src/Pure/Isar/specification.ML
author haftmann
Wed Jan 21 16:47:32 2009 +0100 (2009-01-21)
changeset 29581 b3b33e0298eb
parent 29249 4dc278c8dc59
child 29606 fedb8be05f24
permissions -rw-r--r--
binding is alias for Binding.T
     1 (*  Title:      Pure/Isar/specification.ML
     2     ID:         $Id$
     3     Author:     Makarius
     4 
     5 Derived local theory specifications --- with type-inference and
     6 toplevel polymorphism.
     7 *)
     8 
     9 signature SPECIFICATION =
    10 sig
    11   val print_consts: local_theory -> (string * typ -> bool) -> (string * typ) list -> unit
    12   val check_specification: (binding * typ option * mixfix) list ->
    13     (Attrib.binding * term list) list list -> Proof.context ->
    14     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
    15   val read_specification: (binding * string option * mixfix) list ->
    16     (Attrib.binding * string list) list list -> Proof.context ->
    17     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
    18   val check_free_specification: (binding * typ option * mixfix) list ->
    19     (Attrib.binding * term list) list -> Proof.context ->
    20     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
    21   val read_free_specification: (binding * string option * mixfix) list ->
    22     (Attrib.binding * string list) list -> Proof.context ->
    23     (((binding * typ) * mixfix) list * (Attrib.binding * term list) list) * Proof.context
    24   val axiomatization: (binding * typ option * mixfix) list ->
    25     (Attrib.binding * term list) list -> theory ->
    26     (term list * (string * thm list) list) * theory
    27   val axiomatization_cmd: (binding * string option * mixfix) list ->
    28     (Attrib.binding * string list) list -> theory ->
    29     (term list * (string * thm list) list) * theory
    30   val definition:
    31     (binding * typ option * mixfix) option * (Attrib.binding * term) ->
    32     local_theory -> (term * (string * thm)) * local_theory
    33   val definition_cmd:
    34     (binding * string option * mixfix) option * (Attrib.binding * string) ->
    35     local_theory -> (term * (string * thm)) * local_theory
    36   val abbreviation: Syntax.mode -> (binding * typ option * mixfix) option * term ->
    37     local_theory -> local_theory
    38   val abbreviation_cmd: Syntax.mode -> (binding * string option * mixfix) option * string ->
    39     local_theory -> local_theory
    40   val notation: bool -> Syntax.mode -> (term * mixfix) list -> local_theory -> local_theory
    41   val notation_cmd: bool -> Syntax.mode -> (string * mixfix) list -> local_theory -> local_theory
    42   val theorems: string ->
    43     (Attrib.binding * (thm list * Attrib.src list) list) list ->
    44     local_theory -> (string * thm list) list * local_theory
    45   val theorems_cmd: string ->
    46     (Attrib.binding * (Facts.ref * Attrib.src list) list) list ->
    47     local_theory -> (string * thm list) list * local_theory
    48   val theorem: string -> Method.text option ->
    49     (thm list list -> local_theory -> local_theory) -> Attrib.binding ->
    50     Element.context_i list -> Element.statement_i ->
    51     bool -> local_theory -> Proof.state
    52   val theorem_cmd: string -> Method.text option ->
    53     (thm list list -> local_theory -> local_theory) -> Attrib.binding ->
    54     Element.context list -> Element.statement ->
    55     bool -> local_theory -> Proof.state
    56   val add_theorem_hook: (bool -> Proof.state -> Proof.state) -> Context.generic -> Context.generic
    57 end;
    58 
    59 structure Specification: SPECIFICATION =
    60 struct
    61 
    62 (* diagnostics *)
    63 
    64 fun print_consts _ _ [] = ()
    65   | print_consts ctxt pred cs = Pretty.writeln (ProofDisplay.pretty_consts ctxt pred cs);
    66 
    67 
    68 (* prepare specification *)
    69 
    70 local
    71 
    72 fun close_forms ctxt i xs As =
    73   let
    74     fun add_free (Free (x, _)) = if Variable.is_fixed ctxt x then I else insert (op =) x
    75       | add_free _ = I;
    76 
    77     val commons = map #1 xs;
    78     val _ =
    79       (case duplicates (op =) commons of [] => ()
    80       | dups => error ("Duplicate local variables " ^ commas_quote dups));
    81     val frees = rev ((fold o fold_aterms) add_free As (rev commons));
    82     val types = map (TypeInfer.param i o rpair []) (Name.invents Name.context Name.aT (length frees));
    83     val uniform_typing = the o AList.lookup (op =) (frees ~~ types);
    84 
    85     fun abs_body lev y (Abs (x, T, b)) = Abs (x, T, abs_body (lev + 1) y b)
    86       | abs_body lev y (t $ u) = abs_body lev y t $ abs_body lev y u
    87       | abs_body lev y (t as Free (x, T)) =
    88           if x = y then TypeInfer.constrain (uniform_typing x) (TypeInfer.constrain T (Bound lev))
    89           else t
    90       | abs_body _ _ a = a;
    91     fun close (y, U) B =
    92       let val B' = abs_body 0 y (Term.incr_boundvars 1 B)
    93       in if Term.loose_bvar1 (B', 0) then Term.all dummyT $ Abs (y, U, B') else B end;
    94     fun close_form A =
    95       let
    96         val occ_frees = rev (fold_aterms add_free A []);
    97         val bounds = xs @ map (rpair dummyT) (subtract (op =) commons occ_frees);
    98       in fold_rev close bounds A end;
    99   in map close_form As end;
   100 
   101 fun prep_spec prep_vars parse_prop prep_att do_close raw_vars raw_specss ctxt =
   102   let
   103     val thy = ProofContext.theory_of ctxt;
   104 
   105     val (vars, vars_ctxt) = ctxt |> prep_vars raw_vars;
   106     val (xs, params_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
   107 
   108     val Asss = (map o map) (map (parse_prop params_ctxt) o snd) raw_specss;
   109     val names = Variable.names_of (params_ctxt |> (fold o fold o fold) Variable.declare_term Asss)
   110       |> fold Name.declare xs;
   111     val Asss' = #1 ((fold_map o fold_map o fold_map) Term.free_dummy_patterns Asss names);
   112     val idx = (fold o fold o fold) Term.maxidx_term Asss' ~1 + 1;
   113     val specs =
   114       (if do_close then
   115         #1 (fold_map
   116             (fn Ass => fn i => (burrow (close_forms params_ctxt i []) Ass, i + 1)) Asss' idx)
   117       else Asss')
   118       |> flat |> burrow (Syntax.check_props params_ctxt);
   119     val specs_ctxt = params_ctxt |> (fold o fold) Variable.declare_term specs;
   120 
   121     val Ts = specs_ctxt |> fold_map ProofContext.inferred_param xs |> fst;
   122     val params = map2 (fn (b, _, mx) => fn T => ((b, T), mx)) vars Ts;
   123     val name_atts = map (fn ((name, atts), _) => (name, map (prep_att thy) atts)) (flat raw_specss);
   124   in ((params, name_atts ~~ specs), specs_ctxt) end;
   125 
   126 fun read_spec x = prep_spec ProofContext.read_vars Syntax.parse_prop Attrib.intern_src x;
   127 fun check_spec x = prep_spec ProofContext.cert_vars (K I) (K I) x;
   128 
   129 in
   130 
   131 fun read_specification x = read_spec true x;
   132 fun check_specification x = check_spec true x;
   133 fun read_free_specification vars specs = read_spec false vars [specs];
   134 fun check_free_specification vars specs = check_spec false vars [specs];
   135 
   136 end;
   137 
   138 
   139 (* axiomatization -- within global theory *)
   140 
   141 fun gen_axioms do_print prep raw_vars raw_specs thy =
   142   let
   143     val ((vars, specs), _) = prep raw_vars [raw_specs] (ProofContext.init thy);
   144     val xs = map (fn ((b, T), _) => (Binding.base_name b, T)) vars;
   145 
   146     (*consts*)
   147     val (consts, consts_thy) = thy |> fold_map (Theory.specify_const []) vars;
   148     val subst = Term.subst_atomic (map Free xs ~~ consts);
   149 
   150     (*axioms*)
   151     val (axioms, axioms_thy) = consts_thy |> fold_map (fn ((b, atts), props) =>
   152         fold_map Thm.add_axiom
   153           ((map o apfst) Binding.name (PureThy.name_multi (Binding.base_name b) (map subst props)))
   154         #>> (fn ths => ((b, atts), [(map Drule.standard' ths, [])]))) specs;
   155     val (facts, thy') = axioms_thy |> PureThy.note_thmss Thm.axiomK
   156       (Attrib.map_facts (Attrib.attribute_i axioms_thy) axioms);
   157     val _ =
   158       if not do_print then ()
   159       else print_consts (ProofContext.init thy') (K false) xs;
   160   in ((consts, facts), thy') end;
   161 
   162 val axiomatization = gen_axioms false check_specification;
   163 val axiomatization_cmd = gen_axioms true read_specification;
   164 
   165 
   166 (* definition *)
   167 
   168 fun gen_def do_print prep (raw_var, (raw_a, raw_prop)) lthy =
   169   let
   170     val (vars, [((raw_name, atts), [prop])]) =
   171       fst (prep (the_list raw_var) [(raw_a, [raw_prop])] lthy);
   172     val (((x, T), rhs), prove) = LocalDefs.derived_def lthy true prop;
   173     val name = Binding.map_base (Thm.def_name_optional x) raw_name;
   174     val var =
   175       (case vars of
   176         [] => (Binding.name x, NoSyn)
   177       | [((b, _), mx)] =>
   178           let
   179             val y = Binding.base_name b;
   180             val _ = x = y orelse
   181               error ("Head of definition " ^ quote x ^ " differs from declaration " ^ quote y ^
   182                 Position.str_of (Binding.pos_of b));
   183           in (b, mx) end);
   184     val ((lhs, (_, th)), lthy2) = lthy |> LocalTheory.define Thm.definitionK
   185         (var, ((Binding.map_base (suffix "_raw") name, []), rhs));
   186     val ((def_name, [th']), lthy3) = lthy2 |> LocalTheory.note Thm.definitionK
   187         ((name, Code.add_default_eqn_attrib :: atts), [prove lthy2 th]);
   188 
   189     val lhs' = Morphism.term (LocalTheory.target_morphism lthy3) lhs;
   190     val _ =
   191       if not do_print then ()
   192       else print_consts lthy3 (member (op =) (Term.add_frees lhs' [])) [(x, T)];
   193   in ((lhs, (def_name, th')), lthy3) end;
   194 
   195 val definition = gen_def false check_free_specification;
   196 val definition_cmd = gen_def true read_free_specification;
   197 
   198 
   199 (* abbreviation *)
   200 
   201 fun gen_abbrev do_print prep mode (raw_var, raw_prop) lthy =
   202   let
   203     val ((vars, [(_, [prop])]), _) =
   204       prep (the_list raw_var) [(("", []), [raw_prop])]
   205         (lthy |> ProofContext.set_mode ProofContext.mode_abbrev);
   206     val ((x, T), rhs) = LocalDefs.abs_def (#2 (LocalDefs.cert_def lthy prop));
   207     val var =
   208       (case vars of
   209         [] => (Binding.name x, NoSyn)
   210       | [((b, _), mx)] =>
   211           let
   212             val y = Binding.base_name b;
   213             val _ = x = y orelse
   214               error ("Head of abbreviation " ^ quote x ^ " differs from declaration " ^ quote y ^
   215                 Position.str_of (Binding.pos_of b));
   216           in (b, mx) end);
   217     val lthy' = lthy
   218       |> ProofContext.set_syntax_mode mode    (* FIXME ?!? *)
   219       |> LocalTheory.abbrev mode (var, rhs) |> snd
   220       |> ProofContext.restore_syntax_mode lthy;
   221 
   222     val _ = if not do_print then () else print_consts lthy' (K false) [(x, T)];
   223   in lthy' end;
   224 
   225 val abbreviation = gen_abbrev false check_free_specification;
   226 val abbreviation_cmd = gen_abbrev true read_free_specification;
   227 
   228 
   229 (* notation *)
   230 
   231 fun gen_notation prep_const add mode args lthy =
   232   lthy |> LocalTheory.notation add mode (map (apfst (prep_const lthy)) args);
   233 
   234 val notation = gen_notation (K I);
   235 val notation_cmd = gen_notation ProofContext.read_const;
   236 
   237 
   238 (* fact statements *)
   239 
   240 fun gen_theorems prep_fact prep_att kind raw_facts lthy =
   241   let
   242     val attrib = prep_att (ProofContext.theory_of lthy);
   243     val facts = raw_facts |> map (fn ((name, atts), bs) =>
   244       ((name, map attrib atts),
   245         bs |> map (fn (b, more_atts) => (prep_fact lthy b, map attrib more_atts))));
   246     val (res, lthy') = lthy |> LocalTheory.notes kind facts;
   247     val _ = ProofDisplay.print_results true lthy' ((kind, ""), res);
   248   in (res, lthy') end;
   249 
   250 val theorems = gen_theorems (K I) (K I);
   251 val theorems_cmd = gen_theorems ProofContext.get_fact Attrib.intern_src;
   252 
   253 
   254 (* complex goal statements *)
   255 
   256 local
   257 
   258 fun subtract_prems ctxt1 ctxt2 =
   259   Library.drop (length (Assumption.prems_of ctxt1), Assumption.prems_of ctxt2);
   260 
   261 fun prep_statement prep_att prep_stmt elems concl ctxt =
   262   (case concl of
   263     Element.Shows shows =>
   264       let
   265         val (propp, elems_ctxt) = prep_stmt elems (map snd shows) ctxt;
   266         val prems = subtract_prems ctxt elems_ctxt;
   267         val stmt = Attrib.map_specs prep_att (map fst shows ~~ propp);
   268         val goal_ctxt = fold (fold (Variable.auto_fixes o fst)) propp elems_ctxt;
   269       in ((prems, stmt, []), goal_ctxt) end
   270   | Element.Obtains obtains =>
   271       let
   272         val case_names = obtains |> map_index (fn (i, (b, _)) =>
   273           let val name = Binding.base_name b
   274           in if name = "" then string_of_int (i + 1) else name end);
   275         val constraints = obtains |> map (fn (_, (vars, _)) =>
   276           Element.Constrains
   277             (vars |> map_filter (fn (x, SOME T) => SOME (Binding.base_name x, T) | _ => NONE)));
   278 
   279         val raw_propp = obtains |> map (fn (_, (_, props)) => map (rpair []) props);
   280         val (propp, elems_ctxt) = prep_stmt (elems @ constraints) raw_propp ctxt;
   281 
   282         val thesis = ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
   283 
   284         fun assume_case ((name, (vars, _)), asms) ctxt' =
   285           let
   286             val bs = map fst vars;
   287             val xs = map Binding.base_name bs;
   288             val props = map fst asms;
   289             val (Ts, _) = ctxt'
   290               |> fold Variable.declare_term props
   291               |> fold_map ProofContext.inferred_param xs;
   292             val asm = Term.list_all_free (xs ~~ Ts, Logic.list_implies (props, thesis));
   293           in
   294             ctxt' |> (snd o ProofContext.add_fixes_i (map (fn b => (b, NONE, NoSyn)) bs));
   295             ctxt' |> Variable.auto_fixes asm
   296             |> ProofContext.add_assms_i Assumption.assume_export
   297               [((name, [ContextRules.intro_query NONE]), [(asm, [])])]
   298             |>> (fn [(_, [th])] => th)
   299           end;
   300 
   301         val atts = map (Attrib.internal o K)
   302           [RuleCases.consumes (~ (length obtains)), RuleCases.case_names case_names];
   303         val prems = subtract_prems ctxt elems_ctxt;
   304         val stmt = [((Binding.empty, atts), [(thesis, [])])];
   305 
   306         val (facts, goal_ctxt) = elems_ctxt
   307           |> (snd o ProofContext.add_fixes_i [(Binding.name AutoBind.thesisN, NONE, NoSyn)])
   308           |> fold_map assume_case (obtains ~~ propp)
   309           |-> (fn ths => ProofContext.note_thmss_i Thm.assumptionK
   310                 [((Binding.name Obtain.thatN, []), [(ths, [])])] #> #2 #> pair ths);
   311       in ((prems, stmt, facts), goal_ctxt) end);
   312 
   313 structure TheoremHook = GenericDataFun
   314 (
   315   type T = ((bool -> Proof.state -> Proof.state) * stamp) list;
   316   val empty = [];
   317   val extend = I;
   318   fun merge _ hooks : T = Library.merge (eq_snd op =) hooks;
   319 );
   320 
   321 fun gen_theorem prep_att prep_stmt
   322     kind before_qed after_qed (name, raw_atts) raw_elems raw_concl int lthy =
   323   let
   324     val _ = LocalTheory.affirm lthy;
   325     val thy = ProofContext.theory_of lthy;
   326 
   327     val attrib = prep_att thy;
   328     val atts = map attrib raw_atts;
   329     val elems = raw_elems |> map (Element.map_ctxt_attrib attrib);
   330     val ((prems, stmt, facts), goal_ctxt) =
   331       prep_statement attrib prep_stmt elems raw_concl lthy;
   332 
   333     fun after_qed' results goal_ctxt' =
   334       let val results' =
   335         burrow (map Goal.norm_result o ProofContext.export goal_ctxt' lthy) results
   336       in
   337         lthy
   338         |> LocalTheory.notes kind (map2 (fn (a, _) => fn ths => (a, [(ths, [])])) stmt results')
   339         |> (fn (res, lthy') =>
   340           if Binding.is_empty name andalso null atts then
   341             (ProofDisplay.print_results true lthy' ((kind, ""), res); lthy')
   342           else
   343             let
   344               val ([(res_name, _)], lthy'') = lthy'
   345                 |> LocalTheory.notes kind [((name, atts), [(maps #2 res, [])])];
   346               val _ = ProofDisplay.print_results true lthy' ((kind, res_name), res);
   347             in lthy'' end)
   348         |> after_qed results'
   349       end;
   350   in
   351     goal_ctxt
   352     |> ProofContext.note_thmss_i Thm.assumptionK
   353       [((Binding.name AutoBind.assmsN, []), [(prems, [])])]
   354     |> snd
   355     |> Proof.theorem_i before_qed after_qed' (map snd stmt)
   356     |> Proof.refine_insert facts
   357     |> Library.apply (map (fn (f, _) => f int) (rev (TheoremHook.get (Context.Proof goal_ctxt))))
   358   end;
   359 
   360 in
   361 
   362 val theorem = gen_theorem (K I) Expression.cert_statement;
   363 val theorem_cmd = gen_theorem Attrib.intern_src Expression.read_statement;
   364 
   365 fun add_theorem_hook f = TheoremHook.map (cons (f, stamp ()));
   366 
   367 end;
   368 
   369 end;