wenzelm@7674: (*  Title:      Pure/Isar/obtain.ML
wenzelm@7674:     ID:         $Id$
wenzelm@7674:     Author:     Markus Wenzel, TU Muenchen
wenzelm@7674: 
wenzelm@17858: The 'obtain' and 'guess' language elements -- generalized existence at
wenzelm@17858: the level of proof texts: 'obtain' involves a proof that certain
wenzelm@17858: fixes/assumes may be introduced into the present context; 'guess' is
wenzelm@17858: similar, but derives these elements from the course of reasoning!
wenzelm@7674: 
wenzelm@9468:   <chain_facts>
wenzelm@9468:   obtain x where "P x" <proof> ==
wenzelm@7674: 
wenzelm@12970:   have "!!thesis. (!!x. P x ==> thesis) ==> thesis"
wenzelm@12970:   proof succeed
wenzelm@9468:     fix thesis
wenzelm@12970:     assume that [intro?]: "!!x. P x ==> thesis"
wenzelm@12970:     <chain_facts> show thesis <proof (insert that)>
wenzelm@12970:   qed
wenzelm@10379:   fix x assm (obtained) "P x"
wenzelm@17858: 
wenzelm@17858: 
wenzelm@17858:   <chain_facts>
wenzelm@17858:   guess x <proof body> <proof end> ==
wenzelm@17858: 
wenzelm@17858:   {
wenzelm@17858:     fix thesis
wenzelm@17858:     <chain_facts> have "PROP ?guess"
wenzelm@17974:       apply magic      -- {* turns goal into "thesis ==> Goal thesis" *}
wenzelm@17858:       <proof body>
wenzelm@17974:       apply_end magic  -- {* turns final "(!!x. P x ==> thesis) ==> Goal thesis" into
wenzelm@17974:         "Goal ((!!x. P x ==> thesis) ==> thesis)" which is a finished goal state *}
wenzelm@17858:       <proof end>
wenzelm@17858:   }
wenzelm@17858:   fix x assm (obtained) "P x"
wenzelm@8094: *)
wenzelm@7674: 
wenzelm@7674: signature OBTAIN =
wenzelm@7674: sig
wenzelm@11890:   val obtain: (string list * string option) list ->
wenzelm@17111:     ((string * Attrib.src list) * (string * (string list * string list)) list) list
wenzelm@17357:     -> bool -> Proof.state -> Proof.state
wenzelm@11890:   val obtain_i: (string list * typ option) list ->
wenzelm@11890:     ((string * Proof.context attribute list) * (term * (term list * term list)) list) list
wenzelm@17357:     -> bool -> Proof.state -> Proof.state
wenzelm@17858:   val guess: (string list * string option) list -> bool -> Proof.state -> Proof.state Seq.seq
wenzelm@17858:   val guess_i: (string list * typ option) list -> bool -> Proof.state -> Proof.state Seq.seq
wenzelm@7674: end;
wenzelm@7674: 
wenzelm@10379: structure Obtain: OBTAIN =
wenzelm@7674: struct
wenzelm@7674: 
wenzelm@17858: (** export_obtained **)
wenzelm@8094: 
wenzelm@17858: fun export_obtained state parms rule cprops thm =
wenzelm@9468:   let
wenzelm@17111:     val {thy, prop, maxidx, ...} = Thm.rep_thm thm;
wenzelm@17111:     val cparms = map (Thm.cterm_of thy) parms;
wenzelm@9468: 
wenzelm@9468:     val thm' = thm
wenzelm@11816:       |> Drule.implies_intr_goals cprops
wenzelm@9468:       |> Drule.forall_intr_list cparms
wenzelm@9468:       |> Drule.forall_elim_vars (maxidx + 1);
wenzelm@17974:     val elim_tacs = replicate (length cprops) (Tactic.etac Drule.goalI);
wenzelm@9468: 
wenzelm@9468:     val concl = Logic.strip_assums_concl prop;
wenzelm@9468:     val bads = parms inter (Term.term_frees concl);
wenzelm@9468:   in
wenzelm@9468:     if not (null bads) then
wenzelm@9481:       raise Proof.STATE ("Conclusion contains obtained parameters: " ^
wenzelm@12055:         space_implode " " (map (ProofContext.string_of_term (Proof.context_of state)) bads), state)
wenzelm@17858:     else if not (ObjectLogic.is_judgment thy concl) then
wenzelm@17858:       raise Proof.STATE ("Conclusion in obtained context must be object-logic judgments", state)
wenzelm@9468:     else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule
wenzelm@9468:   end;
wenzelm@9468: 
wenzelm@9468: 
wenzelm@9468: 
wenzelm@17858: (** obtain **)
wenzelm@17858: 
wenzelm@17858: fun bind_judgment ctxt name =
wenzelm@17858:   let val (t as _ $ Free v) =
wenzelm@17858:     ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name
wenzelm@17858:     |> ProofContext.bind_skolem ctxt [name]
wenzelm@17858:   in (v, t) end;
wenzelm@17858: 
wenzelm@17858: local
wenzelm@8094: 
wenzelm@7674: val thatN = "that";
wenzelm@7674: 
wenzelm@17357: fun gen_obtain prep_att prep_vars prep_propp raw_vars raw_asms int state =
wenzelm@7674:   let
wenzelm@9468:     val _ = Proof.assert_forward_or_chain state;
wenzelm@17858:     val ctxt = Proof.context_of state;
wenzelm@17357:     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
wenzelm@7674: 
wenzelm@8543:     (*obtain vars*)
wenzelm@17858:     val (vars, vars_ctxt) = fold_map prep_vars raw_vars ctxt;
wenzelm@17858:     val fix_ctxt = vars_ctxt |> ProofContext.fix_i vars;
skalberg@15570:     val xs = List.concat (map fst vars);
wenzelm@7674: 
wenzelm@8543:     (*obtain asms*)
wenzelm@11890:     val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
skalberg@15570:     val asm_props = List.concat (map (map fst) proppss);
wenzelm@17858:     val asms = map fst (Attrib.map_specs (prep_att (Proof.theory_of state)) raw_asms) ~~ proppss;
wenzelm@10464: 
wenzelm@10582:     val _ = ProofContext.warn_extra_tfrees fix_ctxt asms_ctxt;
wenzelm@7674: 
wenzelm@12970:     (*obtain statements*)
wenzelm@16606:     val thesisN = Term.variant xs AutoBind.thesisN;
wenzelm@17858:     val (thesis_var, thesis) = bind_judgment fix_ctxt thesisN;
wenzelm@9468: 
wenzelm@10582:     fun occs_var x = Library.get_first (fn t =>
wenzelm@10582:       ProofContext.find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;
wenzelm@10582:     val raw_parms = map occs_var xs;
skalberg@15570:     val parms = List.mapPartial I raw_parms;
wenzelm@10582:     val parm_names =
skalberg@15570:       List.mapPartial (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (raw_parms ~~ xs);
wenzelm@10582: 
wenzelm@10582:     val that_prop =
wenzelm@17858:       Term.list_all_free (map #1 parm_names, Logic.list_implies (asm_props, thesis))
wenzelm@10582:       |> Library.curry Logic.list_rename_params (map #2 parm_names);
wenzelm@12970:     val obtain_prop =
wenzelm@12970:       Logic.list_rename_params ([AutoBind.thesisN],
wenzelm@17858:         Term.list_all_free ([thesis_var], Logic.mk_implies (that_prop, thesis)));
wenzelm@7674: 
wenzelm@17357:     fun after_qed _ _ =
wenzelm@17357:       Proof.local_qed (NONE, false)
wenzelm@17858:       #> Seq.map (`Proof.the_fact #-> (fn rule =>
wenzelm@17357:         Proof.fix_i vars
wenzelm@17858:         #> Proof.assm_i (K (export_obtained state parms rule)) asms));
wenzelm@7674:   in
wenzelm@8094:     state
wenzelm@9468:     |> Proof.enter_forward
wenzelm@17858:     |> Proof.have_i NONE (K (K Seq.single)) [(("", []), [(obtain_prop, ([], []))])] int
wenzelm@17858:     |> Proof.proof (SOME Method.succeed_text) |> Seq.hd
skalberg@15531:     |> Proof.fix_i [([thesisN], NONE)]
skalberg@15531:     |> Proof.assume_i [((thatN, [ContextRules.intro_query_local NONE]), [(that_prop, ([], []))])]
wenzelm@16842:     |> `Proof.the_facts
wenzelm@17357:     ||> Proof.chain_facts chain_facts
wenzelm@17858:     ||> Proof.show_i NONE after_qed [(("", []), [(thesis, ([], []))])] false
wenzelm@17357:     |-> (Proof.refine o Method.Basic o K o Method.insert) |> Seq.hd
wenzelm@7674:   end;
wenzelm@7674: 
wenzelm@17858: in
wenzelm@17858: 
wenzelm@17111: val obtain = gen_obtain Attrib.local_attribute ProofContext.read_vars ProofContext.read_propp;
wenzelm@17111: val obtain_i = gen_obtain (K I) ProofContext.cert_vars ProofContext.cert_propp;
wenzelm@8094: 
wenzelm@8094: end;
wenzelm@17858: 
wenzelm@17858: 
wenzelm@17858: 
wenzelm@17858: (** guess **)
wenzelm@17858: 
wenzelm@17858: local
wenzelm@17858: 
wenzelm@17858: fun match_params state vars rule =
wenzelm@17858:   let
wenzelm@17858:     val ctxt = Proof.context_of state;
wenzelm@17858:     val thy = Proof.theory_of state;
wenzelm@17891:     val string_of_typ = ProofContext.string_of_typ ctxt;
wenzelm@17858:     val string_of_term = setmp show_types true (ProofContext.string_of_term ctxt);
wenzelm@17891: 
wenzelm@17891:     fun err msg th = raise Proof.STATE (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th, state);
wenzelm@17858: 
wenzelm@17858:     val params = RuleCases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
wenzelm@17858:     val m = length vars;
wenzelm@17858:     val n = length params;
wenzelm@17891:     val _ = conditional (m > n)
wenzelm@17891:       (fn () => err "More variables than parameters in obtained rule" rule);
wenzelm@17858: 
wenzelm@17858:     fun match ((x, SOME T), (y, U)) tyenv =
wenzelm@17858:         ((x, T), Sign.typ_match thy (U, T) tyenv handle Type.TYPE_MATCH =>
wenzelm@17891:           err ("Failed to match variable " ^
wenzelm@17858:             string_of_term (Free (x, T)) ^ " against parameter " ^
wenzelm@17891:             string_of_term (Syntax.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule)
wenzelm@17858:       | match ((x, NONE), (_, U)) tyenv = ((x, U), tyenv);
wenzelm@17858:     val (xs, tyenv) = fold_map match (vars ~~ Library.take (m, params)) Vartab.empty;
wenzelm@17858:     val ys = Library.drop (m, params);
wenzelm@17858:     val norm_type = Envir.norm_type tyenv;
wenzelm@17858: 
wenzelm@17858:     val xs' = xs |> map (apsnd norm_type);
wenzelm@17858:     val ys' =
wenzelm@17858:       map Syntax.internal (Term.variantlist (map fst ys, map fst xs)) ~~
wenzelm@17858:       map (norm_type o snd) ys;
wenzelm@17858:     val instT =
wenzelm@17858:       fold (Term.add_tvarsT o #2) params []
wenzelm@17858:       |> map (TVar #> (fn T => (Thm.ctyp_of thy T, Thm.ctyp_of thy (norm_type T))));
wenzelm@17858:     val rule' = rule |> Thm.instantiate (instT, []);
wenzelm@17891: 
wenzelm@17891:     val tvars = Drule.tvars_of rule';
wenzelm@17891:     val vars = fold (remove op =) (Term.add_vars (Thm.concl_of rule') []) (Drule.vars_of rule');
wenzelm@17891:     val _ =
wenzelm@17891:       if null tvars andalso null vars then ()
wenzelm@17891:       else err ("Illegal schematic variable(s) " ^
wenzelm@17891:         commas (map (string_of_typ o TVar) tvars @ map (string_of_term o Var) vars) ^ " in") rule';
wenzelm@17858:   in (xs' @ ys', rule') end;
wenzelm@17858: 
wenzelm@17858: fun gen_guess prep_vars raw_vars int state =
wenzelm@17858:   let
wenzelm@17858:     val _ = Proof.assert_forward_or_chain state;
wenzelm@17858:     val thy = Proof.theory_of state;
wenzelm@17858:     val ctxt = Proof.context_of state;
wenzelm@17858:     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
wenzelm@17858: 
wenzelm@17858:     val (thesis_var, thesis) = bind_judgment ctxt AutoBind.thesisN;
wenzelm@17858:     val varss = #1 (fold_map prep_vars raw_vars ctxt);
wenzelm@17858:     val vars = List.concat (map (fn (xs, T) => map (rpair T) xs) varss);
wenzelm@17858: 
wenzelm@17974:     fun check_result th =
wenzelm@17974:       (case Thm.prems_of th of
wenzelm@17974:         [prem] =>
wenzelm@17974:           if Thm.concl_of th aconv thesis andalso
wenzelm@17974:             Logic.strip_assums_concl prem aconv thesis then ()
wenzelm@17974:           else raise Proof.STATE ("Guessed a different clause:\n" ^
wenzelm@17974:             ProofContext.string_of_thm ctxt th, state)
wenzelm@17974:       | [] => raise Proof.STATE ("Goal solved -- nothing guessed.", state)
wenzelm@17858:       | _ => raise Proof.STATE ("Guess split into several cases:\n" ^
wenzelm@17974:         ProofContext.string_of_thm ctxt th, state));
wenzelm@17891: 
wenzelm@17858:     fun guess_context raw_rule =
wenzelm@17858:       let
wenzelm@17858:         val (parms, rule) = match_params state vars raw_rule;
wenzelm@17858:         val ts = map (ProofContext.bind_skolem ctxt (map #1 parms) o Free) parms;
wenzelm@17858:         val ps = map dest_Free ts;
wenzelm@17858:         val asms =
wenzelm@17858:           Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
wenzelm@17858:           |> map (fn asm => (Library.foldl Term.betapply (Term.list_abs (ps, asm), ts), ([], [])));
wenzelm@17974:         val _ = conditional (null asms) (fn () =>
wenzelm@17974:           raise Proof.STATE ("Trivial result -- nothing guessed", state));
wenzelm@17858:       in
wenzelm@17858:         Proof.fix_i (map (fn (x, T) => ([x], SOME T)) parms)
wenzelm@17858:         #> Proof.assm_i (K (export_obtained state ts rule)) [(("", []), asms)]
wenzelm@17974:         #> Proof.add_binds_i AutoBind.no_facts
wenzelm@17858:       end;
wenzelm@17858: 
wenzelm@17858:     val before_qed = SOME (Method.primitive_text (fn th =>
wenzelm@17974:       let val th' = Goal.conclude th
wenzelm@17974:       in th' COMP Drule.incr_indexes_wrt [] [] [] [th'] Drule.goalI end));
wenzelm@17974:     fun after_qed _ [[res]] =
wenzelm@17974:       (check_result res; Proof.end_block #> Seq.map (`Proof.the_fact #-> guess_context));
wenzelm@17858:   in
wenzelm@17858:     state
wenzelm@17858:     |> Proof.enter_forward
wenzelm@17858:     |> Proof.begin_block
wenzelm@17858:     |> Proof.fix_i [([AutoBind.thesisN], NONE)]
wenzelm@17858:     |> Proof.chain_facts chain_facts
wenzelm@17858:     |> Proof.local_goal (ProofDisplay.print_results int) (K I) (apsnd (rpair I))
wenzelm@17858:       "guess" before_qed after_qed [(("", []), [Var (("guess", 0), propT)])]
wenzelm@17974:     |> Proof.refine (Method.primitive_text (K (Goal.init (Thm.cterm_of thy thesis))))
wenzelm@17858:   end;
wenzelm@17858: 
wenzelm@17858: in
wenzelm@17858: 
wenzelm@17858: val guess = gen_guess ProofContext.read_vars;
wenzelm@17858: val guess_i = gen_guess ProofContext.cert_vars;
wenzelm@17858: 
wenzelm@17858: end;
wenzelm@17858: 
wenzelm@17858: end;