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theory TranslCompTp(* Title: HOL/MicroJava/Comp/TranslCompTp.thy ID: $Id: TranslCompTp.thy,v 1.3 2005/02/01 17:02:05 paulson Exp $ Author: Martin Strecker *) theory TranslCompTp imports Index "../BV/JVMType" begin (**********************************************************************) constdefs comb :: "['a => 'b list × 'c, 'c => 'b list × 'd, 'a] => 'b list × 'd" "comb == (λ f1 f2 x0. let (xs1, x1) = f1 x0; (xs2, x2) = f2 x1 in (xs1 @ xs2, x2))" comb_nil :: "'a => 'b list × 'a" "comb_nil a == ([], a)" syntax (xsymbols) "comb" :: "['a => 'b list × 'c, 'c => 'b list × 'd, 'a] => 'b list × '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 ==> ∃ xs1 x1 xs2 x2. (xs1, x1) = (f1 x0) ∧ (xs2, x2) = f2 x1 ∧ xs'= xs1 @ xs2 ∧ 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 × state_type => method_type" sttp_of :: "method_type × state_type => state_type" translations "mt_of" => "fst" "sttp_of" => "snd" consts compTpExpr :: "java_mb => java_mb prog => expr => state_type => method_type × state_type" compTpExprs :: "java_mb => java_mb prog => expr list => state_type => method_type × state_type" compTpStmt :: "java_mb => java_mb prog => stmt => state_type => method_type × state_type" constdefs nochangeST :: "state_type => method_type × state_type" "nochangeST sttp == ([Some sttp], sttp)" pushST :: "[ty list, state_type] => method_type × state_type" "pushST tps == (λ (ST, LT). ([Some (ST, LT)], (tps @ ST, LT)))" dupST :: "state_type => method_type × state_type" "dupST == (λ (ST, LT). ([Some (ST, LT)], (hd ST # ST, LT)))" dup_x1ST :: "state_type => method_type × state_type" "dup_x1ST == (λ (ST, LT). ([Some (ST, LT)], (hd ST # hd (tl ST) # hd ST # (tl (tl ST)), LT)))" popST :: "[nat, state_type] => method_type × state_type" "popST n == (λ (ST, LT). ([Some (ST, LT)], (drop n ST, LT)))" replST :: "[nat, ty, state_type] => method_type × state_type" "replST n tp == (λ (ST, LT). ([Some (ST, LT)], (tp # (drop n ST), LT)))" storeST :: "[nat, ty, state_type] => method_type × state_type" "storeST i tp == (λ (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 (λv. 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) = (λ (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 => (vname * ty) => state_type => method_type × state_type" "compTpInit jmb == (λ (vn,ty). (pushST [ty]) \<box> (storeST (index jmb vn) ty))" consts compTpInitLvars :: "[java_mb, (vname × ty) list] => state_type => method_type × 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 => ty list => nat => locvars_type" "start_LT C pTs n == (OK (Class C))#((map OK pTs))@(replicate n Err)" compTpMethod :: "[java_mb prog, cname, java_mb mdecl] => method_type" "compTpMethod G C == λ ((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) => nat" "ssize_sto sto == case sto of None => 0 | (Some (ST, LT)) => length ST" max_of_list :: "nat list => nat" "max_of_list xs == foldr max xs 0" max_ssize :: "method_type => nat" "max_ssize mt == max_of_list (map ssize_sto mt)" end
lemma comb_nil_left:
comb comb_nil f = f
lemma comb_nil_right:
comb f comb_nil = f
lemma comb_assoc:
comb (comb fa fb) fc = comb fa (comb fb fc)
lemma comb_inv:
(xs', x') = comb f1.0 f2.0 x0.0 ==> ∃xs1 x1 xs2 x2. (xs1, x1) = f1.0 x0.0 ∧ (xs2, x2) = f2.0 x1 ∧ xs' = xs1 @ xs2 ∧ x' = x2