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;
```