box> popST 1 \<box> pushST [PrimT Boolean]
| Add => replST 2 (PrimT Integer))"
"compTpExpr jmb G (LAcc vn) = (\<lambda> (ST, LT).
pushST [ok_val (LT ! (index jmb vn))] (ST, LT))"
"compTpExpr jmb G (vn::=e) =
(compTpExpr jmb G e) \<box> dupST \<box> (popST 1)"
"compTpExpr jmb G ( {cn}e..fn ) =
(compTpExpr jmb G e) \<box> replST 1 (snd (the (field (G,cn) fn)))"
"compTpExpr jmb G (FAss cn e1 fn e2 ) =
(compTpExpr jmb G e1) \<box> (compTpExpr jmb G e2) \<box> dup_x1ST \<box> (popST 2)"
"compTpExpr jmb G ({C}a..mn({fpTs}ps)) =
(compTpExpr jmb G a) \<box> (compTpExprs jmb G ps) \<box>
(replST ((length ps) + 1) (method_rT (the (method (G,C) (mn,fpTs)))))"
(* Expression lists *)
"compTpExprs jmb G [] = comb_nil"
"compTpExprs jmb G (e#es) = (compTpExpr jmb G e) \<box> (compTpExprs jmb G es)"
(* Statements *)
primrec
"compTpStmt jmb G Skip = comb_nil"
"compTpStmt jmb G (Expr e) = (compTpExpr jmb G e) \<box> popST 1"
"compTpStmt jmb G (c1;; c2) = (compTpStmt jmb G c1) \<box> (compTpStmt jmb G c2)"
"compTpStmt jmb G (If(e) c1 Else c2) =
(pushST [PrimT Boolean]) \<box> (compTpExpr jmb G e) \<box> popST 2 \<box>
(compTpStmt jmb G c1) \<box> nochangeST \<box> (compTpStmt jmb G c2)"
"compTpStmt jmb G (While(e) c) =
(pushST [PrimT Boolean]) \<box> (compTpExpr jmb G e) \<box> popST 2 \<box>
(compTpStmt jmb G c) \<box> nochangeST"
constdefs
compTpInit :: "java_mb \<Rightarrow> (vname * ty)
\<Rightarrow> state_type \<Rightarrow> method_type \<times> state_type"
"compTpInit jmb == (\<lambda> (vn,ty). (pushST [ty]) \<box> (storeST (index jmb vn) ty))"
consts
compTpInitLvars :: "[java_mb, (vname \<times> ty) list]
\<Rightarrow> state_type \<Rightarrow> method_type \<times> state_type"
primrec
"compTpInitLvars jmb [] = comb_nil"
"compTpInitLvars jmb (lv#lvars) = (compTpInit jmb lv) \<box> (compTpInitLvars jmb lvars)"
constdefs
start_ST :: "opstack_type"
"start_ST == []"
start_LT :: "cname \<Rightarrow> ty list \<Rightarrow> nat \<Rightarrow> locvars_type"
"start_LT C pTs n == (OK (Class C))#((map OK pTs))@(replicate n Err)"
compTpMethod :: "[java_mb prog, cname, java_mb mdecl] \<Rightarrow> method_type"
"compTpMethod G C == \<lambda> ((mn,pTs),rT, jmb).
let (pns,lvars,blk,res) = jmb
in (mt_of
((compTpInitLvars jmb lvars \<box>
compTpStmt jmb G blk \<box>
compTpExpr jmb G res \<box>
nochangeST)
(start_ST, start_LT C pTs (length lvars))))"
compTp :: "java_mb prog => prog_type"
"compTp G C sig == let (D, rT, jmb) = (the (method (G, C) sig))
in compTpMethod G C (sig, rT, jmb)"
(**********************************************************************)
(* Computing the maximum stack size from the method_type *)
constdefs
ssize_sto :: "(state_type option) \<Rightarrow> nat"
"ssize_sto sto == case sto of None \<Rightarrow> 0 | (Some (ST, LT)) \<Rightarrow> length ST"
max_of_list :: "nat list \<Rightarrow> nat"
"max_of_list xs == foldr max xs 0"
max_ssize :: "method_type \<Rightarrow> nat"
"max_ssize mt == max_of_list (map ssize_sto mt)"
end