(*  Title:      Pure/Isar/specification.ML

     ID:         $Id$

     Author:     Makarius

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

 toplevel polymorphism.

 *)

 signature SPECIFICATION =

 sig

   val quiet_mode: bool ref

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

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

     ((string * Attrib.src list) * string list) list -> local_theory ->

     (((string * typ) * mixfix) list * ((string * Attrib.src list) * term list) list) *

     local_theory

   val cert_specification: (string * typ option * mixfix) list ->

     ((string * Attrib.src list) * term list) list -> local_theory ->

     (((string * typ) * mixfix) list * ((string * Attrib.src list) * term list) list) *

     local_theory

   val axiomatization: (string * string option * mixfix) list ->

     ((bstring * Attrib.src list) * string list) list -> local_theory ->

     (term list * (bstring * thm list) list) * local_theory

   val axiomatization_i: (string * typ option * mixfix) list ->

     ((bstring * Attrib.src list) * term list) list -> local_theory ->

     (term list * (bstring * thm list) list) * local_theory

   val definition:

     (string * string option * mixfix) option * ((string * Attrib.src list) * string) ->

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

   val definition_i:

     (string * typ option * mixfix) option * ((string * Attrib.src list) * term) ->

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

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

     local_theory -> local_theory

   val abbreviation_i: Syntax.mode -> (string * typ option * mixfix) option * term ->

     local_theory -> local_theory

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

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

   val theorems: string -> ((bstring * Attrib.src list) * (thmref * Attrib.src list) list) list

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

   val theorems_i: string -> ((bstring * Attrib.src list) * (thm list * Attrib.src list) list) list

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

   val theorem: string -> Method.text option -> (thm list list -> local_theory -> local_theory) ->

     string * Attrib.src list -> Element.context Locale.element list -> Element.statement ->

     local_theory -> Proof.state

   val theorem_i: string -> Method.text option -> (thm list list -> local_theory -> local_theory) ->

     string * Attrib.src list -> Element.context_i Locale.element list -> Element.statement_i ->

     local_theory -> Proof.state

 end;

 structure Specification: SPECIFICATION =

 struct

 (* diagnostics *)

 val quiet_mode = ref false;

 fun print_consts _ _ [] = ()

   | print_consts ctxt pred cs =

       if ! quiet_mode then () else Pretty.writeln (ProofDisplay.pretty_consts ctxt pred cs);

 fun present_results ctxt res =

   if ! quiet_mode then () else ProofDisplay.present_results ctxt res;

 fun present_results' ctxt kind res = present_results ctxt ((kind, ""), res);

 (* prepare specification *)

 fun prep_specification prep_vars prep_propp prep_att raw_vars raw_specs 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_i vars;

     val ((specs, vs), specs_ctxt) =

       prep_propp (params_ctxt, map (map (rpair []) o snd) raw_specs)

       |> swap |>> map (map fst)

       ||>> fold_map ProofContext.inferred_param xs;

     val params = vs ~~ map #3 vars;

     val names = map (fst o fst) raw_specs;

     val atts = map (map (prep_att thy) o snd o fst) raw_specs;

   in ((params, (names ~~ atts) ~~ specs), specs_ctxt) end;

 fun read_specification x =

   prep_specification ProofContext.read_vars ProofContext.read_propp Attrib.intern_src x;

 fun cert_specification x =

   prep_specification ProofContext.cert_vars ProofContext.cert_propp (K I) x;

 (* axiomatization *)

 fun gen_axioms prep raw_vars raw_specs lthy =

   let

     val (vars, specs) = fst (prep raw_vars raw_specs lthy);

     val cs = map fst vars;

     val spec_frees = member (op =) (fold (fold Term.add_frees o snd) specs []);

     val ((consts, axioms), lthy') = lthy

       |> LocalTheory.consts spec_frees vars

       ||> fold (fold Variable.auto_fixes o snd) specs   (* FIXME !? *)

       ||>> LocalTheory.axioms Thm.axiomK specs;

     (* FIXME generic target!? *)

     val hs = map (Term.head_of o #2 o Logic.dest_equals o Thm.prop_of o #2) consts;

     val lthy'' = lthy' |> LocalTheory.theory (Theory.add_finals_i false hs);

     val _ = print_consts lthy' spec_frees cs;

   in ((map #1 consts, axioms), lthy'') end;

 val axiomatization = gen_axioms read_specification;

 val axiomatization_i = gen_axioms cert_specification;

 (* definition *)

 fun gen_def prep (raw_var, (raw_a, raw_prop)) lthy =

   let

     val (vars, [((raw_name, atts), [prop])]) =

       fst (prep (the_list raw_var) [(raw_a, [raw_prop])] lthy);

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

     val name = Thm.def_name_optional x raw_name;

     val mx = (case vars of [] => NoSyn | [((x', _), mx)] =>

       if x = x' then mx

       else error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote x'));

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

 (*    |> LocalTheory.def ((x, mx), ((name ^ "_raw", []), rhs));  FIXME *)

       |> LocalTheory.def Thm.definitionK ((x, mx), ((name, []), rhs));

     val ((b, [th']), lthy3) = lthy2

       |> LocalTheory.note Thm.definitionK ((name, atts), [prove lthy2 th]);

     val lhs' = Morphism.term (LocalTheory.target_morphism lthy3) lhs;

     val _ = print_consts lthy3 (member (op =) (Term.add_frees lhs' [])) [(x, T)];

   in ((lhs, (b, th')), lthy3) end;

 val definition = gen_def read_specification;

 val definition_i = gen_def cert_specification;

 (* abbreviation *)

 fun gen_abbrev prep mode (raw_var, raw_prop) lthy =

   let

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

       prep (the_list raw_var) [(("", []), [raw_prop])]

         (lthy |> ProofContext.set_expand_abbrevs false);

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

     val mx = (case vars of [] => NoSyn | [((y, _), mx)] =>

       if x = y then mx

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

     val lthy' = lthy

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

       |> LocalTheory.abbrev mode ((x, mx), rhs) |> snd

       |> ProofContext.restore_syntax_mode lthy;

     val _ = print_consts lthy' (K false) [(x, T)]

   in lthy' end;

 val abbreviation = gen_abbrev read_specification;

 val abbreviation_i = gen_abbrev cert_specification;

 (* notation *)

 fun gen_notation prep_const mode args lthy =

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

 val notation = gen_notation ProofContext.read_const;

 val notation_i = gen_notation (K I);

 (* fact statements *)

 fun gen_theorems prep_thms 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_thms lthy b, map attrib more_atts))));

     val (res, lthy') = lthy |> LocalTheory.notes kind facts;

     val _ = present_results' lthy' kind res;

   in (res, lthy') end;

 val theorems = gen_theorems ProofContext.get_thms Attrib.intern_src;

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

 (* complex goal statements *)

 local

 fun subtract_prems ctxt1 ctxt2 =

   Library.drop (length (Assumption.prems_of ctxt1), Assumption.prems_of ctxt2);

 fun prep_statement prep_att prep_stmt elems concl ctxt =

   (case concl of

     Element.Shows shows =>

       let

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

         val prems = subtract_prems loc_ctxt elems_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, []), goal_ctxt) end

   | Element.Obtains obtains =>

       let

         val case_names = obtains |> map_index

           (fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);

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

           Locale.Elem (Element.Constrains

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

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

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

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

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

           let

             val xs = map fst vars;

             val props = map fst asms;

             val (parms, _) = ctxt'

               |> fold Variable.declare_term props

               |> fold_map ProofContext.inferred_param xs;

             val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));

           in

             ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));

             ctxt' |> Variable.auto_fixes asm

             |> ProofContext.add_assms_i Assumption.assume_export

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

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

           end;

         val atts = map (Attrib.internal o K)

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

         val prems = subtract_prems loc_ctxt elems_ctxt;

         val stmt = [(("", atts), [(thesis, [])])];

         val (facts, goal_ctxt) = elems_ctxt

           |> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])

           |> fold_map assume_case (obtains ~~ propp)

           |-> (fn ths => ProofContext.note_thmss_i Thm.assumptionK

                 [((Obtain.thatN, []), [(ths, [])])] #> #2 #> pair ths);

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

 fun gen_theorem prep_att prep_stmt

     kind before_qed after_qed (name, raw_atts) raw_elems raw_concl lthy0 =

   let

     val _ = LocalTheory.assert lthy0;

     val thy = ProofContext.theory_of lthy0;

     val (loc, ctxt, lthy) =

       (case (TheoryTarget.peek lthy0, exists (fn Locale.Expr _ => true | _ => false) raw_elems) of

         (SOME loc, true) => (* workaround non-modularity of in/includes *)  (* FIXME *)

           (SOME loc, ProofContext.init thy, LocalTheory.restore lthy0)

       | _ => (NONE, lthy0, lthy0));

     val attrib = prep_att thy;

     val atts = map attrib raw_atts;

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

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

       prep_statement attrib (prep_stmt loc) elems raw_concl ctxt;

     fun after_qed' results goal_ctxt' =

       let val results' =

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

       in

         lthy

         |> LocalTheory.notes kind (map2 (fn (a, _) => fn ths => (a, [(ths, [])])) stmt results')

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

           (present_results lthy' ((kind, name), res);

             if name = "" andalso null atts then lthy'

             else #2 (LocalTheory.notes kind [((name, atts), [(maps #2 res, [])])] lthy')))

         |> after_qed results'

       end;

   in

     goal_ctxt

     |> ProofContext.note_thmss_i Thm.assumptionK [((AutoBind.assmsN, []), [(prems, [])])]

     |> snd

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

     |> Proof.refine_insert facts

   end;

 in

 val theorem = gen_theorem Attrib.intern_src Locale.read_context_statement_i;

 val theorem_i = gen_theorem (K I) Locale.cert_context_statement;

 end;

 end;