wenzelm@24830: (*  Title:      Tools/induct.ML
wenzelm@24830:     ID:         $Id$
wenzelm@24830:     Author:     Markus Wenzel, TU Muenchen
wenzelm@24830: 
wenzelm@26924: Proof by cases, induction, and coinduction.
wenzelm@24830: *)
wenzelm@24830: 
wenzelm@24830: signature INDUCT_DATA =
wenzelm@24830: sig
wenzelm@24830:   val cases_default: thm
wenzelm@24830:   val atomize: thm list
wenzelm@24830:   val rulify: thm list
wenzelm@24830:   val rulify_fallback: thm list
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: signature INDUCT =
wenzelm@24830: sig
wenzelm@24830:   (*rule declarations*)
wenzelm@24830:   val vars_of: term -> term list
wenzelm@24830:   val dest_rules: Proof.context ->
wenzelm@24861:     {type_cases: (string * thm) list, pred_cases: (string * thm) list,
wenzelm@24861:       type_induct: (string * thm) list, pred_induct: (string * thm) list,
wenzelm@24861:       type_coinduct: (string * thm) list, pred_coinduct: (string * thm) list}
wenzelm@24830:   val print_rules: Proof.context -> unit
wenzelm@24830:   val lookup_casesT: Proof.context -> string -> thm option
wenzelm@24861:   val lookup_casesP: Proof.context -> string -> thm option
wenzelm@24830:   val lookup_inductT: Proof.context -> string -> thm option
wenzelm@24861:   val lookup_inductP: Proof.context -> string -> thm option
wenzelm@24830:   val lookup_coinductT: Proof.context -> string -> thm option
wenzelm@24861:   val lookup_coinductP: Proof.context -> string -> thm option
wenzelm@24830:   val find_casesT: Proof.context -> typ -> thm list
wenzelm@24861:   val find_casesP: Proof.context -> term -> thm list
wenzelm@24830:   val find_inductT: Proof.context -> typ -> thm list
wenzelm@24861:   val find_inductP: Proof.context -> term -> thm list
wenzelm@24830:   val find_coinductT: Proof.context -> typ -> thm list
wenzelm@24861:   val find_coinductP: Proof.context -> term -> thm list
wenzelm@24830:   val cases_type: string -> attribute
wenzelm@24861:   val cases_pred: string -> attribute
wenzelm@27140:   val cases_del: attribute
wenzelm@24830:   val induct_type: string -> attribute
wenzelm@24861:   val induct_pred: string -> attribute
wenzelm@27140:   val induct_del: attribute
wenzelm@24830:   val coinduct_type: string -> attribute
wenzelm@24861:   val coinduct_pred: string -> attribute
wenzelm@27140:   val coinduct_del: attribute
wenzelm@24830:   val casesN: string
wenzelm@24830:   val inductN: string
wenzelm@24830:   val coinductN: string
wenzelm@24830:   val typeN: string
wenzelm@24861:   val predN: string
wenzelm@24830:   val setN: string
wenzelm@24830:   (*proof methods*)
wenzelm@24830:   val fix_tac: Proof.context -> int -> (string * typ) list -> int -> tactic
wenzelm@24830:   val add_defs: (string option * term) option list -> Proof.context ->
wenzelm@24830:     (term option list * thm list) * Proof.context
wenzelm@24830:   val atomize_term: theory -> term -> term
wenzelm@24830:   val atomize_tac: int -> tactic
wenzelm@24830:   val inner_atomize_tac: int -> tactic
wenzelm@24830:   val rulified_term: thm -> theory * term
wenzelm@24830:   val rulify_tac: int -> tactic
wenzelm@24830:   val internalize: int -> thm -> thm
wenzelm@26940:   val guess_instance: Proof.context -> thm -> int -> thm -> thm Seq.seq
wenzelm@26924:   val cases_tac: Proof.context -> term option list list -> thm option ->
wenzelm@24830:     thm list -> int -> cases_tactic
wenzelm@27323:   val get_inductT: Proof.context -> term option list list -> thm list list
wenzelm@26924:   val induct_tac: Proof.context -> (string option * term) option list list ->
wenzelm@26924:     (string * typ) list list -> term option list -> thm list option ->
wenzelm@26924:     thm list -> int -> cases_tactic
wenzelm@26924:   val coinduct_tac: Proof.context -> term option list -> term option list -> thm option ->
wenzelm@26924:     thm list -> int -> cases_tactic
wenzelm@24830:   val setup: theory -> theory
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: functor InductFun(Data: INDUCT_DATA): INDUCT =
wenzelm@24830: struct
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** misc utils **)
wenzelm@24830: 
wenzelm@24830: (* encode_type -- for indexing purposes *)
wenzelm@24830: 
wenzelm@24830: fun encode_type (Type (c, Ts)) = Term.list_comb (Const (c, dummyT), map encode_type Ts)
wenzelm@24830:   | encode_type (TFree (a, _)) = Free (a, dummyT)
wenzelm@24830:   | encode_type (TVar (a, _)) = Var (a, dummyT);
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* variables -- ordered left-to-right, preferring right *)
wenzelm@24830: 
wenzelm@24830: fun vars_of tm =
wenzelm@24830:   rev (distinct (op =) (Term.fold_aterms (fn (t as Var _) => cons t | _ => I) tm []));
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: val mk_var = encode_type o #2 o Term.dest_Var;
wenzelm@24830: 
wenzelm@24830: fun concl_var which thm = mk_var (which (vars_of (Thm.concl_of thm))) handle Empty =>
wenzelm@24830:   raise THM ("No variables in conclusion of rule", 0, [thm]);
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@24830: fun left_var_prem thm = mk_var (hd (vars_of (hd (Thm.prems_of thm)))) handle Empty =>
wenzelm@24830:   raise THM ("No variables in major premise of rule", 0, [thm]);
wenzelm@24830: 
wenzelm@24830: val left_var_concl = concl_var hd;
wenzelm@24830: val right_var_concl = concl_var List.last;
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** induct data **)
wenzelm@24830: 
wenzelm@24830: (* rules *)
wenzelm@24830: 
wenzelm@24830: type rules = (string * thm) NetRules.T;
wenzelm@24830: 
wenzelm@24830: val init_rules =
wenzelm@24830:   NetRules.init (fn ((s1: string, th1), (s2, th2)) => s1 = s2 andalso
wenzelm@24830:     Thm.eq_thm_prop (th1, th2));
wenzelm@24830: 
wenzelm@27140: fun filter_rules (rs: rules) th =
wenzelm@27140:   filter (fn (_, th') => Thm.eq_thm_prop (th, th')) (NetRules.rules rs);
wenzelm@27140: 
wenzelm@24830: fun lookup_rule (rs: rules) = AList.lookup (op =) (NetRules.rules rs);
wenzelm@24830: 
wenzelm@24830: fun pretty_rules ctxt kind rs =
wenzelm@24830:   let val thms = map snd (NetRules.rules rs)
wenzelm@24830:   in Pretty.big_list kind (map (ProofContext.pretty_thm ctxt) thms) end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* context data *)
wenzelm@24830: 
wenzelm@27140: structure InductData = GenericDataFun
wenzelm@24830: (
wenzelm@24830:   type T = (rules * rules) * (rules * rules) * (rules * rules);
wenzelm@24830:   val empty =
wenzelm@24830:     ((init_rules (left_var_prem o #2), init_rules (Thm.major_prem_of o #2)),
wenzelm@24830:      (init_rules (right_var_concl o #2), init_rules (Thm.major_prem_of o #2)),
wenzelm@24830:      (init_rules (left_var_concl o #2), init_rules (Thm.concl_of o #2)));
wenzelm@24830:   val extend = I;
wenzelm@24861:   fun merge _ (((casesT1, casesP1), (inductT1, inductP1), (coinductT1, coinductP1)),
wenzelm@24861:       ((casesT2, casesP2), (inductT2, inductP2), (coinductT2, coinductP2))) =
wenzelm@24861:     ((NetRules.merge (casesT1, casesT2), NetRules.merge (casesP1, casesP2)),
wenzelm@24861:       (NetRules.merge (inductT1, inductT2), NetRules.merge (inductP1, inductP2)),
wenzelm@24861:       (NetRules.merge (coinductT1, coinductT2), NetRules.merge (coinductP1, coinductP2)));
wenzelm@24830: );
wenzelm@24830: 
wenzelm@27140: val get_local = InductData.get o Context.Proof;
wenzelm@24830: 
wenzelm@24830: fun dest_rules ctxt =
wenzelm@24861:   let val ((casesT, casesP), (inductT, inductP), (coinductT, coinductP)) = get_local ctxt in
wenzelm@24830:     {type_cases = NetRules.rules casesT,
wenzelm@24861:      pred_cases = NetRules.rules casesP,
wenzelm@24830:      type_induct = NetRules.rules inductT,
wenzelm@24861:      pred_induct = NetRules.rules inductP,
wenzelm@24830:      type_coinduct = NetRules.rules coinductT,
wenzelm@24861:      pred_coinduct = NetRules.rules coinductP}
wenzelm@24830:   end;
wenzelm@24830: 
wenzelm@24830: fun print_rules ctxt =
wenzelm@24861:   let val ((casesT, casesP), (inductT, inductP), (coinductT, coinductP)) = get_local ctxt in
wenzelm@24830:    [pretty_rules ctxt "coinduct type:" coinductT,
wenzelm@24861:     pretty_rules ctxt "coinduct pred:" coinductP,
wenzelm@24830:     pretty_rules ctxt "induct type:" inductT,
wenzelm@24861:     pretty_rules ctxt "induct pred:" inductP,
wenzelm@24830:     pretty_rules ctxt "cases type:" casesT,
wenzelm@24861:     pretty_rules ctxt "cases pred:" casesP]
wenzelm@24830:     |> Pretty.chunks |> Pretty.writeln
wenzelm@24830:   end;
wenzelm@24830: 
wenzelm@24867: val _ =
wenzelm@24830:   OuterSyntax.improper_command "print_induct_rules" "print induction and cases rules"
wenzelm@24830:     OuterKeyword.diag (Scan.succeed (Toplevel.no_timing o Toplevel.unknown_context o
wenzelm@24867:       Toplevel.keep (print_rules o Toplevel.context_of)));
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* access rules *)
wenzelm@24830: 
wenzelm@24830: val lookup_casesT = lookup_rule o #1 o #1 o get_local;
wenzelm@24861: val lookup_casesP = lookup_rule o #2 o #1 o get_local;
wenzelm@24830: val lookup_inductT = lookup_rule o #1 o #2 o get_local;
wenzelm@24861: val lookup_inductP = lookup_rule o #2 o #2 o get_local;
wenzelm@24830: val lookup_coinductT = lookup_rule o #1 o #3 o get_local;
wenzelm@24861: val lookup_coinductP = lookup_rule o #2 o #3 o get_local;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: fun find_rules which how ctxt x =
wenzelm@24830:   map snd (NetRules.retrieve (which (get_local ctxt)) (how x));
wenzelm@24830: 
wenzelm@24830: val find_casesT = find_rules (#1 o #1) encode_type;
wenzelm@24861: val find_casesP = find_rules (#2 o #1) I;
wenzelm@24830: val find_inductT = find_rules (#1 o #2) encode_type;
wenzelm@24861: val find_inductP = find_rules (#2 o #2) I;
wenzelm@24830: val find_coinductT = find_rules (#1 o #3) encode_type;
wenzelm@24861: val find_coinductP = find_rules (#2 o #3) I;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** attributes **)
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun mk_att f g name arg =
wenzelm@27140:   let val (x, thm) = g arg in (InductData.map (f (name, thm)) x, thm) end;
wenzelm@27140: 
wenzelm@27140: fun del_att which = Thm.declaration_attribute (fn th => InductData.map (which (pairself (fn rs =>
wenzelm@27140:   fold NetRules.delete (filter_rules rs th) rs))));
wenzelm@24830: 
wenzelm@24830: fun map1 f (x, y, z) = (f x, y, z);
wenzelm@24830: fun map2 f (x, y, z) = (x, f y, z);
wenzelm@24830: fun map3 f (x, y, z) = (x, y, f z);
wenzelm@24830: 
wenzelm@24830: fun add_casesT rule x = map1 (apfst (NetRules.insert rule)) x;
wenzelm@24861: fun add_casesP rule x = map1 (apsnd (NetRules.insert rule)) x;
wenzelm@24830: fun add_inductT rule x = map2 (apfst (NetRules.insert rule)) x;
wenzelm@24861: fun add_inductP rule x = map2 (apsnd (NetRules.insert rule)) x;
wenzelm@24830: fun add_coinductT rule x = map3 (apfst (NetRules.insert rule)) x;
wenzelm@24861: fun add_coinductP rule x = map3 (apsnd (NetRules.insert rule)) x;
wenzelm@24830: 
wenzelm@27140: val consumes0 = RuleCases.consumes_default 0;
wenzelm@27140: val consumes1 = RuleCases.consumes_default 1;
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@24830: val cases_type = mk_att add_casesT consumes0;
wenzelm@24861: val cases_pred = mk_att add_casesP consumes1;
wenzelm@27140: val cases_del = del_att map1;
wenzelm@27140: 
wenzelm@24830: val induct_type = mk_att add_inductT consumes0;
wenzelm@24861: val induct_pred = mk_att add_inductP consumes1;
wenzelm@27140: val induct_del = del_att map2;
wenzelm@27140: 
wenzelm@24830: val coinduct_type = mk_att add_coinductT consumes0;
wenzelm@24861: val coinduct_pred = mk_att add_coinductP consumes1;
wenzelm@27140: val coinduct_del = del_att map3;
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** attribute syntax **)
wenzelm@24830: 
wenzelm@24830: val casesN = "cases";
wenzelm@24830: val inductN = "induct";
wenzelm@24830: val coinductN = "coinduct";
wenzelm@24830: 
wenzelm@24830: val typeN = "type";
wenzelm@24861: val predN = "pred";
wenzelm@24830: val setN = "set";
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun spec k arg =
wenzelm@24830:   Scan.lift (Args.$$$ k -- Args.colon) |-- arg ||
wenzelm@24830:   Scan.lift (Args.$$$ k) >> K "";
wenzelm@24830: 
wenzelm@27140: fun attrib add_type add_pred del = Attrib.syntax
wenzelm@24861:  (spec typeN Args.tyname >> add_type ||
wenzelm@24861:   spec predN Args.const >> add_pred ||
wenzelm@27140:   spec setN Args.const >> add_pred ||
wenzelm@27140:   Scan.lift Args.del >> K del);
wenzelm@24830: 
wenzelm@27140: val cases_att = attrib cases_type cases_pred cases_del;
wenzelm@27140: val induct_att = attrib induct_type induct_pred induct_del;
wenzelm@27140: val coinduct_att = attrib coinduct_type coinduct_pred coinduct_del;
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@24830: val attrib_setup = Attrib.add_attributes
wenzelm@27140:  [(casesN, cases_att, "declaration of cases rule"),
wenzelm@27140:   (inductN, induct_att, "declaration of induction rule"),
wenzelm@27140:   (coinductN, coinduct_att, "declaration of coinduction rule")];
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** method utils **)
wenzelm@24830: 
wenzelm@24830: (* alignment *)
wenzelm@24830: 
wenzelm@24830: fun align_left msg xs ys =
wenzelm@24830:   let val m = length xs and n = length ys
wenzelm@24830:   in if m < n then error msg else (Library.take (n, xs) ~~ ys) end;
wenzelm@24830: 
wenzelm@24830: fun align_right msg xs ys =
wenzelm@24830:   let val m = length xs and n = length ys
wenzelm@24830:   in if m < n then error msg else (Library.drop (m - n, xs) ~~ ys) end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* prep_inst *)
wenzelm@24830: 
wenzelm@24830: fun prep_inst thy align tune (tm, ts) =
wenzelm@24830:   let
wenzelm@24830:     val cert = Thm.cterm_of thy;
wenzelm@24830:     fun prep_var (x, SOME t) =
wenzelm@24830:           let
wenzelm@24830:             val cx = cert x;
wenzelm@26626:             val xT = #T (Thm.rep_cterm cx);
wenzelm@24830:             val ct = cert (tune t);
wenzelm@26626:             val tT = Thm.ctyp_of_term ct;
wenzelm@24830:           in
wenzelm@26626:             if Type.could_unify (Thm.typ_of tT, xT) then SOME (cx, ct)
wenzelm@24830:             else error (Pretty.string_of (Pretty.block
wenzelm@24830:              [Pretty.str "Ill-typed instantiation:", Pretty.fbrk,
wenzelm@24830:               Display.pretty_cterm ct, Pretty.str " ::", Pretty.brk 1,
wenzelm@24830:               Display.pretty_ctyp (#T (Thm.crep_cterm ct))]))
wenzelm@24830:           end
wenzelm@24830:       | prep_var (_, NONE) = NONE;
wenzelm@24830:     val xs = vars_of tm;
wenzelm@24830:   in
wenzelm@24830:     align "Rule has fewer variables than instantiations given" xs ts
wenzelm@24830:     |> map_filter prep_var
wenzelm@24830:   end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* trace_rules *)
wenzelm@24830: 
wenzelm@24830: fun trace_rules _ kind [] = error ("Unable to figure out " ^ kind ^ " rule")
wenzelm@24830:   | trace_rules ctxt _ rules = Method.trace ctxt rules;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** cases method **)
wenzelm@24830: 
wenzelm@24830: (*
wenzelm@24830:   rule selection scheme:
wenzelm@24830:           cases         - default case split
wenzelm@24861:     `A t` cases ...     - predicate/set cases
wenzelm@24830:           cases t       - type cases
wenzelm@24830:     ...   cases ... r   - explicit rule
wenzelm@24830: *)
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun get_casesT ctxt ((SOME t :: _) :: _) = find_casesT ctxt (Term.fastype_of t)
wenzelm@24830:   | get_casesT _ _ = [];
wenzelm@24830: 
wenzelm@24861: fun get_casesP ctxt (fact :: _) = find_casesP ctxt (Thm.concl_of fact)
wenzelm@24861:   | get_casesP _ _ = [];
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@26924: fun cases_tac ctxt insts opt_rule facts =
wenzelm@24830:   let
wenzelm@24830:     val thy = ProofContext.theory_of ctxt;
wenzelm@24830:     val cert = Thm.cterm_of thy;
wenzelm@24830: 
wenzelm@24830:     fun inst_rule r =
wenzelm@24830:       if null insts then `RuleCases.get r
wenzelm@24830:       else (align_left "Rule has fewer premises than arguments given" (Thm.prems_of r) insts
wenzelm@24830:         |> maps (prep_inst thy align_left I)
wenzelm@24830:         |> Drule.cterm_instantiate) r |> pair (RuleCases.get r);
wenzelm@24830: 
wenzelm@24830:     val ruleq =
wenzelm@24830:       (case opt_rule of
wenzelm@24830:         SOME r => Seq.single (inst_rule r)
wenzelm@24830:       | NONE =>
wenzelm@24861:           (get_casesP ctxt facts @ get_casesT ctxt insts @ [Data.cases_default])
wenzelm@24830:           |> tap (trace_rules ctxt casesN)
wenzelm@24830:           |> Seq.of_list |> Seq.maps (Seq.try inst_rule));
wenzelm@24830:   in
wenzelm@24830:     fn i => fn st =>
wenzelm@24830:       ruleq
wenzelm@24830:       |> Seq.maps (RuleCases.consume [] facts)
wenzelm@24830:       |> Seq.maps (fn ((cases, (_, more_facts)), rule) =>
wenzelm@26924:         CASES (RuleCases.make_common false (thy, Thm.prop_of rule) cases)
wenzelm@24830:           (Method.insert_tac more_facts i THEN Tactic.rtac rule i) st)
wenzelm@24830:   end;
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** induct method **)
wenzelm@24830: 
wenzelm@24830: val conjunction_congs = [@{thm Pure.all_conjunction}, @{thm imp_conjunction}];
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* atomize *)
wenzelm@24830: 
wenzelm@24830: fun atomize_term thy =
wenzelm@24830:   MetaSimplifier.rewrite_term thy Data.atomize []
wenzelm@24830:   #> ObjectLogic.drop_judgment thy;
wenzelm@24830: 
wenzelm@24830: val atomize_cterm = MetaSimplifier.rewrite true Data.atomize;
wenzelm@24830: 
wenzelm@24830: val atomize_tac = Simplifier.rewrite_goal_tac Data.atomize;
wenzelm@24830: 
wenzelm@24830: val inner_atomize_tac =
wenzelm@24830:   Simplifier.rewrite_goal_tac (map Thm.symmetric conjunction_congs) THEN' atomize_tac;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* rulify *)
wenzelm@24830: 
wenzelm@24830: fun rulify_term thy =
wenzelm@24830:   MetaSimplifier.rewrite_term thy (Data.rulify @ conjunction_congs) [] #>
wenzelm@24830:   MetaSimplifier.rewrite_term thy Data.rulify_fallback [];
wenzelm@24830: 
wenzelm@24830: fun rulified_term thm =
wenzelm@24830:   let
wenzelm@24830:     val thy = Thm.theory_of_thm thm;
wenzelm@24830:     val rulify = rulify_term thy;
wenzelm@24830:     val (As, B) = Logic.strip_horn (Thm.prop_of thm);
wenzelm@24830:   in (thy, Logic.list_implies (map rulify As, rulify B)) end;
wenzelm@24830: 
wenzelm@24830: val rulify_tac =
wenzelm@24830:   Simplifier.rewrite_goal_tac (Data.rulify @ conjunction_congs) THEN'
wenzelm@24830:   Simplifier.rewrite_goal_tac Data.rulify_fallback THEN'
wenzelm@24830:   Goal.conjunction_tac THEN_ALL_NEW
wenzelm@24830:   (Simplifier.rewrite_goal_tac [@{thm Pure.conjunction_imp}] THEN' Goal.norm_hhf_tac);
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* prepare rule *)
wenzelm@24830: 
wenzelm@24830: fun rule_instance thy inst rule =
wenzelm@24830:   Drule.cterm_instantiate (prep_inst thy align_left I (Thm.prop_of rule, inst)) rule;
wenzelm@24830: 
wenzelm@24830: fun internalize k th =
wenzelm@24830:   th |> Thm.permute_prems 0 k
wenzelm@24830:   |> Conv.fconv_rule (Conv.concl_conv (Thm.nprems_of th - k) atomize_cterm);
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* guess rule instantiation -- cannot handle pending goal parameters *)
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun dest_env thy (env as Envir.Envir {iTs, ...}) =
wenzelm@24830:   let
wenzelm@24830:     val cert = Thm.cterm_of thy;
wenzelm@24830:     val certT = Thm.ctyp_of thy;
wenzelm@24830:     val pairs = Envir.alist_of env;
wenzelm@24830:     val ts = map (cert o Envir.norm_term env o #2 o #2) pairs;
wenzelm@24830:     val xs = map2 (curry (cert o Var)) (map #1 pairs) (map (#T o Thm.rep_cterm) ts);
wenzelm@24830:   in (map (fn (xi, (S, T)) => (certT (TVar (xi, S)), certT T)) (Vartab.dest iTs), xs ~~ ts) end;
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@26940: fun guess_instance ctxt rule i st =
wenzelm@24830:   let
wenzelm@26940:     val thy = ProofContext.theory_of ctxt;
wenzelm@26626:     val maxidx = Thm.maxidx_of st;
wenzelm@24830:     val goal = Thm.term_of (Thm.cprem_of st i);  (*exception Subscript*)
wenzelm@24830:     val params = rev (rename_wrt_term goal (Logic.strip_params goal));
wenzelm@24830:   in
wenzelm@24830:     if not (null params) then
wenzelm@24830:       (warning ("Cannot determine rule instantiation due to pending parameter(s): " ^
wenzelm@26940:         commas_quote (map (Syntax.string_of_term ctxt o Syntax.mark_boundT) params));
wenzelm@24830:       Seq.single rule)
wenzelm@24830:     else
wenzelm@24830:       let
wenzelm@24830:         val rule' = Thm.incr_indexes (maxidx + 1) rule;
wenzelm@24830:         val concl = Logic.strip_assums_concl goal;
wenzelm@24830:       in
wenzelm@24830:         Unify.smash_unifiers thy [(Thm.concl_of rule', concl)]
wenzelm@24830:           (Envir.empty (#maxidx (Thm.rep_thm rule')))
wenzelm@24830:         |> Seq.map (fn env => Drule.instantiate (dest_env thy env) rule')
wenzelm@24830:       end
wenzelm@24830:   end handle Subscript => Seq.empty;
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* special renaming of rule parameters *)
wenzelm@24830: 
wenzelm@24830: fun special_rename_params ctxt [[SOME (Free (z, Type (T, _)))]] [thm] =
wenzelm@24830:       let
wenzelm@26712:         val x = Name.clean (ProofContext.revert_skolem ctxt z);
wenzelm@24830:         fun index i [] = []
wenzelm@24830:           | index i (y :: ys) =
wenzelm@24830:               if x = y then x ^ string_of_int i :: index (i + 1) ys
wenzelm@24830:               else y :: index i ys;
wenzelm@24830:         fun rename_params [] = []
wenzelm@24830:           | rename_params ((y, Type (U, _)) :: ys) =
wenzelm@24830:               (if U = T then x else y) :: rename_params ys
wenzelm@24830:           | rename_params ((y, _) :: ys) = y :: rename_params ys;
wenzelm@24830:         fun rename_asm A =
wenzelm@24830:           let
wenzelm@24830:             val xs = rename_params (Logic.strip_params A);
wenzelm@24830:             val xs' =
wenzelm@24830:               (case List.filter (equal x) xs of
wenzelm@24830:                 [] => xs | [_] => xs | _ => index 1 xs);
wenzelm@24830:           in Logic.list_rename_params (xs', A) end;
wenzelm@24830:         fun rename_prop p =
wenzelm@24830:           let val (As, C) = Logic.strip_horn p
wenzelm@24830:           in Logic.list_implies (map rename_asm As, C) end;
wenzelm@24830:         val cp' = cterm_fun rename_prop (Thm.cprop_of thm);
wenzelm@24830:         val thm' = Thm.equal_elim (Thm.reflexive cp') thm;
wenzelm@24830:       in [RuleCases.save thm thm'] end
wenzelm@24830:   | special_rename_params _ _ ths = ths;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* fix_tac *)
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun goal_prefix k ((c as Const ("all", _)) $ Abs (a, T, B)) = c $ Abs (a, T, goal_prefix k B)
wenzelm@24830:   | goal_prefix 0 _ = Term.dummy_pattern propT
wenzelm@24830:   | goal_prefix k ((c as Const ("==>", _)) $ A $ B) = c $ A $ goal_prefix (k - 1) B
wenzelm@24830:   | goal_prefix _ _ = Term.dummy_pattern propT;
wenzelm@24830: 
wenzelm@24830: fun goal_params k (Const ("all", _) $ Abs (_, _, B)) = goal_params k B + 1
wenzelm@24830:   | goal_params 0 _ = 0
wenzelm@24830:   | goal_params k (Const ("==>", _) $ _ $ B) = goal_params (k - 1) B
wenzelm@24830:   | goal_params _ _ = 0;
wenzelm@24830: 
wenzelm@24830: fun meta_spec_tac ctxt n (x, T) = SUBGOAL (fn (goal, i) =>
wenzelm@24830:   let
wenzelm@24830:     val thy = ProofContext.theory_of ctxt;
wenzelm@24830:     val cert = Thm.cterm_of thy;
wenzelm@24830:     val certT = Thm.ctyp_of thy;
wenzelm@24830: 
wenzelm@24830:     val v = Free (x, T);
wenzelm@24830:     fun spec_rule prfx (xs, body) =
wenzelm@24830:       @{thm Pure.meta_spec}
wenzelm@26712:       |> Thm.rename_params_rule ([Name.clean (ProofContext.revert_skolem ctxt x)], 1)
wenzelm@24830:       |> Thm.lift_rule (cert prfx)
wenzelm@24830:       |> `(Thm.prop_of #> Logic.strip_assums_concl)
wenzelm@24830:       |-> (fn pred $ arg =>
wenzelm@24830:         Drule.cterm_instantiate
wenzelm@24830:           [(cert (Term.head_of pred), cert (Logic.rlist_abs (xs, body))),
wenzelm@24830:            (cert (Term.head_of arg), cert (Logic.rlist_abs (xs, v)))]);
wenzelm@24830: 
wenzelm@24830:     fun goal_concl k xs (Const ("all", _) $ Abs (a, T, B)) = goal_concl k ((a, T) :: xs) B
wenzelm@24830:       | goal_concl 0 xs B =
wenzelm@24830:           if not (Term.exists_subterm (fn t => t aconv v) B) then NONE
wenzelm@24830:           else SOME (xs, Term.absfree (x, T, Term.incr_boundvars 1 B))
wenzelm@24830:       | goal_concl k xs (Const ("==>", _) $ _ $ B) = goal_concl (k - 1) xs B
wenzelm@24830:       | goal_concl _ _ _ = NONE;
wenzelm@24830:   in
wenzelm@24830:     (case goal_concl n [] goal of
wenzelm@24830:       SOME concl =>
wenzelm@24830:         (compose_tac (false, spec_rule (goal_prefix n goal) concl, 1) THEN' rtac asm_rl) i
wenzelm@24830:     | NONE => all_tac)
wenzelm@24830:   end);
wenzelm@24830: 
wenzelm@24832: fun miniscope_tac p = CONVERSION o
wenzelm@26568:   Conv.params_conv p (K (MetaSimplifier.rewrite true [Thm.symmetric Drule.norm_hhf_eq]));
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@24830: fun fix_tac _ _ [] = K all_tac
wenzelm@24830:   | fix_tac ctxt n xs = SUBGOAL (fn (goal, i) =>
wenzelm@24830:      (EVERY' (map (meta_spec_tac ctxt n) xs) THEN'
wenzelm@24832:       (miniscope_tac (goal_params n goal) ctxt)) i);
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* add_defs *)
wenzelm@24830: 
wenzelm@24830: fun add_defs def_insts =
wenzelm@24830:   let
wenzelm@24830:     fun add (SOME (SOME x, t)) ctxt =
wenzelm@24830:           let val ([(lhs, (_, th))], ctxt') = LocalDefs.add_defs [((x, NoSyn), (("", []), t))] ctxt
wenzelm@24830:           in ((SOME lhs, [th]), ctxt') end
wenzelm@24830:       | add (SOME (NONE, t)) ctxt = ((SOME t, []), ctxt)
wenzelm@24830:       | add NONE ctxt = ((NONE, []), ctxt);
wenzelm@24830:   in fold_map add def_insts #> apfst (split_list #> apsnd flat) end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (* induct_tac *)
wenzelm@24830: 
wenzelm@24830: (*
wenzelm@24830:   rule selection scheme:
wenzelm@24861:     `A x` induct ...     - predicate/set induction
wenzelm@24830:           induct x       - type induction
wenzelm@24830:     ...   induct ... r   - explicit rule
wenzelm@24830: *)
wenzelm@24830: 
wenzelm@24830: fun get_inductT ctxt insts =
wenzelm@27323:   fold_rev multiply (insts |> map
wenzelm@27323:       ((fn [] => NONE | ts => List.last ts) #>
wenzelm@27323:         (fn NONE => TVar (("'a", 0), []) | SOME t => Term.fastype_of t) #>
wenzelm@27323:         find_inductT ctxt)) [[]]
wenzelm@24830:   |> filter_out (forall PureThy.is_internal);
wenzelm@24830: 
wenzelm@24861: fun get_inductP ctxt (fact :: _) = map single (find_inductP ctxt (Thm.concl_of fact))
wenzelm@24861:   | get_inductP _ _ = [];
wenzelm@24830: 
wenzelm@26924: fun induct_tac ctxt def_insts arbitrary taking opt_rule facts =
wenzelm@24830:   let
wenzelm@24830:     val thy = ProofContext.theory_of ctxt;
wenzelm@24830:     val cert = Thm.cterm_of thy;
wenzelm@24830: 
wenzelm@24830:     val ((insts, defs), defs_ctxt) = fold_map add_defs def_insts ctxt |>> split_list;
wenzelm@24830:     val atomized_defs = map (map (Conv.fconv_rule ObjectLogic.atomize)) defs;
wenzelm@24830: 
wenzelm@24830:     fun inst_rule (concls, r) =
wenzelm@24830:       (if null insts then `RuleCases.get r
wenzelm@24830:        else (align_left "Rule has fewer conclusions than arguments given"
wenzelm@24830:           (map Logic.strip_imp_concl (Logic.dest_conjunctions (Thm.concl_of r))) insts
wenzelm@24830:         |> maps (prep_inst thy align_right (atomize_term thy))
wenzelm@24830:         |> Drule.cterm_instantiate) r |> pair (RuleCases.get r))
wenzelm@24830:       |> (fn ((cases, consumes), th) => (((cases, concls), consumes), th));
wenzelm@24830: 
wenzelm@24830:     val ruleq =
wenzelm@24830:       (case opt_rule of
wenzelm@24830:         SOME rs => Seq.single (inst_rule (RuleCases.strict_mutual_rule ctxt rs))
wenzelm@24830:       | NONE =>
wenzelm@24861:           (get_inductP ctxt facts @
wenzelm@24830:             map (special_rename_params defs_ctxt insts) (get_inductT ctxt insts))
wenzelm@24830:           |> map_filter (RuleCases.mutual_rule ctxt)
wenzelm@24830:           |> tap (trace_rules ctxt inductN o map #2)
wenzelm@24830:           |> Seq.of_list |> Seq.maps (Seq.try inst_rule));
wenzelm@24830: 
wenzelm@24830:     fun rule_cases rule =
wenzelm@26924:       RuleCases.make_nested false (Thm.prop_of rule) (rulified_term rule);
wenzelm@24830:   in
wenzelm@24830:     (fn i => fn st =>
wenzelm@24830:       ruleq
wenzelm@24830:       |> Seq.maps (RuleCases.consume (flat defs) facts)
wenzelm@24830:       |> Seq.maps (fn (((cases, concls), (more_consumes, more_facts)), rule) =>
wenzelm@24830:         (PRECISE_CONJUNCTS (length concls) (ALLGOALS (fn j =>
wenzelm@24830:           (CONJUNCTS (ALLGOALS
wenzelm@24830:             (Method.insert_tac (more_facts @ nth_list atomized_defs (j - 1))
wenzelm@24830:               THEN' fix_tac defs_ctxt
wenzelm@24830:                 (nth concls (j - 1) + more_consumes)
wenzelm@24830:                 (nth_list arbitrary (j - 1))))
wenzelm@24830:           THEN' inner_atomize_tac) j))
wenzelm@24830:         THEN' atomize_tac) i st |> Seq.maps (fn st' =>
wenzelm@26940:             guess_instance ctxt (internalize more_consumes rule) i st'
wenzelm@24865:             |> Seq.map (rule_instance thy (burrow_options (Variable.polymorphic ctxt) taking))
wenzelm@24830:             |> Seq.maps (fn rule' =>
wenzelm@24830:               CASES (rule_cases rule' cases)
wenzelm@24830:                 (Tactic.rtac rule' i THEN
wenzelm@24830:                   PRIMITIVE (singleton (ProofContext.export defs_ctxt ctxt))) st'))))
wenzelm@24830:     THEN_ALL_NEW_CASES rulify_tac
wenzelm@24830:   end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** coinduct method **)
wenzelm@24830: 
wenzelm@24830: (*
wenzelm@24830:   rule selection scheme:
wenzelm@24861:     goal "A x" coinduct ...   - predicate/set coinduction
wenzelm@24830:                coinduct x     - type coinduction
wenzelm@24830:                coinduct ... r - explicit rule
wenzelm@24830: *)
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun get_coinductT ctxt (SOME t :: _) = find_coinductT ctxt (Term.fastype_of t)
wenzelm@24830:   | get_coinductT _ _ = [];
wenzelm@24830: 
wenzelm@24861: fun get_coinductP ctxt goal = find_coinductP ctxt (Logic.strip_assums_concl goal);
wenzelm@24861: 
wenzelm@24861: fun main_prop_of th =
wenzelm@24861:   if RuleCases.get_consumes th > 0 then Thm.major_prem_of th else Thm.concl_of th;
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@26924: fun coinduct_tac ctxt inst taking opt_rule facts =
wenzelm@24830:   let
wenzelm@24830:     val thy = ProofContext.theory_of ctxt;
wenzelm@24830:     val cert = Thm.cterm_of thy;
wenzelm@24830: 
wenzelm@24830:     fun inst_rule r =
wenzelm@24830:       if null inst then `RuleCases.get r
wenzelm@24861:       else Drule.cterm_instantiate (prep_inst thy align_right I (main_prop_of r, inst)) r
wenzelm@24830:         |> pair (RuleCases.get r);
wenzelm@24830: 
wenzelm@24830:     fun ruleq goal =
wenzelm@24830:       (case opt_rule of
wenzelm@24830:         SOME r => Seq.single (inst_rule r)
wenzelm@24830:       | NONE =>
wenzelm@24861:           (get_coinductP ctxt goal @ get_coinductT ctxt inst)
wenzelm@24830:           |> tap (trace_rules ctxt coinductN)
wenzelm@24830:           |> Seq.of_list |> Seq.maps (Seq.try inst_rule));
wenzelm@24830:   in
wenzelm@24830:     SUBGOAL_CASES (fn (goal, i) => fn st =>
wenzelm@24830:       ruleq goal
wenzelm@24830:       |> Seq.maps (RuleCases.consume [] facts)
wenzelm@24830:       |> Seq.maps (fn ((cases, (_, more_facts)), rule) =>
wenzelm@26940:         guess_instance ctxt rule i st
wenzelm@24865:         |> Seq.map (rule_instance thy (burrow_options (Variable.polymorphic ctxt) taking))
wenzelm@24830:         |> Seq.maps (fn rule' =>
wenzelm@26924:           CASES (RuleCases.make_common false (thy, Thm.prop_of rule') cases)
wenzelm@24830:             (Method.insert_tac more_facts i THEN Tactic.rtac rule' i) st)))
wenzelm@24830:   end;
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** concrete syntax **)
wenzelm@24830: 
wenzelm@24830: val arbitraryN = "arbitrary";
wenzelm@24830: val takingN = "taking";
wenzelm@24830: val ruleN = "rule";
wenzelm@24830: 
wenzelm@24830: local
wenzelm@24830: 
wenzelm@24830: fun single_rule [rule] = rule
wenzelm@24830:   | single_rule _ = error "Single rule expected";
wenzelm@24830: 
wenzelm@24830: fun named_rule k arg get =
wenzelm@24830:   Scan.lift (Args.$$$ k -- Args.colon) |-- Scan.repeat arg :|--
wenzelm@24830:     (fn names => Scan.peek (fn context => Scan.succeed (names |> map (fn name =>
wenzelm@24830:       (case get (Context.proof_of context) name of SOME x => x
wenzelm@24830:       | NONE => error ("No rule for " ^ k ^ " " ^ quote name))))));
wenzelm@24830: 
wenzelm@24861: fun rule get_type get_pred =
wenzelm@24830:   named_rule typeN Args.tyname get_type ||
wenzelm@24861:   named_rule predN Args.const get_pred ||
wenzelm@24861:   named_rule setN Args.const get_pred ||
wenzelm@24830:   Scan.lift (Args.$$$ ruleN -- Args.colon) |-- Attrib.thms;
wenzelm@24830: 
wenzelm@24861: val cases_rule = rule lookup_casesT lookup_casesP >> single_rule;
wenzelm@24861: val induct_rule = rule lookup_inductT lookup_inductP;
wenzelm@24861: val coinduct_rule = rule lookup_coinductT lookup_coinductP >> single_rule;
wenzelm@24830: 
wenzelm@24830: val inst = Scan.lift (Args.$$$ "_") >> K NONE || Args.term >> SOME;
wenzelm@24830: 
wenzelm@24830: val def_inst =
wenzelm@25985:   ((Scan.lift (Args.name --| (Args.$$$ "\<equiv>" || Args.$$$ "==")) >> SOME)
wenzelm@24830:       -- Args.term) >> SOME ||
wenzelm@24830:     inst >> Option.map (pair NONE);
wenzelm@24830: 
wenzelm@24830: val free = Scan.state -- Args.term >> (fn (_, Free v) => v | (context, t) =>
wenzelm@24920:   error ("Bad free variable: " ^ Syntax.string_of_term (Context.proof_of context) t));
wenzelm@24830: 
wenzelm@24830: fun unless_more_args scan = Scan.unless (Scan.lift
wenzelm@24830:   ((Args.$$$ arbitraryN || Args.$$$ takingN || Args.$$$ typeN ||
wenzelm@24861:     Args.$$$ predN || Args.$$$ setN || Args.$$$ ruleN) -- Args.colon)) scan;
wenzelm@24830: 
wenzelm@24830: val arbitrary = Scan.optional (Scan.lift (Args.$$$ arbitraryN -- Args.colon) |--
wenzelm@24830:   Args.and_list1 (Scan.repeat (unless_more_args free))) [];
wenzelm@24830: 
wenzelm@24830: val taking = Scan.optional (Scan.lift (Args.$$$ takingN -- Args.colon) |--
wenzelm@24830:   Scan.repeat1 (unless_more_args inst)) [];
wenzelm@24830: 
wenzelm@24830: in
wenzelm@24830: 
wenzelm@24830: fun cases_meth src =
wenzelm@26924:   Method.syntax (Args.and_list (Scan.repeat (unless_more_args inst)) -- Scan.option cases_rule) src
wenzelm@26924:   #> (fn ((insts, opt_rule), ctxt) =>
wenzelm@24830:     Method.METHOD_CASES (fn facts =>
wenzelm@26924:       Seq.DETERM (HEADGOAL (cases_tac ctxt insts opt_rule facts))));
wenzelm@24830: 
wenzelm@24830: fun induct_meth src =
wenzelm@26924:   Method.syntax (Args.and_list (Scan.repeat (unless_more_args def_inst)) --
wenzelm@26924:     (arbitrary -- taking -- Scan.option induct_rule)) src
wenzelm@26924:   #> (fn ((insts, ((arbitrary, taking), opt_rule)), ctxt) =>
wenzelm@24830:     Method.RAW_METHOD_CASES (fn facts =>
wenzelm@26924:       Seq.DETERM (HEADGOAL (induct_tac ctxt insts arbitrary taking opt_rule facts))));
wenzelm@24830: 
wenzelm@24830: fun coinduct_meth src =
wenzelm@26924:   Method.syntax (Scan.repeat (unless_more_args inst) -- taking -- Scan.option coinduct_rule) src
wenzelm@26924:   #> (fn (((insts, taking), opt_rule), ctxt) =>
wenzelm@24830:     Method.RAW_METHOD_CASES (fn facts =>
wenzelm@26924:       Seq.DETERM (HEADGOAL (coinduct_tac ctxt insts taking opt_rule facts))));
wenzelm@24830: 
wenzelm@24830: end;
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: 
wenzelm@24830: (** theory setup **)
wenzelm@24830: 
wenzelm@24830: val setup =
wenzelm@24830:   attrib_setup #>
wenzelm@24830:   Method.add_methods
wenzelm@24861:     [(casesN, cases_meth, "case analysis on types or predicates/sets"),
wenzelm@24861:      (inductN, induct_meth, "induction on types or predicates/sets"),
wenzelm@24861:      (coinductN, coinduct_meth, "coinduction on types or predicates/sets")];
wenzelm@24830: 
wenzelm@24830: end;