src/Pure/Isar/obtain.ML
author wenzelm
Thu Feb 02 16:31:35 2006 +0100 (2006-02-02)
changeset 18907 f984f22f1cb4
parent 18897 b31293969d4f
child 19300 7689f81f8996
permissions -rw-r--r--
Proof.refine_insert;
statements: always use Attrib.src;
     1 (*  Title:      Pure/Isar/obtain.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 The 'obtain' and 'guess' language elements -- generalized existence at
     6 the level of proof texts: 'obtain' involves a proof that certain
     7 fixes/assumes may be introduced into the present context; 'guess' is
     8 similar, but derives these elements from the course of reasoning!
     9 
    10   <chain_facts>
    11   obtain x where "A x" <proof> ==
    12 
    13   have "!!thesis. (!!x. A x ==> thesis) ==> thesis"
    14   proof succeed
    15     fix thesis
    16     assume that [intro?]: "!!x. A x ==> thesis"
    17     <chain_facts>
    18     show thesis
    19       apply (insert that)
    20       <proof>
    21   qed
    22   fix x assm <<obtain_export>> "A x"
    23 
    24 
    25   <chain_facts>
    26   guess x <proof body> <proof end> ==
    27 
    28   {
    29     fix thesis
    30     <chain_facts> have "PROP ?guess"
    31       apply magic      -- {* turns goal into "thesis ==> #thesis" *}
    32       <proof body>
    33       apply_end magic  -- {* turns final "(!!x. P x ==> thesis) ==> #thesis" into
    34         "#((!!x. A x ==> thesis) ==> thesis)" which is a finished goal state *}
    35       <proof end>
    36   }
    37   fix x assm <<obtain_export>> "A x"
    38 *)
    39 
    40 signature OBTAIN =
    41 sig
    42   val obtain: string -> (string * string option) list ->
    43     ((string * Attrib.src list) * (string * (string list * string list)) list) list
    44     -> bool -> Proof.state -> Proof.state
    45   val obtain_i: string -> (string * typ option) list ->
    46     ((string * attribute list) * (term * (term list * term list)) list) list
    47     -> bool -> Proof.state -> Proof.state
    48   val guess: (string * string option) list -> bool -> Proof.state -> Proof.state
    49   val guess_i: (string * typ option) list -> bool -> Proof.state -> Proof.state
    50   val statement: (string * ((string * 'typ option) list * 'term list)) list ->
    51     (('typ, 'term, 'fact) Element.ctxt list *
    52       ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list) *
    53     (((string * Attrib.src list) * (term * (term list * term list)) list) list -> Proof.context ->
    54       (((string * Attrib.src list) * (term * (term list * term list)) list) list * thm list) *
    55         Proof.context)
    56 end;
    57 
    58 structure Obtain: OBTAIN =
    59 struct
    60 
    61 
    62 (** obtain_export **)
    63 
    64 (*
    65   [x, A x]
    66      :
    67      B
    68   --------
    69      B
    70 *)
    71 fun obtain_export ctxt parms rule cprops thm =
    72   let
    73     val {thy, prop, maxidx, ...} = Thm.rep_thm thm;
    74     val cparms = map (Thm.cterm_of thy) parms;
    75 
    76     val thm' = thm
    77       |> Drule.implies_intr_protected cprops
    78       |> Drule.forall_intr_list cparms
    79       |> Drule.forall_elim_vars (maxidx + 1);
    80     val elim_tacs = replicate (length cprops) (Tactic.etac Drule.protectI);
    81 
    82     val concl = Logic.strip_assums_concl prop;
    83     val bads = parms inter (Term.term_frees concl);
    84   in
    85     if not (null bads) then
    86       error ("Conclusion contains obtained parameters: " ^
    87         space_implode " " (map (ProofContext.string_of_term ctxt) bads))
    88     else if not (ObjectLogic.is_judgment thy concl) then
    89       error "Conclusion in obtained context must be object-logic judgments"
    90     else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule
    91   end;
    92 
    93 
    94 
    95 (** obtain **)
    96 
    97 fun bind_judgment ctxt name =
    98   let
    99     val (bind, _) = ProofContext.bind_fixes [name] ctxt;
   100     val (t as _ $ Free v) = bind (ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name);
   101   in (v, t) end;
   102 
   103 val thatN = "that";
   104 
   105 local
   106 
   107 fun gen_obtain prep_att prep_vars prep_propp
   108     name raw_vars raw_asms int state =
   109   let
   110     val _ = Proof.assert_forward_or_chain state;
   111     val ctxt = Proof.context_of state;
   112     val thy = Proof.theory_of state;
   113     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
   114 
   115     (*obtain vars*)
   116     val (vars, vars_ctxt) = prep_vars (map Syntax.no_syn raw_vars) ctxt;
   117     val (_, fix_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
   118     val xs = map #1 vars;
   119 
   120     (*obtain asms*)
   121     val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
   122     val asm_props = List.concat (map (map fst) proppss);
   123     val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;
   124 
   125     val _ = ProofContext.warn_extra_tfrees fix_ctxt asms_ctxt;
   126 
   127     (*obtain statements*)
   128     val thesisN = Term.variant xs AutoBind.thesisN;
   129     val (thesis_var, thesis) = bind_judgment fix_ctxt thesisN;
   130 
   131     fun occs_var x = Library.get_first (fn t =>
   132       Term.find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;
   133     val raw_parms = map occs_var xs;
   134     val parms = List.mapPartial I raw_parms;
   135     val parm_names =
   136       List.mapPartial (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (raw_parms ~~ xs);
   137 
   138     val that_name = if name = "" then thatN else name;
   139     val that_prop =
   140       Term.list_all_free (map #1 parm_names, Logic.list_implies (asm_props, thesis))
   141       |> Library.curry Logic.list_rename_params (map #2 parm_names);
   142     val obtain_prop =
   143       Logic.list_rename_params ([AutoBind.thesisN],
   144         Term.list_all_free ([thesis_var], Logic.mk_implies (that_prop, thesis)));
   145 
   146     fun after_qed _ =
   147       Proof.local_qed (NONE, false)
   148       #> Seq.map (`Proof.the_fact #-> (fn rule =>
   149         Proof.fix_i (xs ~~ map #2 vars)
   150         #> Proof.assm_i (K (obtain_export ctxt parms rule)) asms));
   151   in
   152     state
   153     |> Proof.enter_forward
   154     |> Proof.have_i NONE (K Seq.single) [(("", []), [(obtain_prop, ([], []))])] int
   155     |> Proof.proof (SOME Method.succeed_text) |> Seq.hd
   156     |> Proof.fix_i [(thesisN, NONE)]
   157     |> Proof.assume_i [((that_name, [ContextRules.intro_query NONE]), [(that_prop, ([], []))])]
   158     |> `Proof.the_facts
   159     ||> Proof.chain_facts chain_facts
   160     ||> Proof.show_i NONE after_qed [(("", []), [(thesis, ([], []))])] false
   161     |-> Proof.refine_insert
   162   end;
   163 
   164 in
   165 
   166 val obtain = gen_obtain Attrib.attribute ProofContext.read_vars ProofContext.read_propp;
   167 val obtain_i = gen_obtain (K I) ProofContext.cert_vars ProofContext.cert_propp;
   168 
   169 end;
   170 
   171 
   172 
   173 (** guess **)
   174 
   175 local
   176 
   177 fun match_params ctxt vars rule =
   178   let
   179     val thy = ProofContext.theory_of ctxt;
   180     val string_of_typ = ProofContext.string_of_typ ctxt;
   181     val string_of_term = setmp show_types true (ProofContext.string_of_term ctxt);
   182 
   183     fun err msg th = error (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th);
   184 
   185     val params = RuleCases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
   186     val m = length vars;
   187     val n = length params;
   188     val _ = conditional (m > n)
   189       (fn () => err "More variables than parameters in obtained rule" rule);
   190 
   191     fun match ((x, SOME T), (y, U)) tyenv =
   192         ((x, T), Sign.typ_match thy (U, T) tyenv handle Type.TYPE_MATCH =>
   193           err ("Failed to match variable " ^
   194             string_of_term (Free (x, T)) ^ " against parameter " ^
   195             string_of_term (Syntax.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule)
   196       | match ((x, NONE), (_, U)) tyenv = ((x, U), tyenv);
   197     val (xs, tyenv) = fold_map match (vars ~~ Library.take (m, params)) Vartab.empty;
   198     val ys = Library.drop (m, params);
   199     val norm_type = Envir.norm_type tyenv;
   200 
   201     val xs' = xs |> map (apsnd norm_type);
   202     val ys' =
   203       map Syntax.internal (Term.variantlist (map fst ys, map fst xs)) ~~
   204       map (norm_type o snd) ys;
   205     val instT =
   206       fold (Term.add_tvarsT o #2) params []
   207       |> map (TVar #> (fn T => (Thm.ctyp_of thy T, Thm.ctyp_of thy (norm_type T))));
   208     val rule' = rule |> Thm.instantiate (instT, []);
   209 
   210     val tvars = Drule.tvars_of rule';
   211     val vars = fold (remove op =) (Term.add_vars (Thm.concl_of rule') []) (Drule.vars_of rule');
   212     val _ =
   213       if null tvars andalso null vars then ()
   214       else err ("Illegal schematic variable(s) " ^
   215         commas (map (string_of_typ o TVar) tvars @ map (string_of_term o Var) vars) ^ " in") rule';
   216   in (xs' @ ys', rule') end;
   217 
   218 fun inferred_type (x, _, mx) ctxt =
   219   let val ((_, T), ctxt') = ProofContext.inferred_param x ctxt
   220   in ((x, SOME T, mx), ctxt') end;
   221 
   222 fun gen_guess prep_vars raw_vars int state =
   223   let
   224     val _ = Proof.assert_forward_or_chain state;
   225     val thy = Proof.theory_of state;
   226     val ctxt = Proof.context_of state;
   227     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
   228 
   229     val (thesis_var, thesis) = bind_judgment ctxt AutoBind.thesisN;
   230     val (vars, _) = ctxt |> prep_vars (map Syntax.no_syn raw_vars) |-> fold_map inferred_type;
   231 
   232     fun check_result th =
   233       (case Thm.prems_of th of
   234         [prem] =>
   235           if Thm.concl_of th aconv thesis andalso
   236             Logic.strip_assums_concl prem aconv thesis then ()
   237           else error ("Guessed a different clause:\n" ^ ProofContext.string_of_thm ctxt th)
   238       | [] => error "Goal solved -- nothing guessed."
   239       | _ => error ("Guess split into several cases:\n" ^ ProofContext.string_of_thm ctxt th));
   240 
   241     fun guess_context raw_rule =
   242       let
   243         val (parms, rule) = match_params ctxt (map (fn (x, T, _) => (x, T)) vars) raw_rule;
   244         val (bind, _) = ProofContext.bind_fixes (map #1 parms) ctxt;
   245         val ts = map (bind o Free) parms;
   246         val ps = map dest_Free ts;
   247         val asms =
   248           Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
   249           |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), ([], [])));
   250         val _ = conditional (null asms) (fn () => error "Trivial result -- nothing guessed");
   251       in
   252         Proof.fix_i (map (apsnd SOME) parms)
   253         #> Proof.assm_i (K (obtain_export ctxt ts rule)) [(("", []), asms)]
   254         #> Proof.add_binds_i AutoBind.no_facts
   255       end;
   256 
   257     val before_qed = SOME (Method.primitive_text (Goal.conclude #> Goal.protect));
   258     fun after_qed [[res]] =
   259       (check_result res; Proof.end_block #> Seq.map (`Proof.the_fact #-> guess_context));
   260   in
   261     state
   262     |> Proof.enter_forward
   263     |> Proof.begin_block
   264     |> Proof.fix_i [(AutoBind.thesisN, NONE)]
   265     |> Proof.chain_facts chain_facts
   266     |> Proof.local_goal (ProofDisplay.print_results int) (K I) (apsnd (rpair I))
   267       "guess" before_qed after_qed [(("", []), [Var (("guess", 0), propT)])]
   268     |> Proof.refine (Method.primitive_text (K (Goal.init (Thm.cterm_of thy thesis)))) |> Seq.hd
   269   end;
   270 
   271 in
   272 
   273 val guess = gen_guess ProofContext.read_vars;
   274 val guess_i = gen_guess ProofContext.cert_vars;
   275 
   276 end;
   277 
   278 
   279 
   280 (** statements with several cases **)
   281 
   282 fun statement cases =
   283   let
   284     val names =
   285       cases |> map_index (fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);
   286     val elems = cases |> map (fn (_, (vars, _)) =>
   287       Element.Constrains (vars |> List.mapPartial (fn (x, SOME T) => SOME (x, T) | _ => NONE)));
   288     val concl = cases |> map (fn (_, (_, props)) => (("", []), map (rpair ([], [])) props));
   289 
   290     fun mk_stmt stmt ctxt =
   291       let
   292         val thesis =
   293           ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
   294         val atts = map Attrib.internal
   295           [RuleCases.consumes (~ (length cases)), RuleCases.case_names names];
   296 
   297         fun assume_case ((name, (vars, _)), (_, propp)) ctxt' =
   298           let
   299             val xs = map fst vars;
   300             val props = map fst propp;
   301             val (parms, ctxt'') =
   302               ctxt'
   303               |> fold ProofContext.declare_term props
   304               |> fold_map ProofContext.inferred_param xs;
   305             val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));
   306           in
   307             ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));
   308             ctxt' |> ProofContext.add_assms_i ProofContext.assume_export
   309               [((name, [ContextRules.intro_query NONE]), [(asm, ([], []))])]
   310             |>> (fn [(_, [th])] => th)
   311           end;
   312         val (ths, ctxt') = ctxt
   313           |> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])
   314           |> fold_map assume_case (cases ~~ stmt)
   315           |-> (fn ths => ProofContext.note_thmss_i [((thatN, []), [(ths, [])])] #> #2 #> pair ths);
   316       in (([(("", atts), [(thesis, ([], []))])], ths), ctxt') end;
   317   in ((elems, concl), mk_stmt) end;
   318 
   319 end;