wenzelm@18620: (*  Title:      Pure/Isar/specification.ML
wenzelm@18620:     Author:     Makarius
wenzelm@18620: 
wenzelm@21036: Derived local theory specifications --- with type-inference and
wenzelm@18810: toplevel polymorphism.
wenzelm@18620: *)
wenzelm@18620: 
wenzelm@18620: signature SPECIFICATION =
wenzelm@18620: sig
wenzelm@20890:   val print_consts: local_theory -> (string * typ -> bool) -> (string * typ) list -> unit
haftmann@29581:   val check_specification: (binding * typ option * mixfix) list ->
wenzelm@28084:     (Attrib.binding * term list) list list -> Proof.context ->
haftmann@29581:     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
haftmann@29581:   val read_specification: (binding * string option * mixfix) list ->
wenzelm@28084:     (Attrib.binding * string list) list list -> Proof.context ->
haftmann@29581:     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
haftmann@29581:   val check_free_specification: (binding * typ option * mixfix) list ->
wenzelm@28084:     (Attrib.binding * term list) list -> Proof.context ->
haftmann@29581:     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
haftmann@29581:   val read_free_specification: (binding * string option * mixfix) list ->
wenzelm@28084:     (Attrib.binding * string list) list -> Proof.context ->
haftmann@29581:     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
haftmann@29581:   val axiomatization: (binding * typ option * mixfix) list ->
wenzelm@28114:     (Attrib.binding * term list) list -> theory ->
wenzelm@28114:     (term list * (string * thm list) list) * theory
haftmann@29581:   val axiomatization_cmd: (binding * string option * mixfix) list ->
wenzelm@28114:     (Attrib.binding * string list) list -> theory ->
wenzelm@28114:     (term list * (string * thm list) list) * theory
wenzelm@18954:   val definition:
haftmann@29581:     (binding * typ option * mixfix) option * (Attrib.binding * term) ->
wenzelm@28080:     local_theory -> (term * (string * thm)) * local_theory
wenzelm@24927:   val definition_cmd:
haftmann@29581:     (binding * string option * mixfix) option * (Attrib.binding * string) ->
wenzelm@28080:     local_theory -> (term * (string * thm)) * local_theory
haftmann@29581:   val abbreviation: Syntax.mode -> (binding * typ option * mixfix) option * term ->
wenzelm@21532:     local_theory -> local_theory
haftmann@29581:   val abbreviation_cmd: Syntax.mode -> (binding * string option * mixfix) option * string ->
wenzelm@24927:     local_theory -> local_theory
wenzelm@24949:   val notation: bool -> Syntax.mode -> (term * mixfix) list -> local_theory -> local_theory
wenzelm@24949:   val notation_cmd: bool -> Syntax.mode -> (string * mixfix) list -> local_theory -> local_theory
wenzelm@28080:   val theorems: string ->
wenzelm@28084:     (Attrib.binding * (thm list * Attrib.src list) list) list ->
wenzelm@28080:     local_theory -> (string * thm list) list * local_theory
wenzelm@26336:   val theorems_cmd: string ->
wenzelm@28084:     (Attrib.binding * (Facts.ref * Attrib.src list) list) list ->
wenzelm@28080:     local_theory -> (string * thm list) list * local_theory
wenzelm@24986:   val theorem: string -> Method.text option ->
wenzelm@28084:     (thm list list -> local_theory -> local_theory) -> Attrib.binding ->
ballarin@28710:     Element.context_i list -> Element.statement_i ->
berghofe@24452:     bool -> local_theory -> Proof.state
wenzelm@24986:   val theorem_cmd: string -> Method.text option ->
wenzelm@28084:     (thm list list -> local_theory -> local_theory) -> Attrib.binding ->
ballarin@28710:     Element.context list -> Element.statement ->
berghofe@24452:     bool -> local_theory -> Proof.state
berghofe@24452:   val add_theorem_hook: (bool -> Proof.state -> Proof.state) -> Context.generic -> Context.generic
wenzelm@18620: end;
wenzelm@18620: 
wenzelm@18620: structure Specification: SPECIFICATION =
wenzelm@18620: struct
wenzelm@18620: 
wenzelm@20890: (* diagnostics *)
wenzelm@20890: 
wenzelm@20890: fun print_consts _ _ [] = ()
wenzelm@24986:   | print_consts ctxt pred cs = Pretty.writeln (ProofDisplay.pretty_consts ctxt pred cs);
wenzelm@20914: 
wenzelm@19664: 
wenzelm@18620: (* prepare specification *)
wenzelm@18620: 
wenzelm@24724: local
wenzelm@24724: 
wenzelm@24724: fun close_forms ctxt i xs As =
wenzelm@24724:   let
wenzelm@24724:     fun add_free (Free (x, _)) = if Variable.is_fixed ctxt x then I else insert (op =) x
wenzelm@24724:       | add_free _ = I;
wenzelm@24724: 
wenzelm@24724:     val commons = map #1 xs;
wenzelm@24724:     val _ =
wenzelm@24724:       (case duplicates (op =) commons of [] => ()
wenzelm@24724:       | dups => error ("Duplicate local variables " ^ commas_quote dups));
wenzelm@24724:     val frees = rev ((fold o fold_aterms) add_free As (rev commons));
wenzelm@24848:     val types = map (TypeInfer.param i o rpair []) (Name.invents Name.context Name.aT (length frees));
wenzelm@24724:     val uniform_typing = the o AList.lookup (op =) (frees ~~ types);
wenzelm@24724: 
wenzelm@24724:     fun abs_body lev y (Abs (x, T, b)) = Abs (x, T, abs_body (lev + 1) y b)
wenzelm@24724:       | abs_body lev y (t $ u) = abs_body lev y t $ abs_body lev y u
wenzelm@24724:       | abs_body lev y (t as Free (x, T)) =
wenzelm@24724:           if x = y then TypeInfer.constrain (uniform_typing x) (TypeInfer.constrain T (Bound lev))
wenzelm@24724:           else t
wenzelm@24724:       | abs_body _ _ a = a;
wenzelm@24724:     fun close (y, U) B =
wenzelm@24724:       let val B' = abs_body 0 y (Term.incr_boundvars 1 B)
wenzelm@24724:       in if Term.loose_bvar1 (B', 0) then Term.all dummyT $ Abs (y, U, B') else B end;
wenzelm@24724:     fun close_form A =
wenzelm@24724:       let
wenzelm@24724:         val occ_frees = rev (fold_aterms add_free A []);
wenzelm@24724:         val bounds = xs @ map (rpair dummyT) (subtract (op =) commons occ_frees);
wenzelm@24724:       in fold_rev close bounds A end;
wenzelm@24724:   in map close_form As end;
wenzelm@24724: 
wenzelm@24724: fun prep_spec prep_vars parse_prop prep_att do_close raw_vars raw_specss ctxt =
wenzelm@18620:   let
wenzelm@18670:     val thy = ProofContext.theory_of ctxt;
wenzelm@18620: 
wenzelm@18670:     val (vars, vars_ctxt) = ctxt |> prep_vars raw_vars;
wenzelm@18670:     val (xs, params_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
wenzelm@18620: 
wenzelm@24724:     val Asss = (map o map) (map (parse_prop params_ctxt) o snd) raw_specss;
wenzelm@24734:     val names = Variable.names_of (params_ctxt |> (fold o fold o fold) Variable.declare_term Asss)
wenzelm@24734:       |> fold Name.declare xs;
wenzelm@24734:     val Asss' = #1 ((fold_map o fold_map o fold_map) Term.free_dummy_patterns Asss names);
wenzelm@24734:     val idx = (fold o fold o fold) Term.maxidx_term Asss' ~1 + 1;
wenzelm@24724:     val specs =
wenzelm@24724:       (if do_close then
wenzelm@24734:         #1 (fold_map
wenzelm@24734:             (fn Ass => fn i => (burrow (close_forms params_ctxt i []) Ass, i + 1)) Asss' idx)
wenzelm@24734:       else Asss')
wenzelm@24724:       |> flat |> burrow (Syntax.check_props params_ctxt);
wenzelm@24724:     val specs_ctxt = params_ctxt |> (fold o fold) Variable.declare_term specs;
wenzelm@24724: 
wenzelm@28080:     val Ts = specs_ctxt |> fold_map ProofContext.inferred_param xs |> fst;
wenzelm@28080:     val params = map2 (fn (b, _, mx) => fn T => ((b, T), mx)) vars Ts;
wenzelm@24724:     val name_atts = map (fn ((name, atts), _) => (name, map (prep_att thy) atts)) (flat raw_specss);
wenzelm@24724:   in ((params, name_atts ~~ specs), specs_ctxt) end;
wenzelm@24724: 
wenzelm@24724: fun read_spec x = prep_spec ProofContext.read_vars Syntax.parse_prop Attrib.intern_src x;
wenzelm@24724: fun check_spec x = prep_spec ProofContext.cert_vars (K I) (K I) x;
wenzelm@18620: 
wenzelm@24724: in
wenzelm@21370: 
wenzelm@24724: fun read_specification x = read_spec true x;
wenzelm@24724: fun check_specification x = check_spec true x;
wenzelm@24724: fun read_free_specification vars specs = read_spec false vars [specs];
wenzelm@24724: fun check_free_specification vars specs = check_spec false vars [specs];
wenzelm@24724: 
wenzelm@24724: end;
wenzelm@18620: 
wenzelm@18620: 
wenzelm@28114: (* axiomatization -- within global theory *)
wenzelm@18620: 
wenzelm@28114: fun gen_axioms do_print prep raw_vars raw_specs thy =
wenzelm@18620:   let
wenzelm@28114:     val ((vars, specs), _) = prep raw_vars [raw_specs] (ProofContext.init thy);
haftmann@29006:     val xs = map (fn ((b, T), _) => (Binding.base_name b, T)) vars;
wenzelm@28114: 
wenzelm@28114:     (*consts*)
wenzelm@28114:     val (consts, consts_thy) = thy |> fold_map (Theory.specify_const []) vars;
wenzelm@28114:     val subst = Term.subst_atomic (map Free xs ~~ consts);
wenzelm@28114: 
wenzelm@28114:     (*axioms*)
wenzelm@28114:     val (axioms, axioms_thy) = consts_thy |> fold_map (fn ((b, atts), props) =>
haftmann@29581:         fold_map Thm.add_axiom
haftmann@29581:           ((map o apfst) Binding.name (PureThy.name_multi (Binding.base_name b) (map subst props)))
wenzelm@28114:         #>> (fn ths => ((b, atts), [(map Drule.standard' ths, [])]))) specs;
wenzelm@28114:     val (facts, thy') = axioms_thy |> PureThy.note_thmss Thm.axiomK
wenzelm@28114:       (Attrib.map_facts (Attrib.attribute_i axioms_thy) axioms);
wenzelm@26595:     val _ =
wenzelm@26595:       if not do_print then ()
wenzelm@28114:       else print_consts (ProofContext.init thy') (K false) xs;
wenzelm@28114:   in ((consts, facts), thy') end;
wenzelm@18786: 
wenzelm@26595: val axiomatization = gen_axioms false check_specification;
wenzelm@26595: val axiomatization_cmd = gen_axioms true read_specification;
wenzelm@18620: 
wenzelm@18786: 
wenzelm@18786: (* definition *)
wenzelm@18786: 
wenzelm@26595: fun gen_def do_print prep (raw_var, (raw_a, raw_prop)) lthy =
wenzelm@18786:   let
wenzelm@21705:     val (vars, [((raw_name, atts), [prop])]) =
wenzelm@21705:       fst (prep (the_list raw_var) [(raw_a, [raw_prop])] lthy);
wenzelm@21705:     val (((x, T), rhs), prove) = LocalDefs.derived_def lthy true prop;
haftmann@28965:     val name = Binding.map_base (Thm.def_name_optional x) raw_name;
wenzelm@28080:     val var =
wenzelm@28080:       (case vars of
haftmann@28965:         [] => (Binding.name x, NoSyn)
wenzelm@28080:       | [((b, _), mx)] =>
wenzelm@28080:           let
haftmann@29006:             val y = Binding.base_name b;
wenzelm@28080:             val _ = x = y orelse
wenzelm@28080:               error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote y ^
haftmann@28941:                 Position.str_of (Binding.pos_of b));
wenzelm@28080:           in (b, mx) end);
wenzelm@28080:     val ((lhs, (_, th)), lthy2) = lthy |> LocalTheory.define Thm.definitionK
haftmann@28965:         (var, ((Binding.map_base (suffix "_raw") name, []), rhs));
wenzelm@28080:     val ((def_name, [th']), lthy3) = lthy2 |> LocalTheory.note Thm.definitionK
haftmann@28703:         ((name, Code.add_default_eqn_attrib :: atts), [prove lthy2 th]);
wenzelm@18786: 
wenzelm@21705:     val lhs' = Morphism.term (LocalTheory.target_morphism lthy3) lhs;
wenzelm@26595:     val _ =
wenzelm@26595:       if not do_print then ()
wenzelm@26595:       else print_consts lthy3 (member (op =) (Term.add_frees lhs' [])) [(x, T)];
wenzelm@28080:   in ((lhs, (def_name, th')), lthy3) end;
wenzelm@18786: 
wenzelm@26595: val definition = gen_def false check_free_specification;
wenzelm@26595: val definition_cmd = gen_def true read_free_specification;
wenzelm@18786: 
wenzelm@19080: 
wenzelm@19080: (* abbreviation *)
wenzelm@19080: 
wenzelm@26595: fun gen_abbrev do_print prep mode (raw_var, raw_prop) lthy =
wenzelm@19080:   let
wenzelm@21705:     val ((vars, [(_, [prop])]), _) =
wenzelm@21705:       prep (the_list raw_var) [(("", []), [raw_prop])]
wenzelm@24676:         (lthy |> ProofContext.set_mode ProofContext.mode_abbrev);
wenzelm@21705:     val ((x, T), rhs) = LocalDefs.abs_def (#2 (LocalDefs.cert_def lthy prop));
wenzelm@28080:     val var =
wenzelm@28080:       (case vars of
haftmann@28965:         [] => (Binding.name x, NoSyn)
wenzelm@28080:       | [((b, _), mx)] =>
wenzelm@28080:           let
haftmann@29006:             val y = Binding.base_name b;
wenzelm@28080:             val _ = x = y orelse
wenzelm@28080:               error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y ^
haftmann@28941:                 Position.str_of (Binding.pos_of b));
wenzelm@28080:           in (b, mx) end);
wenzelm@21705:     val lthy' = lthy
wenzelm@24986:       |> ProofContext.set_syntax_mode mode    (* FIXME ?!? *)
wenzelm@28080:       |> LocalTheory.abbrev mode (var, rhs) |> snd
wenzelm@21705:       |> ProofContext.restore_syntax_mode lthy;
wenzelm@24724: 
wenzelm@26595:     val _ = if not do_print then () else print_consts lthy' (K false) [(x, T)];
wenzelm@21532:   in lthy' end;
wenzelm@19080: 
wenzelm@26595: val abbreviation = gen_abbrev false check_free_specification;
wenzelm@26595: val abbreviation_cmd = gen_abbrev true read_free_specification;
wenzelm@19080: 
wenzelm@19664: 
wenzelm@21230: (* notation *)
wenzelm@19664: 
wenzelm@24949: fun gen_notation prep_const add mode args lthy =
wenzelm@25371:   lthy |> LocalTheory.notation add mode (map (apfst (prep_const lthy)) args);
wenzelm@19664: 
wenzelm@24927: val notation = gen_notation (K I);
wenzelm@24927: val notation_cmd = gen_notation ProofContext.read_const;
wenzelm@19664: 
wenzelm@20914: 
wenzelm@21036: (* fact statements *)
wenzelm@20914: 
wenzelm@26345: fun gen_theorems prep_fact prep_att kind raw_facts lthy =
wenzelm@20914:   let
wenzelm@20914:     val attrib = prep_att (ProofContext.theory_of lthy);
wenzelm@20914:     val facts = raw_facts |> map (fn ((name, atts), bs) =>
wenzelm@20914:       ((name, map attrib atts),
wenzelm@26345:         bs |> map (fn (b, more_atts) => (prep_fact lthy b, map attrib more_atts))));
wenzelm@21435:     val (res, lthy') = lthy |> LocalTheory.notes kind facts;
wenzelm@28093:     val _ = ProofDisplay.print_results true lthy' ((kind, ""), res);
wenzelm@20914:   in (res, lthy') end;
wenzelm@20914: 
wenzelm@24927: val theorems = gen_theorems (K I) (K I);
wenzelm@26345: val theorems_cmd = gen_theorems ProofContext.get_fact Attrib.intern_src;
wenzelm@20914: 
wenzelm@21036: 
wenzelm@21230: (* complex goal statements *)
wenzelm@21036: 
wenzelm@21036: local
wenzelm@21036: 
wenzelm@21450: fun subtract_prems ctxt1 ctxt2 =
wenzelm@21450:   Library.drop (length (Assumption.prems_of ctxt1), Assumption.prems_of ctxt2);
wenzelm@21450: 
wenzelm@21236: fun prep_statement prep_att prep_stmt elems concl ctxt =
wenzelm@21236:   (case concl of
wenzelm@21236:     Element.Shows shows =>
wenzelm@21230:       let
ballarin@28880:         val (propp, elems_ctxt) = prep_stmt elems (map snd shows) ctxt;
ballarin@28877:         val prems = subtract_prems ctxt elems_ctxt;
wenzelm@21450:         val stmt = Attrib.map_specs prep_att (map fst shows ~~ propp);
wenzelm@21370:         val goal_ctxt = fold (fold (Variable.auto_fixes o fst)) propp elems_ctxt;
wenzelm@21450:       in ((prems, stmt, []), goal_ctxt) end
wenzelm@21236:   | Element.Obtains obtains =>
wenzelm@21230:       let
haftmann@28862:         val case_names = obtains |> map_index (fn (i, (b, _)) =>
haftmann@29006:           let val name = Binding.base_name b
wenzelm@28080:           in if name = "" then string_of_int (i + 1) else name end);
wenzelm@21236:         val constraints = obtains |> map (fn (_, (vars, _)) =>
ballarin@28710:           Element.Constrains
haftmann@29006:             (vars |> map_filter (fn (x, SOME T) => SOME (Binding.base_name x, T) | _ => NONE)));
wenzelm@21036: 
wenzelm@21236:         val raw_propp = obtains |> map (fn (_, (_, props)) => map (rpair []) props);
ballarin@28880:         val (propp, elems_ctxt) = prep_stmt (elems @ constraints) raw_propp ctxt;
wenzelm@21236: 
wenzelm@21236:         val thesis = ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
wenzelm@21036: 
wenzelm@21236:         fun assume_case ((name, (vars, _)), asms) ctxt' =
wenzelm@21236:           let
wenzelm@28080:             val bs = map fst vars;
haftmann@29006:             val xs = map Binding.base_name bs;
wenzelm@21236:             val props = map fst asms;
wenzelm@28080:             val (Ts, _) = ctxt'
wenzelm@21236:               |> fold Variable.declare_term props
wenzelm@21236:               |> fold_map ProofContext.inferred_param xs;
wenzelm@28080:             val asm = Term.list_all_free (xs ~~ Ts, Logic.list_implies (props, thesis));
wenzelm@21236:           in
wenzelm@28080:             ctxt' |> (snd o ProofContext.add_fixes_i (map (fn b => (b, NONE, NoSyn)) bs));
wenzelm@21370:             ctxt' |> Variable.auto_fixes asm
wenzelm@21236:             |> ProofContext.add_assms_i Assumption.assume_export
wenzelm@21236:               [((name, [ContextRules.intro_query NONE]), [(asm, [])])]
wenzelm@21236:             |>> (fn [(_, [th])] => th)
wenzelm@21236:           end;
wenzelm@21236: 
wenzelm@21658:         val atts = map (Attrib.internal o K)
wenzelm@21236:           [RuleCases.consumes (~ (length obtains)), RuleCases.case_names case_names];
ballarin@28877:         val prems = subtract_prems ctxt elems_ctxt;
haftmann@28965:         val stmt = [((Binding.empty, atts), [(thesis, [])])];
wenzelm@21236: 
wenzelm@21236:         val (facts, goal_ctxt) = elems_ctxt
haftmann@28965:           |> (snd o ProofContext.add_fixes_i [(Binding.name AutoBind.thesisN, NONE, NoSyn)])
wenzelm@21236:           |> fold_map assume_case (obtains ~~ propp)
wenzelm@21435:           |-> (fn ths => ProofContext.note_thmss_i Thm.assumptionK
haftmann@28965:                 [((Binding.name Obtain.thatN, []), [(ths, [])])] #> #2 #> pair ths);
wenzelm@21450:       in ((prems, stmt, facts), goal_ctxt) end);
wenzelm@21036: 
berghofe@24452: structure TheoremHook = GenericDataFun
berghofe@24452: (
berghofe@24452:   type T = ((bool -> Proof.state -> Proof.state) * stamp) list;
berghofe@24452:   val empty = [];
berghofe@24452:   val extend = I;
wenzelm@24464:   fun merge _ hooks : T = Library.merge (eq_snd op =) hooks;
berghofe@24452: );
berghofe@24452: 
wenzelm@21036: fun gen_theorem prep_att prep_stmt
wenzelm@28858:     kind before_qed after_qed (name, raw_atts) raw_elems raw_concl int lthy =
wenzelm@21036:   let
wenzelm@28858:     val _ = LocalTheory.affirm lthy;
wenzelm@28858:     val thy = ProofContext.theory_of lthy;
wenzelm@21036: 
wenzelm@21435:     val attrib = prep_att thy;
wenzelm@21435:     val atts = map attrib raw_atts;
ballarin@28710:     val elems = raw_elems |> map (Element.map_ctxt_attrib attrib);
wenzelm@21450:     val ((prems, stmt, facts), goal_ctxt) =
ballarin@28880:       prep_statement attrib prep_stmt elems raw_concl lthy;
wenzelm@21036: 
wenzelm@21036:     fun after_qed' results goal_ctxt' =
wenzelm@21602:       let val results' =
wenzelm@21602:         burrow (map Goal.norm_result o ProofContext.export goal_ctxt' lthy) results
wenzelm@21602:       in
wenzelm@21036:         lthy
wenzelm@21435:         |> LocalTheory.notes kind (map2 (fn (a, _) => fn ths => (a, [(ths, [])])) stmt results')
wenzelm@21036:         |> (fn (res, lthy') =>
haftmann@28965:           if Binding.is_empty name andalso null atts then
wenzelm@28093:             (ProofDisplay.print_results true lthy' ((kind, ""), res); lthy')
wenzelm@28080:           else
wenzelm@28080:             let
wenzelm@28080:               val ([(res_name, _)], lthy'') = lthy'
wenzelm@28080:                 |> LocalTheory.notes kind [((name, atts), [(maps #2 res, [])])];
wenzelm@28093:               val _ = ProofDisplay.print_results true lthy' ((kind, res_name), res);
wenzelm@28080:             in lthy'' end)
wenzelm@21036:         |> after_qed results'
wenzelm@21036:       end;
wenzelm@21036:   in
wenzelm@21036:     goal_ctxt
wenzelm@28080:     |> ProofContext.note_thmss_i Thm.assumptionK
haftmann@28965:       [((Binding.name AutoBind.assmsN, []), [(prems, [])])]
wenzelm@21450:     |> snd
wenzelm@21435:     |> Proof.theorem_i before_qed after_qed' (map snd stmt)
wenzelm@24557:     |> Proof.refine_insert facts
wenzelm@24542:     |> Library.apply (map (fn (f, _) => f int) (rev (TheoremHook.get (Context.Proof goal_ctxt))))
wenzelm@21036:   end;
wenzelm@21036: 
wenzelm@21230: in
wenzelm@21230: 
ballarin@29249: val theorem = gen_theorem (K I) Expression.cert_statement;
ballarin@29249: val theorem_cmd = gen_theorem Attrib.intern_src Expression.read_statement;
wenzelm@21036: 
berghofe@24452: fun add_theorem_hook f = TheoremHook.map (cons (f, stamp ()));
berghofe@24452: 
wenzelm@18620: end;
wenzelm@21036: 
wenzelm@21036: end;