src/Pure/Isar/obtain.ML
 author wenzelm Thu Jul 27 13:43:01 2006 +0200 (2006-07-27) changeset 20224 9c40a144ee0e parent 20218 be3bfb0699ba child 20308 ddb7e7129481 permissions -rw-r--r--
moved basic assumption operations from structure ProofContext to Assumption;
```     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 * mixfix) list ->
```
```    43     ((string * Attrib.src list) * (string * string list) list) list
```
```    44     -> bool -> Proof.state -> Proof.state
```
```    45   val obtain_i: string -> (string * typ option * mixfix) list ->
```
```    46     ((string * attribute list) * (term * term list) list) list
```
```    47     -> bool -> Proof.state -> Proof.state
```
```    48   val guess: (string * string option * mixfix) list -> bool -> Proof.state -> Proof.state
```
```    49   val guess_i: (string * typ option * mixfix) 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) list) list) *
```
```    53     (((string * Attrib.src list) * (term * term list) list) list -> Proof.context ->
```
```    54       (((string * Attrib.src list) * (term * term list) list) list * thm list) * Proof.context)
```
```    55 end;
```
```    56
```
```    57 structure Obtain: OBTAIN =
```
```    58 struct
```
```    59
```
```    60
```
```    61 (** obtain_export **)
```
```    62
```
```    63 (*
```
```    64   [x, A x]
```
```    65      :
```
```    66      B
```
```    67   --------
```
```    68      B
```
```    69 *)
```
```    70 fun obtain_export ctxt parms rule cprops thm =
```
```    71   let
```
```    72     val {thy, prop, ...} = Thm.rep_thm thm;
```
```    73     val concl = Logic.strip_assums_concl prop;
```
```    74     val bads = Term.fold_aterms (fn v as Free (x, _) =>
```
```    75       if member (op =) parms x then insert (op aconv) v else I | _ => I) concl [];
```
```    76
```
```    77     val thm' = thm |> Drule.implies_intr_protected cprops |> Drule.generalize ([], parms);
```
```    78     val elim_tacs = replicate (length cprops) (Tactic.etac Drule.protectI);
```
```    79   in
```
```    80     if not (null bads) then
```
```    81       error ("Conclusion contains obtained parameters: " ^
```
```    82         space_implode " " (map (ProofContext.string_of_term ctxt) bads))
```
```    83     else if not (ObjectLogic.is_judgment thy concl) then
```
```    84       error "Conclusion in obtained context must be object-logic judgment"
```
```    85     else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule
```
```    86   end;
```
```    87
```
```    88
```
```    89
```
```    90 (** obtain **)
```
```    91
```
```    92 fun bind_judgment ctxt name =
```
```    93   let
```
```    94     val (bind, _) = ProofContext.bind_fixes [name] ctxt;
```
```    95     val (t as _ \$ Free v) = bind (ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name);
```
```    96   in (v, t) end;
```
```    97
```
```    98 val thatN = "that";
```
```    99
```
```   100 local
```
```   101
```
```   102 fun find_free t x =
```
```   103   let
```
```   104     exception Found of term;
```
```   105     fun find (t as Free (x', _)) = if x = x' then raise Found t else I
```
```   106       | find _ = I;
```
```   107   in (fold_aterms find t (); NONE) handle Found v => SOME v end;
```
```   108
```
```   109 fun gen_obtain prep_att prep_vars prep_propp
```
```   110     name raw_vars raw_asms int state =
```
```   111   let
```
```   112     val _ = Proof.assert_forward_or_chain state;
```
```   113     val ctxt = Proof.context_of state;
```
```   114     val thy = Proof.theory_of state;
```
```   115     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
```
```   116
```
```   117     (*obtain vars*)
```
```   118     val (vars, vars_ctxt) = prep_vars raw_vars ctxt;
```
```   119     val (_, fix_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
```
```   120     val xs = map #1 vars;
```
```   121
```
```   122     (*obtain asms*)
```
```   123     val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
```
```   124     val asm_props = maps (map fst) proppss;
```
```   125     val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;
```
```   126
```
```   127     val _ = Variable.warn_extra_tfrees fix_ctxt asms_ctxt;
```
```   128
```
```   129     (*obtain statements*)
```
```   130     val thesisN = Name.variant xs AutoBind.thesisN;
```
```   131     val (thesis_var, thesis) = bind_judgment fix_ctxt thesisN;
```
```   132
```
```   133     fun occs_var x = Library.get_first (fn t =>
```
```   134       find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;
```
```   135     val parms =
```
```   136       map_filter (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (map occs_var xs ~~ xs);
```
```   137
```
```   138     val that_name = if name = "" then thatN else name;
```
```   139     val that_prop =
```
```   140       Term.list_all_free (map #1 parms, Logic.list_implies (asm_props, thesis))
```
```   141       |> Library.curry Logic.list_rename_params (map #2 parms);
```
```   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 (map2 (fn x => fn (_, T, mx) => (x, T, mx)) xs vars)
```
```   150         #> Proof.assm_i (K (obtain_export ctxt (map (#1 o #1) 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, NoSyn)]
```
```   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 unify_params vars thesis_name raw_rule ctxt =
```
```   178   let
```
```   179     val thy = ProofContext.theory_of ctxt;
```
```   180     val certT = Thm.ctyp_of thy;
```
```   181     val cert = Thm.cterm_of thy;
```
```   182     val string_of_typ = ProofContext.string_of_typ ctxt;
```
```   183     val string_of_term = setmp show_types true (ProofContext.string_of_term ctxt);
```
```   184
```
```   185     fun err msg th = error (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th);
```
```   186
```
```   187     val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
```
```   188     val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
```
```   189
```
```   190     val params = RuleCases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
```
```   191     val m = length vars;
```
```   192     val n = length params;
```
```   193     val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
```
```   194
```
```   195     fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
```
```   196       handle Type.TUNIFY =>
```
```   197         err ("Failed to unify variable " ^
```
```   198           string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
```
```   199           string_of_term (Syntax.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule;
```
```   200     val (tyenv, _) = fold unify (map #1 vars ~~ Library.take (m, params))
```
```   201       (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
```
```   202     val norm_type = Envir.norm_type tyenv;
```
```   203
```
```   204     val xs = map (apsnd norm_type o fst) vars;
```
```   205     val ys = map (apsnd norm_type) (Library.drop (m, params));
```
```   206     val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;
```
```   207     val terms = map (Drule.mk_term o cert o Free) (xs @ ys');
```
```   208
```
```   209     val instT =
```
```   210       fold (Term.add_tvarsT o #2) params []
```
```   211       |> map (TVar #> (fn T => (certT T, certT (norm_type T))));
```
```   212     val ((_, rule' :: terms'), ctxt') =
```
```   213       Variable.import false (Thm.instantiate (instT, []) rule :: terms) ctxt;
```
```   214
```
```   215     val vars' =
```
```   216       map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
```
```   217       (map snd vars @ replicate (length ys) NoSyn);
```
```   218     val rule'' = Drule.generalize ([], [thesis_name]) rule';
```
```   219   in ((vars', rule''), ctxt') end;
```
```   220
```
```   221 fun inferred_type (x, _, mx) ctxt =
```
```   222   let val ((_, T), ctxt') = ProofContext.inferred_param x ctxt
```
```   223   in ((x, T, mx), ctxt') end;
```
```   224
```
```   225 fun polymorphic ctxt vars =
```
```   226   let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
```
```   227   in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
```
```   228
```
```   229 fun gen_guess prep_vars raw_vars int state =
```
```   230   let
```
```   231     val _ = Proof.assert_forward_or_chain state;
```
```   232     val thy = Proof.theory_of state;
```
```   233     val ctxt = Proof.context_of state;
```
```   234     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
```
```   235
```
```   236     val ((thesis_name, _), thesis) = bind_judgment ctxt AutoBind.thesisN;
```
```   237     val vars = ctxt |> prep_vars raw_vars |-> fold_map inferred_type |> fst |> polymorphic ctxt;
```
```   238
```
```   239     fun check_result th =
```
```   240       (case Thm.prems_of th of
```
```   241         [prem] =>
```
```   242           if Thm.concl_of th aconv thesis andalso
```
```   243             Logic.strip_assums_concl prem aconv thesis then ()
```
```   244           else error ("Guessed a different clause:\n" ^ ProofContext.string_of_thm ctxt th)
```
```   245       | [] => error "Goal solved -- nothing guessed."
```
```   246       | _ => error ("Guess split into several cases:\n" ^ ProofContext.string_of_thm ctxt th));
```
```   247
```
```   248     fun guess_context raw_rule state' =
```
```   249       let
```
```   250         val ((parms, rule), ctxt') =
```
```   251           unify_params vars thesis_name raw_rule (Proof.context_of state');
```
```   252         val (bind, _) = ProofContext.bind_fixes (map (#1 o #1) parms) ctxt';
```
```   253         val ts = map (bind o Free o #1) parms;
```
```   254         val ps = map dest_Free ts;
```
```   255         val asms =
```
```   256           Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
```
```   257           |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), []));
```
```   258         val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
```
```   259       in
```
```   260         state'
```
```   261         |> Proof.map_context (K ctxt')
```
```   262         |> Proof.fix_i (map (fn ((x, T), mx) => (x, SOME T, mx)) parms)
```
```   263         |> Proof.assm_i (K (obtain_export ctxt' (map #1 ps) rule)) [(("", []), asms)]
```
```   264         |> Proof.add_binds_i AutoBind.no_facts
```
```   265       end;
```
```   266
```
```   267     val goal = Var (("guess", 0), propT);
```
```   268     fun print_result ctxt' (k, [(s, [_, th])]) =
```
```   269       ProofDisplay.print_results int ctxt' (k, [(s, [th])]);
```
```   270     val before_qed = SOME (Method.primitive_text (Goal.conclude #> (fn th =>
```
```   271       Goal.protect (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))));
```
```   272     fun after_qed [[_, res]] =
```
```   273       (check_result res; Proof.end_block #> Seq.map (guess_context res));
```
```   274   in
```
```   275     state
```
```   276     |> Proof.enter_forward
```
```   277     |> Proof.begin_block
```
```   278     |> Proof.fix_i [(AutoBind.thesisN, NONE, NoSyn)]
```
```   279     |> Proof.chain_facts chain_facts
```
```   280     |> Proof.local_goal print_result (K I) (apsnd (rpair I))
```
```   281       "guess" before_qed after_qed [(("", []), [Logic.mk_term goal, goal])]
```
```   282     |> Proof.refine (Method.primitive_text (K (Goal.init (Thm.cterm_of thy thesis)))) |> Seq.hd
```
```   283   end;
```
```   284
```
```   285 in
```
```   286
```
```   287 val guess = gen_guess ProofContext.read_vars;
```
```   288 val guess_i = gen_guess ProofContext.cert_vars;
```
```   289
```
```   290 end;
```
```   291
```
```   292
```
```   293
```
```   294 (** statements with several cases **)
```
```   295
```
```   296 fun statement cases =
```
```   297   let
```
```   298     val names =
```
```   299       cases |> map_index (fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);
```
```   300     val elems = cases |> map (fn (_, (vars, _)) =>
```
```   301       Element.Constrains (vars |> map_filter (fn (x, SOME T) => SOME (x, T) | _ => NONE)));
```
```   302     val concl = cases |> map (fn (_, (_, props)) => (("", []), map (rpair []) props));
```
```   303
```
```   304     fun mk_stmt stmt ctxt =
```
```   305       let
```
```   306         val thesis =
```
```   307           ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
```
```   308         val atts = map Attrib.internal
```
```   309           [RuleCases.consumes (~ (length cases)), RuleCases.case_names names];
```
```   310
```
```   311         fun assume_case ((name, (vars, _)), (_, propp)) ctxt' =
```
```   312           let
```
```   313             val xs = map fst vars;
```
```   314             val props = map fst propp;
```
```   315             val (parms, ctxt'') =
```
```   316               ctxt'
```
```   317               |> fold Variable.declare_term props
```
```   318               |> fold_map ProofContext.inferred_param xs;
```
```   319             val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));
```
```   320           in
```
```   321             ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));
```
```   322             ctxt' |> ProofContext.add_assms_i Assumption.assume_export
```
```   323               [((name, [ContextRules.intro_query NONE]), [(asm, [])])]
```
```   324             |>> (fn [(_, [th])] => th)
```
```   325           end;
```
```   326         val (ths, ctxt') = ctxt
```
```   327           |> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])
```
```   328           |> fold_map assume_case (cases ~~ stmt)
```
```   329           |-> (fn ths => ProofContext.note_thmss_i [((thatN, []), [(ths, [])])] #> #2 #> pair ths);
```
```   330       in (([(("", atts), [(thesis, [])])], ths), ctxt') end;
```
```   331   in ((elems, concl), mk_stmt) end;
```
```   332
```
```   333 end;
```