(*  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 !? *)

      |> TermSyntax.abbrev mode ((x, mx), rhs)

      |> 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 |> TermSyntax.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;