(*  Title:      Pure/Isar/specification.ML

     Author:     Makarius

 Derived local theory specifications --- with type-inference and

 toplevel polymorphism.

 *)

 signature SPECIFICATION =

 sig

   val print_consts: local_theory -> (string * typ -> bool) -> (string * typ) list -> unit

   val check_spec:

     (binding * typ option * mixfix) list -> (Attrib.binding * term) list -> Proof.context ->

     (((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context

   val read_spec:

     (binding * string option * mixfix) list -> (Attrib.binding * string) list -> Proof.context ->

     (((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context

   val check_free_spec:

     (binding * typ option * mixfix) list -> (Attrib.binding * term) list -> Proof.context ->

     (((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context

   val read_free_spec:

     (binding * string option * mixfix) list -> (Attrib.binding * string) list -> Proof.context ->

     (((binding * typ) * mixfix) list * (Attrib.binding * term) list) * Proof.context

   val check_specification: (binding * typ option * mixfix) list ->

     (Attrib.binding * term list) list -> Proof.context ->

     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context

   val read_specification: (binding * string option * mixfix) list ->

     (Attrib.binding * string list) list -> Proof.context ->

     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context

   val axiomatization: (binding * typ option * mixfix) list ->

     (Attrib.binding * term list) list -> theory ->

     (term list * thm list list) * theory

   val axiomatization_cmd: (binding * string option * mixfix) list ->

     (Attrib.binding * string list) list -> theory ->

     (term list * thm list list) * theory

   val definition:

     (binding * typ option * mixfix) option * (Attrib.binding * term) ->

     local_theory -> (term * (string * thm)) * local_theory

   val definition_cmd:

     (binding * string option * mixfix) option * (Attrib.binding * string) ->

     local_theory -> (term * (string * thm)) * local_theory

   val abbreviation: Syntax.mode -> (binding * typ option * mixfix) option * term ->

     local_theory -> local_theory

   val abbreviation_cmd: Syntax.mode -> (binding * string option * mixfix) option * string ->

     local_theory -> local_theory

   val type_notation: bool -> Syntax.mode -> (typ * mixfix) list -> local_theory -> local_theory

   val type_notation_cmd: bool -> Syntax.mode -> (string * mixfix) list -> local_theory -> local_theory

   val notation: bool -> Syntax.mode -> (term * mixfix) list -> local_theory -> local_theory

   val notation_cmd: bool -> Syntax.mode -> (string * mixfix) list -> local_theory -> local_theory

   val theorems: string ->

     (Attrib.binding * (thm list * Attrib.src list) list) list ->

     local_theory -> (string * thm list) list * local_theory

   val theorems_cmd: string ->

     (Attrib.binding * (Facts.ref * Attrib.src list) list) list ->

     local_theory -> (string * thm list) list * local_theory

   val theorem: string -> Method.text option ->

     (thm list list -> local_theory -> local_theory) -> Attrib.binding ->

     Element.context_i list -> Element.statement_i ->

     bool -> local_theory -> Proof.state

   val theorem_cmd: string -> Method.text option ->

     (thm list list -> local_theory -> local_theory) -> Attrib.binding ->

     Element.context list -> Element.statement ->

     bool -> local_theory -> Proof.state

   val add_theorem_hook: (bool -> Proof.state -> Proof.state) -> Context.generic -> Context.generic

 end;

 structure Specification: SPECIFICATION =

 struct

 (* diagnostics *)

 fun print_consts _ _ [] = ()

   | print_consts ctxt pred cs = Pretty.writeln (Proof_Display.pretty_consts ctxt pred cs);

 (* prepare specification *)

 local

 fun close_forms ctxt i xs As =

   let

     fun add_free (Free (x, _)) = if Variable.is_fixed ctxt x then I else insert (op =) x

       | add_free _ = I;

     val commons = map #1 xs;

     val _ =

       (case duplicates (op =) commons of [] => ()

       | dups => error ("Duplicate local variables " ^ commas_quote dups));

     val frees = rev ((fold o fold_aterms) add_free As (rev commons));

     val types = map (TypeInfer.param i o rpair []) (Name.invents Name.context Name.aT (length frees));

     val uniform_typing = the o AList.lookup (op =) (frees ~~ types);

     fun abs_body lev y (Abs (x, T, b)) = Abs (x, T, abs_body (lev + 1) y b)

       | abs_body lev y (t $ u) = abs_body lev y t $ abs_body lev y u

       | abs_body lev y (t as Free (x, T)) =

           if x = y then TypeInfer.constrain (uniform_typing x) (TypeInfer.constrain T (Bound lev))

           else t

       | abs_body _ _ a = a;

     fun close (y, U) B =

       let val B' = abs_body 0 y (Term.incr_boundvars 1 B)

       in if Term.loose_bvar1 (B', 0) then Term.all dummyT $ Abs (y, U, B') else B end;

     fun close_form A =

       let

         val occ_frees = rev (fold_aterms add_free A []);

         val bounds = xs @ map (rpair dummyT) (subtract (op =) commons occ_frees);

       in fold_rev close bounds A end;

   in map close_form As end;

 fun prepare prep_vars parse_prop prep_att do_close raw_vars raw_specss ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     val (vars, vars_ctxt) = ctxt |> prep_vars raw_vars;

     val (xs, params_ctxt) = vars_ctxt |> ProofContext.add_fixes vars;

     val Asss = (map o map) (map (parse_prop params_ctxt) o snd) raw_specss;

     val names = Variable.names_of (params_ctxt |> (fold o fold o fold) Variable.declare_term Asss)

       |> fold Name.declare xs;

     val Asss' = #1 ((fold_map o fold_map o fold_map) Term.free_dummy_patterns Asss names);

     val idx = (fold o fold o fold) Term.maxidx_term Asss' ~1 + 1;

     val specs =

       (if do_close then

         #1 (fold_map

             (fn Ass => fn i => (burrow (close_forms params_ctxt i []) Ass, i + 1)) Asss' idx)

       else Asss')

       |> flat |> burrow (Syntax.check_props params_ctxt);

     val specs_ctxt = params_ctxt |> (fold o fold) Variable.declare_term specs;

     val Ts = specs_ctxt |> fold_map ProofContext.inferred_param xs |> fst;

     val params = map2 (fn (b, _, mx) => fn T => ((b, T), mx)) vars Ts;

     val name_atts = map (fn ((name, atts), _) => (name, map (prep_att thy) atts)) (flat raw_specss);

   in ((params, name_atts ~~ specs), specs_ctxt) end;

 fun single_spec (a, prop) = [(a, [prop])];

 fun the_spec (a, [prop]) = (a, prop);

 fun prep_spec prep_vars parse_prop prep_att do_close vars specs =

   prepare prep_vars parse_prop prep_att do_close

     vars (map single_spec specs) #>> apsnd (map the_spec);

 in

 fun check_spec x = prep_spec ProofContext.cert_vars (K I) (K I) true x;

 fun read_spec x = prep_spec ProofContext.read_vars Syntax.parse_prop Attrib.intern_src true x;

 fun check_free_spec x = prep_spec ProofContext.cert_vars (K I) (K I) false x;

 fun read_free_spec x = prep_spec ProofContext.read_vars Syntax.parse_prop Attrib.intern_src false x;

 fun check_specification vars specs =

   prepare ProofContext.cert_vars (K I) (K I) true vars [specs];

 fun read_specification vars specs =

   prepare ProofContext.read_vars Syntax.parse_prop Attrib.intern_src true vars [specs];

 end;

 (* axiomatization -- within global theory *)

 fun gen_axioms do_print prep raw_vars raw_specs thy =

   let

     val ((vars, specs), _) = prep raw_vars raw_specs (ProofContext.init thy);

     val xs = map (fn ((b, T), _) => (Name.of_binding b, T)) vars;

     (*consts*)

     val (consts, consts_thy) = thy |> fold_map Theory.specify_const vars;

     val subst = Term.subst_atomic (map Free xs ~~ consts);

     (*axioms*)

     val (axioms, axioms_thy) = (specs, consts_thy) |-> fold_map (fn ((b, atts), props) =>

         fold_map Thm.add_axiom

           (map (apfst (fn a => Binding.map_name (K a) b))

             (PureThy.name_multi (Name.of_binding b) (map subst props)))

         #>> (fn ths => ((b, atts), [(ths, [])])));

     (*facts*)

     val (facts, facts_lthy) = axioms_thy

       |> Theory_Target.init NONE

       |> Spec_Rules.add Spec_Rules.Unknown (consts, maps (maps #1 o #2) axioms)

       |> Local_Theory.notes axioms;

     val _ =

       if not do_print then ()

       else print_consts facts_lthy (K false) xs;

   in ((consts, map #2 facts), Local_Theory.exit_global facts_lthy) end;

 val axiomatization = gen_axioms false check_specification;

 val axiomatization_cmd = gen_axioms true read_specification;

 (* definition *)

 fun gen_def do_print prep (raw_var, raw_spec) lthy =

   let

     val (vars, [((raw_name, atts), prop)]) = fst (prep (the_list raw_var) [raw_spec] lthy);

     val (((x, T), rhs), prove) = LocalDefs.derived_def lthy true prop;

     val var as (b, _) =

       (case vars of

         [] => (Binding.name x, NoSyn)

       | [((b, _), mx)] =>

           let

             val y = Name.of_binding b;

             val _ = x = y orelse

               error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote y ^

                 Position.str_of (Binding.pos_of b));

           in (b, mx) end);

     val name = Thm.def_binding_optional b raw_name;

     val ((lhs, (_, raw_th)), lthy2) = lthy

       |> Local_Theory.define (var, ((Binding.suffix_name "_raw" name, []), rhs));

     val th = prove lthy2 raw_th;

     val lthy3 = lthy2 |> Spec_Rules.add Spec_Rules.Equational ([lhs], [th]);

     val ([(def_name, [th'])], lthy4) = lthy3

       |> Local_Theory.notes_kind Thm.definitionK

         [((name, Code.add_default_eqn_attrib :: atts), [([th], [])])];

     val lhs' = Morphism.term (Local_Theory.target_morphism lthy4) lhs;

     val _ =

       if not do_print then ()

       else print_consts lthy4 (member (op =) (Term.add_frees lhs' [])) [(x, T)];

   in ((lhs, (def_name, th')), lthy4) end;

 val definition = gen_def false check_free_spec;

 val definition_cmd = gen_def true read_free_spec;

 (* abbreviation *)

 fun gen_abbrev do_print prep mode (raw_var, raw_prop) lthy =

   let

     val ((vars, [(_, prop)]), _) =

       prep (the_list raw_var) [(Attrib.empty_binding, raw_prop)]

         (lthy |> ProofContext.set_mode ProofContext.mode_abbrev);

     val ((x, T), rhs) = LocalDefs.abs_def (#2 (LocalDefs.cert_def lthy prop));

     val var =

       (case vars of

         [] => (Binding.name x, NoSyn)

       | [((b, _), mx)] =>

           let

             val y = Name.of_binding b;

             val _ = x = y orelse

               error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y ^

                 Position.str_of (Binding.pos_of b));

           in (b, mx) end);

     val lthy' = lthy

       |> ProofContext.set_syntax_mode mode    (* FIXME ?!? *)

       |> Local_Theory.abbrev mode (var, rhs) |> snd

       |> ProofContext.restore_syntax_mode lthy;

     val _ = if not do_print then () else print_consts lthy' (K false) [(x, T)];

   in lthy' end;

 val abbreviation = gen_abbrev false check_free_spec;

 val abbreviation_cmd = gen_abbrev true read_free_spec;

 (* notation *)

 local

 fun gen_type_notation prep_type add mode args lthy =

   lthy |> Local_Theory.type_notation add mode (map (apfst (prep_type lthy)) args);

 fun gen_notation prep_const add mode args lthy =

   lthy |> Local_Theory.notation add mode (map (apfst (prep_const lthy)) args);

 in

 val type_notation = gen_type_notation (K I);

 val type_notation_cmd = gen_type_notation (fn ctxt => ProofContext.read_type_name ctxt false);

 val notation = gen_notation (K I);

 val notation_cmd = gen_notation (fn ctxt => ProofContext.read_const ctxt false);

 end;

 (* fact statements *)

 fun gen_theorems prep_fact prep_att kind raw_facts lthy =

   let

     val attrib = prep_att (ProofContext.theory_of lthy);

     val facts = raw_facts |> map (fn ((name, atts), bs) =>

       ((name, map attrib atts),

         bs |> map (fn (b, more_atts) => (prep_fact lthy b, map attrib more_atts))));

     val (res, lthy') = lthy |> Local_Theory.notes_kind kind facts;

     val _ = Proof_Display.print_results true lthy' ((kind, ""), res);

   in (res, lthy') end;

 val theorems = gen_theorems (K I) (K I);

 val theorems_cmd = gen_theorems ProofContext.get_fact Attrib.intern_src;

 (* complex goal statements *)

 local

 fun prep_statement prep_att prep_stmt elems concl ctxt =

   (case concl of

     Element.Shows shows =>

       let

         val (propp, elems_ctxt) = prep_stmt elems (map snd shows) ctxt;

         val prems = Assumption.local_prems_of elems_ctxt ctxt;

         val stmt = Attrib.map_specs prep_att (map fst shows ~~ propp);

         val goal_ctxt = fold (fold (Variable.auto_fixes o fst)) propp elems_ctxt;

       in ((prems, stmt, NONE), goal_ctxt) end

   | Element.Obtains obtains =>

       let

         val case_names = obtains |> map_index (fn (i, (b, _)) =>

           if Binding.is_empty b then string_of_int (i + 1) else Name.of_binding b);

         val constraints = obtains |> map (fn (_, (vars, _)) =>

           Element.Constrains

             (vars |> map_filter (fn (x, SOME T) => SOME (Name.of_binding x, T) | _ => NONE)));

         val raw_propp = obtains |> map (fn (_, (_, props)) => map (rpair []) props);

         val (propp, elems_ctxt) = prep_stmt (elems @ constraints) raw_propp ctxt;

         val thesis = ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) Auto_Bind.thesisN;

         fun assume_case ((name, (vars, _)), asms) ctxt' =

           let

             val bs = map fst vars;

             val xs = map Name.of_binding bs;

             val props = map fst asms;

             val (Ts, _) = ctxt'

               |> fold Variable.declare_term props

               |> fold_map ProofContext.inferred_param xs;

             val asm = Term.list_all_free (xs ~~ Ts, Logic.list_implies (props, thesis));

           in

             ctxt' |> (snd o ProofContext.add_fixes (map (fn b => (b, NONE, NoSyn)) bs));

             ctxt' |> Variable.auto_fixes asm

             |> ProofContext.add_assms_i Assumption.assume_export

               [((name, [Context_Rules.intro_query NONE]), [(asm, [])])]

             |>> (fn [(_, [th])] => th)

           end;

         val atts = map (Attrib.internal o K)

           [Rule_Cases.consumes (~ (length obtains)), Rule_Cases.case_names case_names];

         val prems = Assumption.local_prems_of elems_ctxt ctxt;

         val stmt = [((Binding.empty, atts), [(thesis, [])])];

         val (facts, goal_ctxt) = elems_ctxt

           |> (snd o ProofContext.add_fixes [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)])

           |> fold_map assume_case (obtains ~~ propp)

           |-> (fn ths =>

             ProofContext.note_thmss "" [((Binding.name Obtain.thatN, []), [(ths, [])])] #>

             #2 #> pair ths);

       in ((prems, stmt, SOME facts), goal_ctxt) end);

 structure TheoremHook = Generic_Data

 (

   type T = ((bool -> Proof.state -> Proof.state) * stamp) list;

   val empty = [];

   val extend = I;

   fun merge hooks : T = Library.merge (eq_snd op =) hooks;

 );

 fun gen_theorem prep_att prep_stmt

     kind before_qed after_qed (name, raw_atts) raw_elems raw_concl int lthy =

   let

     val _ = Local_Theory.affirm lthy;

     val thy = ProofContext.theory_of lthy;

     val attrib = prep_att thy;

     val atts = map attrib raw_atts;

     val elems = raw_elems |> map (Element.map_ctxt_attrib attrib);

     val ((prems, stmt, facts), goal_ctxt) =

       prep_statement attrib prep_stmt elems raw_concl lthy;

     fun after_qed' results goal_ctxt' =

       let val results' =

         burrow (map Goal.norm_result o ProofContext.export goal_ctxt' lthy) results

       in

         lthy

         |> Local_Theory.notes_kind kind

           (map2 (fn (a, _) => fn ths => (a, [(ths, [])])) stmt results')

         |> (fn (res, lthy') =>

           if Binding.is_empty name andalso null atts then

             (Proof_Display.print_results true lthy' ((kind, ""), res); lthy')

           else

             let

               val ([(res_name, _)], lthy'') = lthy'

                 |> Local_Theory.notes_kind kind [((name, atts), [(maps #2 res, [])])];

               val _ = Proof_Display.print_results true lthy' ((kind, res_name), res);

             in lthy'' end)

         |> after_qed results'

       end;

   in

     goal_ctxt

     |> ProofContext.note_thmss "" [((Binding.name Auto_Bind.assmsN, []), [(prems, [])])]

     |> snd

     |> Proof.theorem_i before_qed after_qed' (map snd stmt)

     |> (case facts of NONE => I | SOME ths => Proof.refine_insert ths)

     |> Library.apply (map (fn (f, _) => f int) (rev (TheoremHook.get (Context.Proof goal_ctxt))))

   end;

 in

 val theorem = gen_theorem (K I) Expression.cert_statement;

 val theorem_cmd = gen_theorem Attrib.intern_src Expression.read_statement;

 fun add_theorem_hook f = TheoremHook.map (cons (f, stamp ()));

 end;

 end;