# Theory TranslCompTp

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theory TranslCompTp
imports Index JVMType
`(*  Title:      HOL/MicroJava/Comp/TranslCompTp.thy    Author:     Martin Strecker*)theory TranslCompTpimports Index "../BV/JVMType"begin(**********************************************************************)definition comb :: "['a => 'b list × 'c, 'c => 'b list × 'd, 'a] => 'b list × 'd" where   "comb == (λ f1 f2 x0. let (xs1, x1) = f1 x0;                             (xs2, x2) = f2 x1                         in  (xs1 @ xs2, x2))"definition comb_nil :: "'a => 'b list × 'a" where  "comb_nil a == ([], a)"notation (xsymbols)  comb  (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(**********************************************************************)abbreviation (input)  mt_of :: "method_type × state_type => method_type"  where "mt_of == fst"abbreviation (input)  sttp_of :: "method_type × state_type => state_type"  where "sttp_of == snd"definition nochangeST :: "state_type => method_type × state_type" where  "nochangeST sttp == ([Some sttp], sttp)"definition pushST :: "[ty list, state_type] => method_type × state_type" where  "pushST tps == (λ (ST, LT). ([Some (ST, LT)], (tps @ ST, LT)))"definition dupST :: "state_type => method_type × state_type" where  "dupST == (λ (ST, LT). ([Some (ST, LT)], (hd ST # ST, LT)))"definition dup_x1ST :: "state_type => method_type × state_type" where  "dup_x1ST == (λ (ST, LT). ([Some (ST, LT)],                              (hd ST # hd (tl ST) # hd ST # (tl (tl ST)), LT)))"definition popST :: "[nat, state_type] => method_type × state_type" where  "popST n == (λ (ST, LT). ([Some (ST, LT)], (drop n ST, LT)))"definition replST :: "[nat, ty, state_type] => method_type × state_type" where  "replST n tp == (λ (ST, LT). ([Some (ST, LT)], (tp # (drop n ST), LT)))"definition storeST :: "[nat, ty, state_type] => method_type × state_type" where  "storeST i tp == (λ (ST, LT). ([Some (ST, LT)], (tl ST, LT [i:= OK tp])))"(* Expressions *)primrec compTpExpr :: "java_mb => java_mb prog => expr =>    state_type => method_type × state_type"  and compTpExprs :: "java_mb => java_mb prog => expr list =>    state_type => method_type × state_type"where  "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)))))"| "compTpExprs jmb G [] = comb_nil"| "compTpExprs jmb G (e#es) = (compTpExpr jmb G e) \<box> (compTpExprs jmb G es)"(* Statements *)primrec compTpStmt :: "java_mb => java_mb prog => stmt =>     state_type => method_type × state_type"where  "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"definition compTpInit :: "java_mb => (vname * ty)                   => state_type => method_type × state_type" where  "compTpInit jmb == (λ (vn,ty). (pushST [ty]) \<box>  (storeST (index jmb vn) ty))"primrec compTpInitLvars :: "[java_mb, (vname × ty) list] =>    state_type => method_type × state_type"where  "compTpInitLvars jmb [] = comb_nil"| "compTpInitLvars jmb (lv#lvars) = (compTpInit jmb lv) \<box> (compTpInitLvars jmb lvars)"definition start_ST :: "opstack_type" where  "start_ST == []"definition start_LT :: "cname => ty list => nat => locvars_type" where  "start_LT C pTs n ==  (OK (Class C))#((map OK pTs))@(replicate n Err)"definition compTpMethod  :: "[java_mb prog, cname, java_mb mdecl] => method_type" where  "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))))"definition compTp :: "java_mb prog => prog_type" where  "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 *)definition ssize_sto :: "(state_type option) => nat" where  "ssize_sto sto ==  case sto of None => 0 | (Some (ST, LT)) => length ST"definition max_of_list :: "nat list => nat" where  "max_of_list xs == foldr max xs 0"definition max_ssize :: "method_type => nat" where  "max_ssize mt == max_of_list (map ssize_sto mt)"end`