berghofe@41809: (*  Title:      HOL/SPARK/Tools/spark_vcs.ML
berghofe@41809:     Author:     Stefan Berghofer
berghofe@41809:     Copyright:  secunet Security Networks AG
berghofe@41809: 
berghofe@41809: Store for verification conditions generated by SPARK/Ada.
berghofe@41809: *)
berghofe@41809: 
berghofe@41809: signature SPARK_VCS =
berghofe@41809: sig
berghofe@43227:   val set_vcs: Fdl_Parser.decls -> Fdl_Parser.rules ->
berghofe@43267:     (string * string) * Fdl_Parser.vcs -> Path.T -> string -> theory -> theory
berghofe@41809:   val add_proof_fun: (typ option -> 'a -> term) ->
berghofe@41809:     string * ((string list * string) option * 'a) ->
berghofe@41809:     theory -> theory
berghofe@47596:   val add_type: string * (typ * (string * string) list) -> theory -> theory
berghofe@49182:   val lookup_vc: theory -> bool -> string -> (Element.context_i list *
berghofe@42767:     (string * thm list option * Element.context_i * Element.statement_i)) option
berghofe@49182:   val get_vcs: theory -> bool ->
berghofe@42767:     Element.context_i list * (binding * thm) list * (string *
berghofe@42767:     (string * thm list option * Element.context_i * Element.statement_i)) list
berghofe@42767:   val mark_proved: string -> thm list -> theory -> theory
berghofe@49182:   val close: bool -> theory -> theory
berghofe@41809:   val is_closed: theory -> bool
berghofe@41809: end;
berghofe@41809: 
berghofe@41809: structure SPARK_VCs: SPARK_VCS =
berghofe@41809: struct
berghofe@41809: 
berghofe@41809: open Fdl_Parser;
berghofe@41809: 
berghofe@41809: 
berghofe@43227: (** theory data **)
berghofe@43227: 
berghofe@43227: fun err_unfinished () = error "An unfinished SPARK environment is still open."
berghofe@43227: 
berghofe@43227: val strip_number = pairself implode o take_suffix Fdl_Lexer.is_digit o raw_explode;
berghofe@43227: 
berghofe@43227: val name_ord = prod_ord string_ord (option_ord int_ord) o
berghofe@43227:   pairself (strip_number ##> Int.fromString);
berghofe@43227: 
berghofe@43227: structure VCtab = Table(type key = string val ord = name_ord);
berghofe@43227: 
berghofe@43227: structure VCs = Theory_Data
berghofe@43227: (
berghofe@43227:   type T =
berghofe@43227:     {pfuns: ((string list * string) option * term) Symtab.table,
berghofe@47596:      type_map: (typ * (string * string) list) Symtab.table,
berghofe@43227:      env:
berghofe@43227:        {ctxt: Element.context_i list,
berghofe@43227:         defs: (binding * thm) list,
berghofe@43227:         types: fdl_type tab,
berghofe@43227:         funs: (string list * string) tab,
berghofe@47438:         pfuns: ((string list * string) option * term) Symtab.table,
berghofe@43227:         ids: (term * string) Symtab.table * Name.context,
berghofe@43227:         proving: bool,
berghofe@43227:         vcs: (string * thm list option *
berghofe@43227:           (string * expr) list * (string * expr) list) VCtab.table,
berghofe@43267:         path: Path.T,
berghofe@43267:         prefix: string} option}
berghofe@43227:   val empty : T = {pfuns = Symtab.empty, type_map = Symtab.empty, env = NONE}
berghofe@43227:   val extend = I
berghofe@43227:   fun merge ({pfuns = pfuns1, type_map = type_map1, env = NONE},
berghofe@43227:         {pfuns = pfuns2, type_map = type_map2, env = NONE}) =
berghofe@43227:         {pfuns = Symtab.merge (eq_pair (op =) (op aconv)) (pfuns1, pfuns2),
berghofe@43227:          type_map = Symtab.merge (op =) (type_map1, type_map2),
berghofe@43227:          env = NONE}
berghofe@43227:     | merge _ = err_unfinished ()
berghofe@43227: )
berghofe@43227: 
berghofe@43227: 
berghofe@41809: (** utilities **)
berghofe@41809: 
berghofe@43227: val to_lower = raw_explode #> map Symbol.to_ascii_lower #> implode;
berghofe@43227: 
berghofe@43227: val lcase_eq = (op =) o pairself (to_lower o Long_Name.base_name);
berghofe@43227: 
berghofe@43267: fun lookup_prfx "" tab s = Symtab.lookup tab s
berghofe@43267:   | lookup_prfx prfx tab s = (case Symtab.lookup tab s of
berghofe@43267:         NONE => Symtab.lookup tab (prfx ^ "__" ^ s)
berghofe@43267:       | x => x);
berghofe@43267: 
berghofe@43267: fun strip_prfx s =
berghofe@43267:   let
berghofe@43267:     fun strip ys [] = ("", implode ys)
berghofe@43267:       | strip ys ("_" :: "_" :: xs) = (implode (rev xs), implode ys)
berghofe@43267:       | strip ys (x :: xs) = strip (x :: ys) xs
berghofe@43267:   in strip [] (rev (raw_explode s)) end;
berghofe@43267: 
berghofe@47596: fun unprefix_pfun "" s = s
berghofe@47596:   | unprefix_pfun prfx s =
berghofe@47596:       let val (prfx', s') = strip_prfx s
berghofe@47596:       in if prfx = prfx' then s' else s end;
berghofe@47596: 
berghofe@41809: fun mk_unop s t =
berghofe@41809:   let val T = fastype_of t
berghofe@41809:   in Const (s, T --> T) $ t end;
berghofe@41809: 
berghofe@41809: fun mk_times (t, u) =
berghofe@41809:   let
berghofe@41809:     val setT = fastype_of t;
berghofe@41809:     val T = HOLogic.dest_setT setT;
berghofe@41809:     val U = HOLogic.dest_setT (fastype_of u)
berghofe@41809:   in
berghofe@41809:     Const (@{const_name Sigma}, setT --> (T --> HOLogic.mk_setT U) -->
berghofe@41809:       HOLogic.mk_setT (HOLogic.mk_prodT (T, U))) $ t $ Abs ("", T, u)
berghofe@41809:   end;
berghofe@41809: 
berghofe@43267: fun get_type thy prfx ty =
berghofe@43227:   let val {type_map, ...} = VCs.get thy
berghofe@43267:   in lookup_prfx prfx type_map ty end;
berghofe@43227: 
berghofe@47596: fun mk_type' _ _ "integer" = (HOLogic.intT, [])
berghofe@47596:   | mk_type' _ _ "boolean" = (HOLogic.boolT, [])
berghofe@47596:   | mk_type' thy prfx ty =
berghofe@43267:       (case get_type thy prfx ty of
berghofe@43227:          NONE =>
berghofe@47596:            (Syntax.check_typ (Proof_Context.init_global thy)
berghofe@47596:               (Type (Sign.full_name thy (Binding.name ty), [])),
berghofe@47596:             [])
berghofe@47596:        | SOME p => p);
berghofe@47596: 
berghofe@47596: fun mk_type thy prfx ty = fst (mk_type' thy prfx ty);
berghofe@41809: 
berghofe@41809: val booleanN = "boolean";
berghofe@41809: val integerN = "integer";
berghofe@41809: 
berghofe@41809: fun define_overloaded (def_name, eq) lthy =
berghofe@41809:   let
berghofe@41809:     val ((c, _), rhs) = eq |> Syntax.check_term lthy |>
berghofe@41809:       Logic.dest_equals |>> dest_Free;
berghofe@41809:     val ((_, (_, thm)), lthy') = Local_Theory.define
berghofe@41809:       ((Binding.name c, NoSyn), ((Binding.name def_name, []), rhs)) lthy
wenzelm@43232:     val ctxt_thy = Proof_Context.init_global (Proof_Context.theory_of lthy');
wenzelm@43232:     val thm' = singleton (Proof_Context.export lthy' ctxt_thy) thm
berghofe@41809:   in (thm', lthy') end;
berghofe@41809: 
berghofe@41809: fun strip_underscores s =
berghofe@41809:   strip_underscores (unsuffix "_" s) handle Fail _ => s;
berghofe@41809: 
berghofe@41809: fun strip_tilde s =
berghofe@41809:   unsuffix "~" s ^ "_init" handle Fail _ => s;
berghofe@41809: 
berghofe@41809: val mangle_name = strip_underscores #> strip_tilde;
berghofe@41809: 
berghofe@43267: fun mk_variables thy prfx xs ty (tab, ctxt) =
berghofe@41809:   let
berghofe@43267:     val T = mk_type thy prfx ty;
wenzelm@44208:     val (ys, ctxt') = fold_map Name.variant (map mangle_name xs) ctxt;
berghofe@41809:     val zs = map (Free o rpair T) ys;
berghofe@41809:   in (zs, (fold (Symtab.update o apsnd (rpair ty)) (xs ~~ zs) tab, ctxt')) end;
berghofe@41809: 
berghofe@43227: fun get_record_info thy T = (case Record.dest_recTs T of
berghofe@43227:     [(tyname, [@{typ unit}])] =>
berghofe@43227:       Record.get_info thy (Long_Name.qualifier tyname)
berghofe@43227:   | _ => NONE);
berghofe@43227: 
berghofe@47596: fun find_field [] fname fields =
berghofe@47596:       find_first (curry lcase_eq fname o fst) fields
berghofe@47596:   | find_field cmap fname fields =
berghofe@47596:       (case AList.lookup (op =) cmap fname of
berghofe@47596:          NONE => NONE
berghofe@47596:        | SOME fname' => SOME (fname', the (AList.lookup (op =) fields fname')));
berghofe@43227: 
berghofe@43227: fun find_field' fname = get_first (fn (flds, fldty) =>
berghofe@43227:   if member (op =) flds fname then SOME fldty else NONE);
berghofe@43227: 
berghofe@43227: fun assoc_ty_err thy T s msg =
berghofe@43227:   error ("Type " ^ Syntax.string_of_typ_global thy T ^
berghofe@43227:     " associated with SPARK type " ^ s ^ "\n" ^ msg);
berghofe@43227: 
berghofe@41809: 
berghofe@41809: (** generate properties of enumeration types **)
berghofe@41809: 
berghofe@43227: fun add_enum_type tyname tyname' thy =
berghofe@41809:   let
wenzelm@46777:     val {case_name, ...} = the (Datatype.get_info thy tyname');
wenzelm@46777:     val cs = map Const (the (Datatype.get_constrs thy tyname'));
berghofe@43227:     val k = length cs;
berghofe@41809:     val T = Type (tyname', []);
berghofe@41809:     val p = Const (@{const_name pos}, T --> HOLogic.intT);
berghofe@41809:     val v = Const (@{const_name val}, HOLogic.intT --> T);
berghofe@41809:     val card = Const (@{const_name card},
berghofe@41809:       HOLogic.mk_setT T --> HOLogic.natT) $ HOLogic.mk_UNIV T;
berghofe@41809: 
berghofe@41809:     fun mk_binrel_def s f = Logic.mk_equals
berghofe@41809:       (Const (s, T --> T --> HOLogic.boolT),
berghofe@41809:        Abs ("x", T, Abs ("y", T,
berghofe@41809:          Const (s, HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $
berghofe@41809:            (f $ Bound 1) $ (f $ Bound 0))));
berghofe@41809: 
berghofe@41809:     val (((def1, def2), def3), lthy) = thy |>
berghofe@41809: 
berghofe@43273:       Class.instantiation ([tyname'], [], @{sort spark_enum}) |>
berghofe@41809: 
berghofe@41809:       define_overloaded ("pos_" ^ tyname ^ "_def", Logic.mk_equals
berghofe@41809:         (p,
berghofe@41809:          list_comb (Const (case_name, replicate k HOLogic.intT @
berghofe@41809:              [T] ---> HOLogic.intT),
berghofe@41809:            map (HOLogic.mk_number HOLogic.intT) (0 upto k - 1)))) ||>>
berghofe@41809: 
berghofe@41809:       define_overloaded ("less_eq_" ^ tyname ^ "_def",
berghofe@41809:         mk_binrel_def @{const_name less_eq} p) ||>>
berghofe@41809:       define_overloaded ("less_" ^ tyname ^ "_def",
berghofe@41809:         mk_binrel_def @{const_name less} p);
berghofe@41809: 
berghofe@41809:     val UNIV_eq = Goal.prove lthy [] []
berghofe@41809:       (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@41809:          (HOLogic.mk_UNIV T, HOLogic.mk_set T cs)))
berghofe@41809:       (fn _ =>
berghofe@41809:          rtac @{thm subset_antisym} 1 THEN
berghofe@41809:          rtac @{thm subsetI} 1 THEN
wenzelm@46777:          Datatype_Aux.exh_tac (K (#exhaust (Datatype.the_info
wenzelm@43232:            (Proof_Context.theory_of lthy) tyname'))) 1 THEN
berghofe@41809:          ALLGOALS (asm_full_simp_tac (simpset_of lthy)));
berghofe@41809: 
berghofe@41809:     val finite_UNIV = Goal.prove lthy [] []
berghofe@41809:       (HOLogic.mk_Trueprop (Const (@{const_name finite},
berghofe@41809:          HOLogic.mk_setT T --> HOLogic.boolT) $ HOLogic.mk_UNIV T))
berghofe@41809:       (fn _ => simp_tac (simpset_of lthy addsimps [UNIV_eq]) 1);
berghofe@41809: 
berghofe@41809:     val card_UNIV = Goal.prove lthy [] []
berghofe@41809:       (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@41809:          (card, HOLogic.mk_number HOLogic.natT k)))
berghofe@41809:       (fn _ => simp_tac (simpset_of lthy addsimps [UNIV_eq]) 1);
berghofe@41809: 
berghofe@41809:     val range_pos = Goal.prove lthy [] []
berghofe@41809:       (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@41809:          (Const (@{const_name image}, (T --> HOLogic.intT) -->
berghofe@41809:             HOLogic.mk_setT T --> HOLogic.mk_setT HOLogic.intT) $
berghofe@41809:               p $ HOLogic.mk_UNIV T,
berghofe@41809:           Const (@{const_name atLeastLessThan}, HOLogic.intT -->
berghofe@41809:             HOLogic.intT --> HOLogic.mk_setT HOLogic.intT) $
berghofe@41809:               HOLogic.mk_number HOLogic.intT 0 $
berghofe@41809:               (@{term int} $ card))))
berghofe@41809:       (fn _ =>
berghofe@41809:          simp_tac (simpset_of lthy addsimps [card_UNIV]) 1 THEN
berghofe@41809:          simp_tac (simpset_of lthy addsimps [UNIV_eq, def1]) 1 THEN
berghofe@41809:          rtac @{thm subset_antisym} 1 THEN
berghofe@41809:          simp_tac (simpset_of lthy) 1 THEN
berghofe@41809:          rtac @{thm subsetI} 1 THEN
berghofe@41809:          asm_full_simp_tac (simpset_of lthy addsimps @{thms interval_expand}
berghofe@41809:            delsimps @{thms atLeastLessThan_iff}) 1);
berghofe@41809: 
berghofe@41809:     val lthy' =
berghofe@41809:       Class.prove_instantiation_instance (fn _ =>
berghofe@41809:         Class.intro_classes_tac [] THEN
berghofe@41809:         rtac finite_UNIV 1 THEN
berghofe@41809:         rtac range_pos 1 THEN
berghofe@41809:         simp_tac (HOL_basic_ss addsimps [def3]) 1 THEN
berghofe@41809:         simp_tac (HOL_basic_ss addsimps [def2]) 1) lthy;
berghofe@41809: 
berghofe@41809:     val (pos_eqs, val_eqs) = split_list (map_index (fn (i, c) =>
berghofe@41809:       let
berghofe@41809:         val n = HOLogic.mk_number HOLogic.intT i;
berghofe@41809:         val th = Goal.prove lthy' [] []
berghofe@41809:           (HOLogic.mk_Trueprop (HOLogic.mk_eq (p $ c, n)))
berghofe@41809:           (fn _ => simp_tac (simpset_of lthy' addsimps [def1]) 1);
berghofe@41809:         val th' = Goal.prove lthy' [] []
berghofe@41809:           (HOLogic.mk_Trueprop (HOLogic.mk_eq (v $ n, c)))
berghofe@41809:           (fn _ =>
berghofe@41809:              rtac (@{thm inj_pos} RS @{thm injD}) 1 THEN
berghofe@41809:              simp_tac (simpset_of lthy' addsimps
berghofe@41809:                [@{thm pos_val}, range_pos, card_UNIV, th]) 1)
berghofe@41809:       in (th, th') end) cs);
berghofe@41809: 
berghofe@41809:     val first_el = Goal.prove lthy' [] []
berghofe@41809:       (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@41809:          (Const (@{const_name first_el}, T), hd cs)))
berghofe@41809:       (fn _ => simp_tac (simpset_of lthy' addsimps
berghofe@41809:          [@{thm first_el_def}, hd val_eqs]) 1);
berghofe@41809: 
berghofe@41809:     val last_el = Goal.prove lthy' [] []
berghofe@41809:       (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@41809:          (Const (@{const_name last_el}, T), List.last cs)))
berghofe@41809:       (fn _ => simp_tac (simpset_of lthy' addsimps
berghofe@41809:          [@{thm last_el_def}, List.last val_eqs, card_UNIV]) 1);
berghofe@41809:   in
berghofe@43227:     lthy' |>
berghofe@43227:     Local_Theory.note
wenzelm@46463:       ((Binding.name (tyname ^ "_card"), @{attributes [simp]}), [card_UNIV]) ||>>
berghofe@43227:     Local_Theory.note
wenzelm@46463:       ((Binding.name (tyname ^ "_pos"), @{attributes [simp]}), pos_eqs) ||>>
berghofe@43227:     Local_Theory.note
wenzelm@46463:       ((Binding.name (tyname ^ "_val"), @{attributes [simp]}), val_eqs) ||>>
berghofe@43227:     Local_Theory.note
wenzelm@46463:       ((Binding.name (tyname ^ "_first_el"), @{attributes [simp]}), [first_el]) ||>>
berghofe@43227:     Local_Theory.note
wenzelm@46463:       ((Binding.name (tyname ^ "_last_el"), @{attributes [simp]}), [last_el]) |> snd |>
berghofe@43227:     Local_Theory.exit_global
berghofe@41809:   end;
berghofe@41809: 
berghofe@41809: 
berghofe@43267: fun check_no_assoc thy prfx s = case get_type thy prfx s of
berghofe@43227:     NONE => ()
berghofe@43227:   | SOME _ => error ("Cannot associate a type with " ^ s ^
berghofe@43227:       "\nsince it is no record or enumeration type");
berghofe@43227: 
berghofe@43227: fun check_enum [] [] = NONE 
berghofe@43227:   | check_enum els [] = SOME ("has no element(s) " ^ commas els)
berghofe@43227:   | check_enum [] cs = SOME ("has extra element(s) " ^
berghofe@43227:       commas (map (Long_Name.base_name o fst) cs))
berghofe@43227:   | check_enum (el :: els) ((cname, _) :: cs) =
berghofe@43227:       if lcase_eq (el, cname) then check_enum els cs
berghofe@43227:       else SOME ("either has no element " ^ el ^
berghofe@43227:         " or it is at the wrong position");
berghofe@43227: 
berghofe@47596: fun invert_map [] = I
berghofe@47596:   | invert_map cmap =
berghofe@47596:       map (apfst (the o AList.lookup (op =) (map swap cmap)));
berghofe@47596:  
berghofe@43267: fun add_type_def prfx (s, Basic_Type ty) (ids, thy) =
berghofe@43267:       (check_no_assoc thy prfx s;
berghofe@43227:        (ids,
berghofe@43227:         Typedecl.abbrev_global (Binding.name s, [], NoSyn)
berghofe@43267:           (mk_type thy prfx ty) thy |> snd))
berghofe@41809: 
berghofe@43267:   | add_type_def prfx (s, Enum_Type els) ((tab, ctxt), thy) =
berghofe@43227:       let
berghofe@43267:         val (thy', tyname) = (case get_type thy prfx s of
berghofe@43227:             NONE =>
berghofe@43227:               let
berghofe@43227:                 val tyb = Binding.name s;
berghofe@43227:                 val tyname = Sign.full_name thy tyb
berghofe@43227:               in
berghofe@43227:                 (thy |>
wenzelm@46572:                  Datatype.add_datatype {strict = true, quiet = true}
berghofe@47596:                    [((tyb, [], NoSyn),
berghofe@47596:                      map (fn s => (Binding.name s, [], NoSyn)) els)] |> snd |>
berghofe@43227:                  add_enum_type s tyname,
berghofe@43227:                  tyname)
berghofe@43227:               end
berghofe@47596:           | SOME (T as Type (tyname, []), cmap) =>
wenzelm@46777:               (case Datatype.get_constrs thy tyname of
berghofe@43227:                  NONE => assoc_ty_err thy T s "is not a datatype"
berghofe@43267:                | SOME cs =>
berghofe@47596:                    let val (prfx', _) = strip_prfx s
berghofe@43267:                    in
berghofe@47596:                      case check_enum (map (unprefix_pfun prfx') els)
berghofe@47596:                          (invert_map cmap cs) of
berghofe@43267:                        NONE => (thy, tyname)
berghofe@43267:                      | SOME msg => assoc_ty_err thy T s msg
berghofe@47438:                    end)
berghofe@47596:           | SOME (T, _) => assoc_ty_err thy T s "is not a datatype");
wenzelm@46777:         val cs = map Const (the (Datatype.get_constrs thy' tyname));
berghofe@43227:       in
berghofe@43227:         ((fold (Symtab.update_new o apsnd (rpair s)) (els ~~ cs) tab,
berghofe@43227:           fold Name.declare els ctxt),
berghofe@43227:          thy')
berghofe@43227:       end
berghofe@41809: 
berghofe@43267:   | add_type_def prfx (s, Array_Type (argtys, resty)) (ids, thy) =
berghofe@43267:       (check_no_assoc thy prfx s;
berghofe@43227:        (ids,
berghofe@43227:         Typedecl.abbrev_global (Binding.name s, [], NoSyn)
berghofe@43267:           (foldr1 HOLogic.mk_prodT (map (mk_type thy prfx) argtys) -->
berghofe@43267:              mk_type thy prfx resty) thy |> snd))
berghofe@41809: 
berghofe@43267:   | add_type_def prfx (s, Record_Type fldtys) (ids, thy) =
berghofe@41809:       (ids,
berghofe@43227:        let val fldTs = maps (fn (flds, ty) =>
berghofe@43267:          map (rpair (mk_type thy prfx ty)) flds) fldtys
berghofe@43267:        in case get_type thy prfx s of
berghofe@43227:            NONE =>
wenzelm@45524:              Record.add_record ([], Binding.name s) NONE
berghofe@43227:                (map (fn (fld, T) => (Binding.name fld, T, NoSyn)) fldTs) thy
berghofe@47596:          | SOME (rT, cmap) =>
berghofe@43227:              (case get_record_info thy rT of
berghofe@43227:                 NONE => assoc_ty_err thy rT s "is not a record type"
berghofe@43227:               | SOME {fields, ...} =>
berghofe@47596:                   let val fields' = invert_map cmap fields
berghofe@47596:                   in
berghofe@47596:                     (case subtract (lcase_eq o pairself fst) fldTs fields' of
berghofe@47596:                        [] => ()
berghofe@47596:                      | flds => assoc_ty_err thy rT s ("has extra field(s) " ^
berghofe@47596:                          commas (map (Long_Name.base_name o fst) flds));
berghofe@47596:                      map (fn (fld, T) =>
berghofe@47596:                        case AList.lookup lcase_eq fields' fld of
berghofe@47596:                          NONE => assoc_ty_err thy rT s ("has no field " ^ fld)
berghofe@47596:                        | SOME U => T = U orelse assoc_ty_err thy rT s
berghofe@47596:                            ("has field " ^
berghofe@47596:                             fld ^ " whose type\n" ^
berghofe@47596:                             Syntax.string_of_typ_global thy U ^
berghofe@47596:                             "\ndoes not match declared type\n" ^
berghofe@47596:                             Syntax.string_of_typ_global thy T)) fldTs;
berghofe@47596:                      thy)
berghofe@47596:                   end)
berghofe@43227:        end)
berghofe@41809: 
berghofe@43267:   | add_type_def prfx (s, Pending_Type) (ids, thy) =
berghofe@44901:       (ids,
berghofe@44901:        case get_type thy prfx s of
berghofe@44901:          SOME _ => thy
berghofe@44901:        | NONE => Typedecl.typedecl_global
berghofe@44901:            (Binding.name s, [], NoSyn) thy |> snd);
berghofe@41809: 
berghofe@41809: 
berghofe@43267: fun term_of_expr thy prfx types pfuns =
berghofe@41809:   let
berghofe@41809:     fun tm_of vs (Funct ("->", [e, e'])) =
berghofe@41809:           (HOLogic.mk_imp (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("<->", [e, e'])) =
berghofe@41809:           (HOLogic.mk_eq (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("or", [e, e'])) =
berghofe@41809:           (HOLogic.mk_disj (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("and", [e, e'])) =
berghofe@41809:           (HOLogic.mk_conj (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("not", [e])) =
berghofe@41809:           (HOLogic.mk_not (fst (tm_of vs e)), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("=", [e, e'])) =
berghofe@41809:           (HOLogic.mk_eq (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("<>", [e, e'])) = (HOLogic.mk_not
berghofe@41809:           (HOLogic.mk_eq (fst (tm_of vs e), fst (tm_of vs e'))), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("<", [e, e'])) = (HOLogic.mk_binrel @{const_name less}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct (">", [e, e'])) = (HOLogic.mk_binrel @{const_name less}
berghofe@41809:           (fst (tm_of vs e'), fst (tm_of vs e)), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("<=", [e, e'])) = (HOLogic.mk_binrel @{const_name less_eq}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct (">=", [e, e'])) = (HOLogic.mk_binrel @{const_name less_eq}
berghofe@41809:           (fst (tm_of vs e'), fst (tm_of vs e)), booleanN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("+", [e, e'])) = (HOLogic.mk_binop @{const_name plus}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("-", [e, e'])) = (HOLogic.mk_binop @{const_name minus}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("*", [e, e'])) = (HOLogic.mk_binop @{const_name times}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("/", [e, e'])) = (HOLogic.mk_binop @{const_name divide}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("div", [e, e'])) = (HOLogic.mk_binop @{const_name sdiv}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41883:       | tm_of vs (Funct ("mod", [e, e'])) = (HOLogic.mk_binop @{const_name mod}
berghofe@41809:           (fst (tm_of vs e), fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("-", [e])) =
berghofe@41809:           (mk_unop @{const_name uminus} (fst (tm_of vs e)), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct ("**", [e, e'])) =
berghofe@41809:           (Const (@{const_name power}, HOLogic.intT --> HOLogic.natT -->
berghofe@41809:              HOLogic.intT) $ fst (tm_of vs e) $
berghofe@41809:                (@{const nat} $ fst (tm_of vs e')), integerN)
berghofe@41809: 
berghofe@41809:       | tm_of (tab, _) (Ident s) =
berghofe@41809:           (case Symtab.lookup tab s of
berghofe@41809:              SOME t_ty => t_ty
berghofe@43370:            | NONE => (case lookup_prfx prfx pfuns s of
berghofe@43370:                SOME (SOME ([], resty), t) => (t, resty)
berghofe@43370:              | _ => error ("Undeclared identifier " ^ s)))
berghofe@41809: 
berghofe@41809:       | tm_of _ (Number i) = (HOLogic.mk_number HOLogic.intT i, integerN)
berghofe@41809: 
berghofe@41809:       | tm_of vs (Quantifier (s, xs, ty, e)) =
berghofe@41809:           let
berghofe@43267:             val (ys, vs') = mk_variables thy prfx xs ty vs;
berghofe@41809:             val q = (case s of
berghofe@41809:                 "for_all" => HOLogic.mk_all
berghofe@41809:               | "for_some" => HOLogic.mk_exists)
berghofe@41809:           in
berghofe@41809:             (fold_rev (fn Free (x, T) => fn t => q (x, T, t))
berghofe@41809:                ys (fst (tm_of vs' e)),
berghofe@41809:              booleanN)
berghofe@41809:           end
berghofe@41809: 
berghofe@41809:       | tm_of vs (Funct (s, es)) =
berghofe@41809: 
berghofe@41809:           (* record field selection *)
berghofe@41809:           (case try (unprefix "fld_") s of
berghofe@41809:              SOME fname => (case es of
berghofe@41809:                [e] =>
berghofe@43227:                  let
berghofe@43227:                    val (t, rcdty) = tm_of vs e;
berghofe@47596:                    val (rT, cmap) = mk_type' thy prfx rcdty
berghofe@43227:                  in case (get_record_info thy rT, lookup types rcdty) of
berghofe@43227:                      (SOME {fields, ...}, SOME (Record_Type fldtys)) =>
berghofe@47596:                        (case (find_field cmap fname fields,
berghofe@43227:                             find_field' fname fldtys) of
berghofe@43227:                           (SOME (fname', fT), SOME fldty) =>
berghofe@43227:                             (Const (fname', rT --> fT) $ t, fldty)
berghofe@43227:                         | _ => error ("Record " ^ rcdty ^
berghofe@41809:                             " has no field named " ^ fname))
berghofe@41809:                    | _ => error (rcdty ^ " is not a record type")
berghofe@41809:                  end
berghofe@41809:              | _ => error ("Function " ^ s ^ " expects one argument"))
berghofe@41809:            | NONE =>
berghofe@41809: 
berghofe@41809:           (* record field update *)
berghofe@41809:           (case try (unprefix "upf_") s of
berghofe@41809:              SOME fname => (case es of
berghofe@41809:                [e, e'] =>
berghofe@41809:                  let
berghofe@41809:                    val (t, rcdty) = tm_of vs e;
berghofe@47596:                    val (rT, cmap) = mk_type' thy prfx rcdty;
berghofe@41809:                    val (u, fldty) = tm_of vs e';
berghofe@43267:                    val fT = mk_type thy prfx fldty
berghofe@43227:                  in case get_record_info thy rT of
berghofe@43227:                      SOME {fields, ...} =>
berghofe@47596:                        (case find_field cmap fname fields of
berghofe@43227:                           SOME (fname', fU) =>
berghofe@43227:                             if fT = fU then
berghofe@43227:                               (Const (fname' ^ "_update",
berghofe@41809:                                  (fT --> fT) --> rT --> rT) $
berghofe@41809:                                    Abs ("x", fT, u) $ t,
berghofe@41809:                                rcdty)
berghofe@43227:                             else error ("Type\n" ^
berghofe@43227:                               Syntax.string_of_typ_global thy fT ^
berghofe@43227:                               "\ndoes not match type\n" ^
berghofe@43227:                               Syntax.string_of_typ_global thy fU ^
berghofe@43227:                               "\nof field " ^ fname)
berghofe@41809:                         | NONE => error ("Record " ^ rcdty ^
berghofe@41809:                             " has no field named " ^ fname))
berghofe@41809:                    | _ => error (rcdty ^ " is not a record type")
berghofe@41809:                  end
berghofe@41809:              | _ => error ("Function " ^ s ^ " expects two arguments"))
berghofe@41809:            | NONE =>
berghofe@41809: 
berghofe@41809:           (* enumeration type to integer *)
berghofe@41809:           (case try (unsuffix "__pos") s of
berghofe@41809:              SOME tyname => (case es of
berghofe@41809:                [e] => (Const (@{const_name pos},
berghofe@43267:                    mk_type thy prfx tyname --> HOLogic.intT) $ fst (tm_of vs e),
berghofe@43267:                  integerN)
berghofe@41809:              | _ => error ("Function " ^ s ^ " expects one argument"))
berghofe@41809:            | NONE =>
berghofe@41809: 
berghofe@41809:           (* integer to enumeration type *)
berghofe@41809:           (case try (unsuffix "__val") s of
berghofe@41809:              SOME tyname => (case es of
berghofe@41809:                [e] => (Const (@{const_name val},
berghofe@43267:                    HOLogic.intT --> mk_type thy prfx tyname) $ fst (tm_of vs e),
berghofe@43267:                  tyname)
berghofe@41809:              | _ => error ("Function " ^ s ^ " expects one argument"))
berghofe@41809:            | NONE =>
berghofe@41809: 
berghofe@41809:           (* successor / predecessor of enumeration type element *)
berghofe@41809:           if s = "succ" orelse s = "pred" then (case es of
berghofe@41809:               [e] =>
berghofe@41809:                 let
berghofe@41809:                   val (t, tyname) = tm_of vs e;
berghofe@43267:                   val T = mk_type thy prfx tyname
berghofe@41809:                 in (Const
berghofe@41809:                   (if s = "succ" then @{const_name succ}
berghofe@41809:                    else @{const_name pred}, T --> T) $ t, tyname)
berghofe@41809:                 end
berghofe@41809:             | _ => error ("Function " ^ s ^ " expects one argument"))
berghofe@41809: 
berghofe@41809:           (* user-defined proof function *)
berghofe@41809:           else
berghofe@43267:             (case lookup_prfx prfx pfuns s of
berghofe@41809:                SOME (SOME (_, resty), t) =>
berghofe@41809:                  (list_comb (t, map (fst o tm_of vs) es), resty)
berghofe@41809:              | _ => error ("Undeclared proof function " ^ s))))))
berghofe@41809: 
berghofe@41809:       | tm_of vs (Element (e, es)) =
berghofe@41809:           let val (t, ty) = tm_of vs e
berghofe@41809:           in case lookup types ty of
berghofe@41809:               SOME (Array_Type (_, elty)) =>
berghofe@41809:                 (t $ foldr1 HOLogic.mk_prod (map (fst o tm_of vs) es), elty)
berghofe@41809:             | _ => error (ty ^ " is not an array type")
berghofe@41809:           end
berghofe@41809: 
berghofe@41809:       | tm_of vs (Update (e, es, e')) =
berghofe@41809:           let val (t, ty) = tm_of vs e
berghofe@41809:           in case lookup types ty of
berghofe@41809:               SOME (Array_Type (idxtys, elty)) =>
berghofe@41809:                 let
berghofe@43267:                   val T = foldr1 HOLogic.mk_prodT
berghofe@43267:                     (map (mk_type thy prfx) idxtys);
berghofe@43267:                   val U = mk_type thy prfx elty;
berghofe@41809:                   val fT = T --> U
berghofe@41809:                 in
berghofe@41809:                   (Const (@{const_name fun_upd}, fT --> T --> U --> fT) $
berghofe@41809:                      t $ foldr1 HOLogic.mk_prod (map (fst o tm_of vs) es) $
berghofe@41809:                        fst (tm_of vs e'),
berghofe@41809:                    ty)
berghofe@41809:                 end
berghofe@41809:             | _ => error (ty ^ " is not an array type")
berghofe@41809:           end
berghofe@41809: 
berghofe@41809:       | tm_of vs (Record (s, flds)) =
berghofe@43227:           let
berghofe@47596:             val (T, cmap) = mk_type' thy prfx s;
berghofe@43227:             val {extension = (ext_name, _), fields, ...} =
berghofe@43227:               (case get_record_info thy T of
berghofe@43227:                  NONE => error (s ^ " is not a record type")
berghofe@43227:                | SOME info => info);
berghofe@43227:             val flds' = map (apsnd (tm_of vs)) flds;
berghofe@47596:             val fnames = fields |> invert_map cmap |>
berghofe@47596:               map (Long_Name.base_name o fst);
berghofe@43227:             val fnames' = map fst flds;
berghofe@43227:             val (fvals, ftys) = split_list (map (fn s' =>
berghofe@43227:               case AList.lookup lcase_eq flds' s' of
berghofe@43227:                 SOME fval_ty => fval_ty
berghofe@43227:               | NONE => error ("Field " ^ s' ^ " missing in record " ^ s))
berghofe@43227:                   fnames);
berghofe@43227:             val _ = (case subtract lcase_eq fnames fnames' of
berghofe@43227:                 [] => ()
berghofe@43227:               | xs => error ("Extra field(s) " ^ commas xs ^
berghofe@43227:                   " in record " ^ s));
berghofe@43227:             val _ = (case duplicates (op =) fnames' of
berghofe@43227:                 [] => ()
berghofe@43227:               | xs => error ("Duplicate field(s) " ^ commas xs ^
berghofe@43227:                   " in record " ^ s))
berghofe@43227:           in
berghofe@43227:             (list_comb
berghofe@43227:                (Const (ext_name,
berghofe@43267:                   map (mk_type thy prfx) ftys @ [HOLogic.unitT] ---> T),
berghofe@43227:                 fvals @ [HOLogic.unit]),
berghofe@43227:              s)
berghofe@43227:           end
berghofe@41809: 
berghofe@41809:       | tm_of vs (Array (s, default, assocs)) =
berghofe@41809:           (case lookup types s of
berghofe@41809:              SOME (Array_Type (idxtys, elty)) =>
berghofe@41809:                let
berghofe@43267:                  val Ts = map (mk_type thy prfx) idxtys;
berghofe@41809:                  val T = foldr1 HOLogic.mk_prodT Ts;
berghofe@43267:                  val U = mk_type thy prfx elty;
berghofe@41809:                  fun mk_idx' T (e, NONE) = HOLogic.mk_set T [fst (tm_of vs e)]
berghofe@41809:                    | mk_idx' T (e, SOME e') = Const (@{const_name atLeastAtMost},
berghofe@41809:                        T --> T --> HOLogic.mk_setT T) $
berghofe@41809:                          fst (tm_of vs e) $ fst (tm_of vs e');
berghofe@41809:                  fun mk_idx idx =
berghofe@41809:                    if length Ts <> length idx then
berghofe@41809:                      error ("Arity mismatch in construction of array " ^ s)
berghofe@41809:                    else foldr1 mk_times (map2 mk_idx' Ts idx);
berghofe@41809:                  fun mk_upd (idxs, e) t =
berghofe@41809:                    if length idxs = 1 andalso forall (is_none o snd) (hd idxs)
berghofe@41809:                    then
berghofe@41809:                      Const (@{const_name fun_upd}, (T --> U) -->
berghofe@41809:                          T --> U --> T --> U) $ t $
berghofe@41809:                        foldl1 HOLogic.mk_prod
berghofe@41809:                          (map (fst o tm_of vs o fst) (hd idxs)) $
berghofe@41809:                        fst (tm_of vs e)
berghofe@41809:                    else
berghofe@41809:                      Const (@{const_name fun_upds}, (T --> U) -->
berghofe@41809:                          HOLogic.mk_setT T --> U --> T --> U) $ t $
berghofe@41809:                        foldl1 (HOLogic.mk_binop @{const_name sup})
berghofe@41809:                          (map mk_idx idxs) $
berghofe@41809:                        fst (tm_of vs e)
berghofe@41809:                in
berghofe@41809:                  (fold mk_upd assocs
berghofe@41809:                     (case default of
berghofe@41809:                        SOME e => Abs ("x", T, fst (tm_of vs e))
berghofe@41809:                      | NONE => Const (@{const_name undefined}, T --> U)),
berghofe@41809:                   s)
berghofe@41809:                end
berghofe@41809:            | _ => error (s ^ " is not an array type"))
berghofe@41809: 
berghofe@41809:   in tm_of end;
berghofe@41809: 
berghofe@41809: 
berghofe@43267: fun term_of_rule thy prfx types pfuns ids rule =
berghofe@43267:   let val tm_of = fst o term_of_expr thy prfx types pfuns ids
berghofe@41809:   in case rule of
berghofe@41809:       Inference_Rule (es, e) => Logic.list_implies
berghofe@41809:         (map (HOLogic.mk_Trueprop o tm_of) es, HOLogic.mk_Trueprop (tm_of e))
berghofe@41809:     | Substitution_Rule (es, e, e') => Logic.list_implies
berghofe@41809:         (map (HOLogic.mk_Trueprop o tm_of) es,
berghofe@41809:          HOLogic.mk_Trueprop (HOLogic.mk_eq (tm_of e, tm_of e')))
berghofe@41809:   end;
berghofe@41809: 
berghofe@41809: 
berghofe@41809: val builtin = Symtab.make (map (rpair ())
berghofe@41809:   ["->", "<->", "or", "and", "not", "=", "<>", "<", ">", "<=", ">=",
berghofe@41809:    "+", "-", "*", "/", "div", "mod", "**"]);
berghofe@41809: 
berghofe@41809: fun complex_expr (Number _) = false
berghofe@41809:   | complex_expr (Ident _) = false 
berghofe@41809:   | complex_expr (Funct (s, es)) =
berghofe@41809:       not (Symtab.defined builtin s) orelse exists complex_expr es
berghofe@41809:   | complex_expr (Quantifier (_, _, _, e)) = complex_expr e
berghofe@41809:   | complex_expr _ = true;
berghofe@41809: 
berghofe@41809: fun complex_rule (Inference_Rule (es, e)) =
berghofe@41809:       complex_expr e orelse exists complex_expr es
berghofe@41809:   | complex_rule (Substitution_Rule (es, e, e')) =
berghofe@41809:       complex_expr e orelse complex_expr e' orelse
berghofe@41809:       exists complex_expr es;
berghofe@41809: 
berghofe@41809: val is_pfun =
berghofe@41809:   Symtab.defined builtin orf
berghofe@41809:   can (unprefix "fld_") orf can (unprefix "upf_") orf
berghofe@41809:   can (unsuffix "__pos") orf can (unsuffix "__val") orf
berghofe@41809:   equal "succ" orf equal "pred";
berghofe@41809: 
berghofe@41809: fun fold_opt f = the_default I o Option.map f;
berghofe@41809: fun fold_pair f g (x, y) = f x #> g y;
berghofe@41809: 
berghofe@41809: fun fold_expr f g (Funct (s, es)) = f s #> fold (fold_expr f g) es
berghofe@41809:   | fold_expr f g (Ident s) = g s
berghofe@41809:   | fold_expr f g (Number _) = I
berghofe@41809:   | fold_expr f g (Quantifier (_, _, _, e)) = fold_expr f g e
berghofe@41809:   | fold_expr f g (Element (e, es)) =
berghofe@41809:       fold_expr f g e #> fold (fold_expr f g) es
berghofe@41809:   | fold_expr f g (Update (e, es, e')) =
berghofe@41809:       fold_expr f g e #> fold (fold_expr f g) es #> fold_expr f g e'
berghofe@41809:   | fold_expr f g (Record (_, flds)) = fold (fold_expr f g o snd) flds
berghofe@41809:   | fold_expr f g (Array (_, default, assocs)) =
berghofe@41809:       fold_opt (fold_expr f g) default #>
berghofe@41809:       fold (fold_pair
berghofe@41809:         (fold (fold (fold_pair
berghofe@41809:           (fold_expr f g) (fold_opt (fold_expr f g)))))
berghofe@41809:         (fold_expr f g)) assocs;
berghofe@41809: 
berghofe@43370: fun add_expr_pfuns funs = fold_expr
berghofe@43370:   (fn s => if is_pfun s then I else insert (op =) s)
berghofe@43370:   (fn s => if is_none (lookup funs s) then I else insert (op =) s);
berghofe@41809: 
berghofe@41809: val add_expr_idents = fold_expr (K I) (insert (op =));
berghofe@41809: 
berghofe@43267: fun pfun_type thy prfx (argtys, resty) =
berghofe@43267:   map (mk_type thy prfx) argtys ---> mk_type thy prfx resty;
berghofe@41809: 
berghofe@43267: fun check_pfun_type thy prfx s t optty1 optty2 =
berghofe@41809:   let
berghofe@41809:     val T = fastype_of t;
berghofe@41809:     fun check ty =
berghofe@43267:       let val U = pfun_type thy prfx ty
berghofe@41809:       in
berghofe@41809:         T = U orelse
berghofe@41809:         error ("Type\n" ^
berghofe@41809:           Syntax.string_of_typ_global thy T ^
berghofe@41809:           "\nof function " ^
berghofe@41809:           Syntax.string_of_term_global thy t ^
berghofe@41809:           " associated with proof function " ^ s ^
berghofe@41809:           "\ndoes not match declared type\n" ^
berghofe@41809:           Syntax.string_of_typ_global thy U)
berghofe@41809:       end
berghofe@41809:   in (Option.map check optty1; Option.map check optty2; ()) end;
berghofe@41809: 
berghofe@41809: fun upd_option x y = if is_some x then x else y;
berghofe@41809: 
berghofe@43267: fun check_pfuns_types thy prfx funs =
berghofe@41809:   Symtab.map (fn s => fn (optty, t) =>
berghofe@47438:    let val optty' = lookup funs (unprefix_pfun prfx s)
berghofe@41809:    in
berghofe@43267:      (check_pfun_type thy prfx s t optty optty';
berghofe@41809:       (NONE |> upd_option optty |> upd_option optty', t))
berghofe@41809:    end);
berghofe@41809: 
berghofe@41809: 
berghofe@41809: (** the VC store **)
berghofe@41809: 
berghofe@49182: fun pp_vcs msg vcs = Pretty.big_list msg (map (Pretty.str o fst) vcs);
berghofe@49182: 
berghofe@49182: fun pp_open_vcs [] = Pretty.str "All verification conditions have been proved."
berghofe@49182:   | pp_open_vcs vcs = pp_vcs
berghofe@49182:       "The following verification conditions remain to be proved:" vcs;
berghofe@49182: 
berghofe@49182: fun partition_vcs vcs = VCtab.fold_rev
berghofe@49182:   (fn (name, (trace, SOME thms, ps, cs)) =>
berghofe@49182:         apfst (cons (name, (trace, thms, ps, cs)))
berghofe@49182:     | (name, (trace, NONE, ps, cs)) =>
berghofe@49182:         apsnd (cons (name, (trace, ps, cs))))
berghofe@49182:   vcs ([], []);
berghofe@49182: 
berghofe@49182: fun insert_break prt = Pretty.blk (0, [Pretty.fbrk, prt]);
berghofe@49182: 
berghofe@49182: fun print_open_vcs f vcs =
berghofe@49182:   (Pretty.writeln (f (pp_open_vcs (snd (partition_vcs vcs)))); vcs);
berghofe@41809: 
berghofe@47438: fun set_env ctxt defs types funs ids vcs path prefix thy = VCs.map (fn
berghofe@43227:     {pfuns, type_map, env = NONE} =>
berghofe@47438:       {pfuns = pfuns,
berghofe@43227:        type_map = type_map,
berghofe@47438:        env = SOME
berghofe@47438:          {ctxt = ctxt, defs = defs, types = types, funs = funs,
berghofe@47438:           pfuns = check_pfuns_types thy prefix funs pfuns,
berghofe@49182:           ids = ids, proving = false, vcs = print_open_vcs I vcs, path = path,
berghofe@47438:           prefix = prefix}}
berghofe@41809:   | _ => err_unfinished ()) thy;
berghofe@41809: 
berghofe@41809: fun mk_pat s = (case Int.fromString s of
berghofe@41809:     SOME i => [HOLogic.mk_Trueprop (Var (("C", i), HOLogic.boolT))]
berghofe@41809:   | NONE => error ("Bad conclusion identifier: C" ^ s));
berghofe@41809: 
berghofe@49182: fun mk_vc thy prfx types pfuns ids name_concl (tr, proved, ps, cs) =
berghofe@41809:   let val prop_of =
berghofe@43267:     HOLogic.mk_Trueprop o fst o term_of_expr thy prfx types pfuns ids
berghofe@41809:   in
berghofe@41809:     (tr, proved,
berghofe@41809:      Element.Assumes (map (fn (s', e) =>
berghofe@41809:        ((Binding.name ("H" ^ s'), []), [(prop_of e, [])])) ps),
berghofe@41809:      Element.Shows (map (fn (s', e) =>
berghofe@49182:        (if name_concl then (Binding.name ("C" ^ s'), [])
berghofe@49182:         else Attrib.empty_binding,
berghofe@49182:         [(prop_of e, mk_pat s')])) cs))
berghofe@41809:   end;
berghofe@41809: 
berghofe@41809: fun fold_vcs f vcs =
berghofe@41809:   VCtab.fold (fn (_, (_, _, ps, cs)) => fold f ps #> fold f cs) vcs;
berghofe@41809: 
berghofe@43370: fun pfuns_of_vcs prfx funs pfuns vcs =
berghofe@43370:   fold_vcs (add_expr_pfuns funs o snd) vcs [] |>
berghofe@43267:   filter (is_none o lookup_prfx prfx pfuns);
berghofe@41809: 
berghofe@43267: fun declare_missing_pfuns thy prfx funs pfuns vcs (tab, ctxt) =
berghofe@41809:   let
berghofe@41809:     val (fs, (tys, Ts)) =
berghofe@43370:       pfuns_of_vcs prfx funs pfuns vcs |>
berghofe@41809:       map_filter (fn s => lookup funs s |>
berghofe@43267:         Option.map (fn ty => (s, (SOME ty, pfun_type thy prfx ty)))) |>
berghofe@41809:       split_list ||> split_list;
wenzelm@44208:     val (fs', ctxt') = fold_map Name.variant fs ctxt
berghofe@41809:   in
berghofe@41809:     (fold Symtab.update_new (fs ~~ (tys ~~ map Free (fs' ~~ Ts))) pfuns,
berghofe@41809:      Element.Fixes (map2 (fn s => fn T =>
berghofe@41809:        (Binding.name s, SOME T, NoSyn)) fs' Ts),
berghofe@41809:      (tab, ctxt'))
berghofe@41809:   end;
berghofe@41809: 
berghofe@47438: fun map_pfuns f {pfuns, type_map, env} =
berghofe@47438:   {pfuns = f pfuns, type_map = type_map, env = env}
berghofe@47438: 
berghofe@47438: fun map_pfuns_env f {pfuns, type_map,
berghofe@47438:       env = SOME {ctxt, defs, types, funs, pfuns = pfuns_env,
berghofe@47438:         ids, proving, vcs, path, prefix}} =
berghofe@47438:   if proving then err_unfinished ()
berghofe@47438:   else
berghofe@47438:     {pfuns = pfuns, type_map = type_map,
berghofe@47438:      env = SOME {ctxt = ctxt, defs = defs, types = types, funs = funs,
berghofe@47438:        pfuns = f pfuns_env, ids = ids, proving = false, vcs = vcs,
berghofe@47438:        path = path, prefix = prefix}};
berghofe@47438: 
berghofe@41809: fun add_proof_fun prep (s, (optty, raw_t)) thy =
berghofe@47438:   VCs.map (fn data as {env, ...} =>
berghofe@47438:     let
berghofe@47438:       val (optty', prfx, map_pf) = (case env of
berghofe@47438:           SOME {funs, prefix, ...} =>
berghofe@47438:             (lookup funs (unprefix_pfun prefix s),
berghofe@47438:              prefix, map_pfuns_env)
berghofe@47438:         | NONE => (NONE, "", map_pfuns));
berghofe@47438:       val optty'' = NONE |> upd_option optty |> upd_option optty';
berghofe@47438:       val t = prep (Option.map (pfun_type thy prfx) optty'') raw_t;
berghofe@47438:       val _ = (case fold_aterms (fn u =>
berghofe@47438:           if is_Var u orelse is_Free u then insert (op =) u else I) t [] of
berghofe@47438:           [] => ()
berghofe@47438:         | ts => error ("Term\n" ^ Syntax.string_of_term_global thy t ^
berghofe@47438:             "\nto be associated with proof function " ^ s ^
berghofe@47438:             " contains free variable(s) " ^
berghofe@47438:             commas (map (Syntax.string_of_term_global thy) ts)));
berghofe@47438:     in
berghofe@47438:       (check_pfun_type thy prfx s t optty optty';
berghofe@47438:        if is_some optty'' orelse is_none env then
berghofe@47438:          map_pf (Symtab.update_new (s, (optty'', t))) data
berghofe@47438:            handle Symtab.DUP _ => error ("Proof function " ^ s ^
berghofe@47438:              " already associated with function")
berghofe@47438:        else error ("Undeclared proof function " ^ s))
berghofe@47438:     end) thy;
berghofe@41809: 
berghofe@47596: fun check_mapping _ _ [] _ = ()
berghofe@47596:   | check_mapping err s cmap cs =
berghofe@47596:       (case duplicates (op = o pairself fst) cmap of
berghofe@47596:          [] => (case duplicates (op = o pairself snd) cmap of
berghofe@47596:              [] => (case subtract (op = o apsnd snd) cs cmap of
berghofe@47596:                  [] => (case subtract (op = o apfst snd) cmap cs of
berghofe@47596:                      [] => ()
berghofe@47596:                    | zs => err ("has extra " ^ s ^ "(s) " ^ commas zs))
berghofe@47596:                | zs => err ("does not have " ^ s ^ "(s) " ^
berghofe@47596:                    commas (map snd zs)))
berghofe@47596:            | zs => error ("Several SPARK names are mapped to " ^
berghofe@47596:                commas (map snd zs)))
berghofe@47596:        | zs => error ("The SPARK names " ^ commas (map fst zs) ^
berghofe@47596:            " are mapped to more than one name"));
berghofe@47596: 
berghofe@47596: fun add_type (s, (T as Type (tyname, Ts), cmap)) thy =
berghofe@47596:       let val cmap' = map (apsnd (Sign.intern_const thy)) cmap
berghofe@47596:       in
berghofe@47596:         thy |>
berghofe@47596:         VCs.map (fn
berghofe@47596:             {env = SOME _, ...} => err_unfinished ()
berghofe@47596:           | {pfuns, type_map, env} =>
berghofe@47596:               {pfuns = pfuns,
berghofe@47596:                type_map = Symtab.update_new (s, (T, cmap')) type_map,
berghofe@47596:                env = env}
berghofe@47596:                 handle Symtab.DUP _ => error ("SPARK type " ^ s ^
berghofe@47596:                   " already associated with type")) |>
berghofe@47596:         (fn thy' =>
berghofe@47596:            case Datatype.get_constrs thy' tyname of
berghofe@47596:              NONE => (case get_record_info thy' T of
berghofe@47596:                NONE => thy'
berghofe@47596:              | SOME {fields, ...} =>
berghofe@47596:                  (check_mapping (assoc_ty_err thy' T s) "field"
berghofe@47596:                     cmap' (map fst fields);
berghofe@47596:                   thy'))
berghofe@47596:            | SOME cs =>
berghofe@47596:                if null Ts then
berghofe@47596:                  (map
berghofe@47596:                     (fn (_, Type (_, [])) => ()
berghofe@47596:                       | (cname, _) => assoc_ty_err thy' T s
berghofe@47596:                           ("has illegal constructor " ^
berghofe@47596:                            Long_Name.base_name cname)) cs;
berghofe@47596:                   check_mapping (assoc_ty_err thy' T s) "constructor"
berghofe@47596:                     cmap' (map fst cs);
berghofe@47596:                   add_enum_type s tyname thy')
berghofe@47596:                else assoc_ty_err thy' T s "is illegal")
berghofe@47596:       end
berghofe@47596:   | add_type (s, (T, _)) thy = assoc_ty_err thy T s "is illegal";
berghofe@43227: 
berghofe@41809: val is_closed = is_none o #env o VCs.get;
berghofe@41809: 
berghofe@49182: fun lookup_vc thy name_concl name =
berghofe@41809:   (case VCs.get thy of
berghofe@47438:     {env = SOME {vcs, types, funs, pfuns, ids, ctxt, prefix, ...}, ...} =>
berghofe@41809:       (case VCtab.lookup vcs name of
berghofe@43267:          SOME vc =>
berghofe@41809:            let val (pfuns', ctxt', ids') =
berghofe@43267:              declare_missing_pfuns thy prefix funs pfuns vcs ids
berghofe@49182:            in
berghofe@49182:              SOME (ctxt @ [ctxt'],
berghofe@49182:                mk_vc thy prefix types pfuns' ids' name_concl vc)
berghofe@49182:            end
berghofe@41809:        | NONE => NONE)
berghofe@41809:   | _ => NONE);
berghofe@41809: 
berghofe@49182: fun get_vcs thy name_concl = (case VCs.get thy of
berghofe@47438:     {env = SOME {vcs, types, funs, pfuns, ids, ctxt, defs, prefix, ...}, ...} =>
berghofe@41809:       let val (pfuns', ctxt', ids') =
berghofe@43267:         declare_missing_pfuns thy prefix funs pfuns vcs ids
berghofe@41809:       in
berghofe@41809:         (ctxt @ [ctxt'], defs,
berghofe@41809:          VCtab.dest vcs |>
berghofe@49182:          map (apsnd (mk_vc thy prefix types pfuns' ids' name_concl)))
berghofe@41809:       end
berghofe@41809:   | _ => ([], [], []));
berghofe@41809: 
berghofe@42767: fun mark_proved name thms = VCs.map (fn
berghofe@43227:     {pfuns, type_map,
berghofe@47438:      env = SOME {ctxt, defs, types, funs, pfuns = pfuns_env,
berghofe@47438:         ids, vcs, path, prefix, ...}} =>
berghofe@41809:       {pfuns = pfuns,
berghofe@43227:        type_map = type_map,
berghofe@41809:        env = SOME {ctxt = ctxt, defs = defs,
berghofe@47438:          types = types, funs = funs, pfuns = pfuns_env,
berghofe@47438:          ids = ids,
berghofe@41809:          proving = true,
berghofe@49182:          vcs = print_open_vcs insert_break (VCtab.map_entry name
berghofe@49182:            (fn (trace, _, ps, cs) => (trace, SOME thms, ps, cs)) vcs),
berghofe@43267:          path = path,
berghofe@43267:          prefix = prefix}}
berghofe@41809:   | x => x);
berghofe@41809: 
berghofe@49182: fun close incomplete thy =
berghofe@43227:   thy |>
berghofe@43227:   VCs.map (fn
berghofe@43227:       {pfuns, type_map, env = SOME {vcs, path, ...}} =>
berghofe@49182:         let
berghofe@49182:           val (proved, unproved) = partition_vcs vcs;
berghofe@49182:           val _ = Thm.join_proofs (maps (#2 o snd) proved);
berghofe@49182:           val (proved', proved'') = List.partition (fn (_, (_, thms, _, _)) =>
berghofe@49182:             exists (#oracle o Thm.status_of) thms) proved
berghofe@49182:         in
berghofe@49182:           (if null unproved then ()
berghofe@49182:            else (if incomplete then warning else error)
berghofe@49182:              (Pretty.string_of (pp_open_vcs unproved));
berghofe@49182:            if null proved' then ()
berghofe@49182:            else warning (Pretty.string_of (pp_vcs
berghofe@49182:              "The following VCs are not marked as proved \
berghofe@49182:              \because their proofs contain oracles:" proved'));
berghofe@49182:            File.write (Path.ext "prv" path)
berghofe@49182:              (implode (map (fn (s, _) => snd (strip_number s) ^
berghofe@49182:                 " -- proved by " ^ Distribution.version ^ "\n") proved''));
berghofe@49182:            {pfuns = pfuns, type_map = type_map, env = NONE})
berghofe@49182:         end
berghofe@43227:     | _ => error "No SPARK environment is currently open") |>
berghofe@43227:   Sign.parent_path;
berghofe@41809: 
berghofe@41809: 
berghofe@41809: (** set up verification conditions **)
berghofe@41809: 
berghofe@41809: fun partition_opt f =
berghofe@41809:   let
berghofe@41809:     fun part ys zs [] = (rev ys, rev zs)
berghofe@41809:       | part ys zs (x :: xs) = (case f x of
berghofe@41809:             SOME y => part (y :: ys) zs xs
berghofe@41809:           | NONE => part ys (x :: zs) xs)
berghofe@41809:   in part [] [] end;
berghofe@41809: 
berghofe@41809: fun dest_def (id, (Substitution_Rule ([], Ident s, rhs))) = SOME (id, (s, rhs))
berghofe@41809:   | dest_def _ = NONE;
berghofe@41809: 
berghofe@41809: fun mk_rulename (s, i) = Binding.name (s ^ string_of_int i);
berghofe@41809: 
berghofe@43267: fun add_const prfx (s, ty) ((tab, ctxt), thy) =
berghofe@41809:   let
berghofe@43267:     val T = mk_type thy prfx ty;
berghofe@41809:     val b = Binding.name s;
berghofe@41809:     val c = Const (Sign.full_name thy b, T)
berghofe@41809:   in
berghofe@41809:     (c,
berghofe@41809:      ((Symtab.update (s, (c, ty)) tab, Name.declare s ctxt),
berghofe@41809:       Sign.add_consts_i [(b, T, NoSyn)] thy))
berghofe@41809:   end;
berghofe@41809: 
berghofe@43267: fun add_def prfx types pfuns consts (id, (s, e)) (ids as (tab, ctxt), thy) =
berghofe@41809:   (case lookup consts s of
berghofe@41809:      SOME ty =>
berghofe@41809:        let
berghofe@43267:          val (t, ty') = term_of_expr thy prfx types pfuns ids e;
berghofe@43267:          val T = mk_type thy prfx ty;
berghofe@43267:          val T' = mk_type thy prfx ty';
berghofe@42749:          val _ = T = T' orelse
berghofe@41809:            error ("Declared type " ^ ty ^ " of " ^ s ^
berghofe@41809:              "\ndoes not match type " ^ ty' ^ " in definition");
berghofe@41809:          val id' = mk_rulename id;
berghofe@41809:          val lthy = Named_Target.theory_init thy;
berghofe@41809:          val ((t', (_, th)), lthy') = Specification.definition
berghofe@41809:            (NONE, ((id', []), HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@42749:              (Free (s, T), t)))) lthy;
wenzelm@43232:          val phi = Proof_Context.export_morphism lthy' lthy
berghofe@41809:        in
berghofe@41809:          ((id', Morphism.thm phi th),
berghofe@41809:           ((Symtab.update (s, (Morphism.term phi t', ty)) tab,
berghofe@41809:             Name.declare s ctxt),
berghofe@41809:            Local_Theory.exit_global lthy'))
berghofe@41809:        end
berghofe@41809:    | NONE => error ("Undeclared constant " ^ s));
berghofe@41809: 
berghofe@43267: fun add_var prfx (s, ty) (ids, thy) =
berghofe@43267:   let val ([Free p], ids') = mk_variables thy prfx [s] ty ids
berghofe@41809:   in (p, (ids', thy)) end;
berghofe@41809: 
berghofe@43267: fun add_init_vars prfx vcs (ids_thy as ((tab, _), _)) =
berghofe@43267:   fold_map (add_var prfx)
berghofe@41809:     (map_filter
berghofe@41809:        (fn s => case try (unsuffix "~") s of
berghofe@41809:           SOME s' => (case Symtab.lookup tab s' of
berghofe@41809:             SOME (_, ty) => SOME (s, ty)
berghofe@41809:           | NONE => error ("Undeclared identifier " ^ s'))
berghofe@41809:         | NONE => NONE)
berghofe@41809:        (fold_vcs (add_expr_idents o snd) vcs []))
berghofe@41809:     ids_thy;
berghofe@41809: 
berghofe@41809: fun is_trivial_vc ([], [(_, Ident "true")]) = true
berghofe@41809:   | is_trivial_vc _ = false;
berghofe@41809: 
berghofe@41809: fun rulenames rules = commas
berghofe@41809:   (map (fn ((s, i), _) => s ^ "(" ^ string_of_int i ^ ")") rules);
berghofe@41809: 
berghofe@41809: (* sort definitions according to their dependency *)
berghofe@43370: fun sort_defs _ _ _ _ [] sdefs = rev sdefs
berghofe@43370:   | sort_defs prfx funs pfuns consts defs sdefs =
berghofe@41809:       (case find_first (fn (_, (_, e)) =>
berghofe@43370:          forall (is_some o lookup_prfx prfx pfuns)
berghofe@43370:            (add_expr_pfuns funs e []) andalso
berghofe@41809:          forall (fn id =>
berghofe@41809:            member (fn (s, (_, (s', _))) => s = s') sdefs id orelse
berghofe@42749:            consts id)
berghofe@41809:              (add_expr_idents e [])) defs of
berghofe@43370:          SOME d => sort_defs prfx funs pfuns consts
berghofe@41809:            (remove (op =) d defs) (d :: sdefs)
berghofe@41809:        | NONE => error ("Bad definitions: " ^ rulenames defs));
berghofe@41809: 
berghofe@43227: fun set_vcs ({types, vars, consts, funs} : decls)
berghofe@49468:       (rules, _) ((_, ident), vcs) path opt_prfx thy =
berghofe@41809:   let
berghofe@49468:     val prfx' =
berghofe@49468:       if opt_prfx = "" then
berghofe@49468:         space_implode "__" (Long_Name.explode (Long_Name.qualifier ident))
berghofe@49468:       else opt_prfx;
berghofe@49468:     val prfx = to_lower prfx';
berghofe@41809:     val {pfuns, ...} = VCs.get thy;
berghofe@42749:     val (defs, rules') = partition_opt dest_def rules;
berghofe@41809:     val consts' =
berghofe@42749:       subtract (fn ((_, (s, _)), (s', _)) => s = s') defs (items consts);
berghofe@41809:     (* ignore all complex rules in rls files *)
berghofe@41809:     val (rules'', other_rules) =
berghofe@41809:       List.partition (complex_rule o snd) rules';
berghofe@41809:     val _ = if null rules'' then ()
berghofe@41809:       else warning ("Ignoring rules: " ^ rulenames rules'');
berghofe@41809: 
berghofe@41809:     val vcs' = VCtab.make (maps (fn (tr, vcs) =>
berghofe@42767:       map (fn (s, (ps, cs)) => (s, (tr, NONE, ps, cs)))
berghofe@41809:         (filter_out (is_trivial_vc o snd) vcs)) vcs);
berghofe@41809: 
berghofe@41809:     val _ = (case filter_out (is_some o lookup funs)
berghofe@43370:         (pfuns_of_vcs prfx funs pfuns vcs') of
berghofe@41809:         [] => ()
berghofe@41809:       | fs => error ("Undeclared proof function(s) " ^ commas fs));
berghofe@41809: 
berghofe@41809:     val (((defs', vars''), ivars), (ids, thy')) =
berghofe@41809:       ((Symtab.empty |>
wenzelm@46611:         Symtab.update ("false", (@{term False}, booleanN)) |>
wenzelm@46611:         Symtab.update ("true", (@{term True}, booleanN)),
berghofe@43227:         Name.context),
berghofe@47595:        thy |> Sign.add_path
berghofe@49468:          ((if prfx' = "" then "" else prfx' ^ "__") ^ Long_Name.base_name ident)) |>
berghofe@43267:       fold (add_type_def prfx) (items types) |>
berghofe@43267:       fold (snd oo add_const prfx) consts' |> (fn ids_thy as ((tab, _), _) =>
berghofe@42749:         ids_thy |>
berghofe@43267:         fold_map (add_def prfx types pfuns consts)
berghofe@43370:           (sort_defs prfx funs pfuns (Symtab.defined tab) defs []) ||>>
berghofe@43267:         fold_map (add_var prfx) (items vars) ||>>
berghofe@43267:         add_init_vars prfx vcs');
berghofe@41809: 
berghofe@41809:     val ctxt =
berghofe@41809:       [Element.Fixes (map (fn (s, T) =>
berghofe@41809:          (Binding.name s, SOME T, NoSyn)) (vars'' @ ivars)),
berghofe@41809:        Element.Assumes (map (fn (id, rl) =>
berghofe@41809:          ((mk_rulename id, []),
berghofe@43267:           [(term_of_rule thy' prfx types pfuns ids rl, [])]))
berghofe@41809:            other_rules),
wenzelm@43311:        Element.Notes ("", [((Binding.name "defns", []), map (rpair [] o single o snd) defs')])]
berghofe@41809:           
berghofe@41809:   in
berghofe@47438:     set_env ctxt defs' types funs ids vcs' path prfx thy'
berghofe@41809:   end;
berghofe@41809: 
berghofe@41809: end;