(*  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;