src/Pure/Isar/obtain.ML
author wenzelm
Tue Sep 13 22:19:42 2005 +0200 (2005-09-13)
changeset 17357 ee2bdca144c7
parent 17111 d2ea9c974570
child 17858 bc4db8cfd92f
permissions -rw-r--r--
tuned Isar proof elements;
     1 (*  Title:      Pure/Isar/obtain.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 The 'obtain' language element -- generalized existence at the level of
     6 proof texts.
     7 
     8   <chain_facts>
     9   obtain x where "P x" <proof> ==
    10 
    11   have "!!thesis. (!!x. P x ==> thesis) ==> thesis"
    12   proof succeed
    13     fix thesis
    14     assume that [intro?]: "!!x. P x ==> thesis"
    15     <chain_facts> show thesis <proof (insert that)>
    16   qed
    17   fix x assm (obtained) "P x"
    18 *)
    19 
    20 signature OBTAIN =
    21 sig
    22   val obtain: (string list * string option) list ->
    23     ((string * Attrib.src list) * (string * (string list * string list)) list) list
    24     -> bool -> Proof.state -> Proof.state
    25   val obtain_i: (string list * typ option) list ->
    26     ((string * Proof.context attribute list) * (term * (term list * term list)) list) list
    27     -> bool -> Proof.state -> Proof.state
    28 end;
    29 
    30 structure Obtain: OBTAIN =
    31 struct
    32 
    33 
    34 (** export_obtain **)
    35 
    36 fun export_obtain state parms rule _ cprops thm =
    37   let
    38     val {thy, prop, maxidx, ...} = Thm.rep_thm thm;
    39     val cparms = map (Thm.cterm_of thy) parms;
    40 
    41     val thm' = thm
    42       |> Drule.implies_intr_goals cprops
    43       |> Drule.forall_intr_list cparms
    44       |> Drule.forall_elim_vars (maxidx + 1);
    45     val elim_tacs = replicate (length cprops) (Tactic.etac Drule.triv_goal);
    46 
    47     val concl = Logic.strip_assums_concl prop;
    48     val bads = parms inter (Term.term_frees concl);
    49   in
    50     if not (null bads) then
    51       raise Proof.STATE ("Conclusion contains obtained parameters: " ^
    52         space_implode " " (map (ProofContext.string_of_term (Proof.context_of state)) bads), state)
    53     else if not (ObjectLogic.is_judgment thy (Logic.strip_assums_concl prop)) then
    54       raise Proof.STATE ("Conclusions of 'obtain' context must be object-logic judgments", state)
    55     else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule
    56   end;
    57 
    58 
    59 
    60 (** obtain(_i) **)
    61 
    62 val thatN = "that";
    63 
    64 fun gen_obtain prep_att prep_vars prep_propp raw_vars raw_asms int state =
    65   let
    66     val _ = Proof.assert_forward_or_chain state;
    67     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
    68     val thy = Proof.theory_of state;
    69 
    70     (*obtain vars*)
    71     val (vars_ctxt, vars) = foldl_map prep_vars (Proof.context_of state, raw_vars);
    72     val xs = List.concat (map fst vars);
    73     val fix_ctxt = vars_ctxt |> ProofContext.fix_i vars;
    74 
    75     (*obtain asms*)
    76     val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
    77     val asm_props = List.concat (map (map fst) proppss);
    78     val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;
    79 
    80     val _ = ProofContext.warn_extra_tfrees fix_ctxt asms_ctxt;
    81 
    82     (*obtain statements*)
    83     val thesisN = Term.variant xs AutoBind.thesisN;
    84     val bind_thesis = ProofContext.bind_skolem fix_ctxt [thesisN];
    85     val bound_thesis = bind_thesis (ObjectLogic.fixed_judgment thy thesisN);
    86     val bound_thesis_raw as (bound_thesis_name, _) =
    87       Term.dest_Free (bind_thesis (Free (thesisN, propT)));
    88     val bound_thesis_var =
    89       fold_aterms (fn Free (x, T) => (fn v => if x = bound_thesis_name then (x, T) else v)
    90         | _ => I) bound_thesis bound_thesis_raw;
    91 
    92     fun occs_var x = Library.get_first (fn t =>
    93       ProofContext.find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;
    94     val raw_parms = map occs_var xs;
    95     val parms = List.mapPartial I raw_parms;
    96     val parm_names =
    97       List.mapPartial (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (raw_parms ~~ xs);
    98 
    99     val that_prop =
   100       Term.list_all_free (map #1 parm_names, Logic.list_implies (asm_props, bound_thesis))
   101       |> Library.curry Logic.list_rename_params (map #2 parm_names);
   102     val obtain_prop =
   103       Logic.list_rename_params ([AutoBind.thesisN],
   104         Term.list_all_free ([bound_thesis_var], Logic.mk_implies (that_prop, bound_thesis)));
   105 
   106     fun after_qed _ _ =
   107       Proof.local_qed (NONE, false)
   108       #> Seq.map (`Proof.the_fact #-> (fn this =>
   109         Proof.fix_i vars
   110         #> Proof.assm_i (export_obtain state parms this) asms));
   111   in
   112     state
   113     |> Proof.enter_forward
   114     |> Proof.have_i (K (K Seq.single)) [(("", []), [(obtain_prop, ([], []))])] int
   115     |> Proof.proof (SOME (Method.Basic (K Method.succeed))) |> Seq.hd
   116     |> Proof.fix_i [([thesisN], NONE)]
   117     |> Proof.assume_i [((thatN, [ContextRules.intro_query_local NONE]), [(that_prop, ([], []))])]
   118     |> `Proof.the_facts
   119     ||> Proof.chain_facts chain_facts
   120     ||> Proof.show_i after_qed [(("", []), [(bound_thesis, ([], []))])] false
   121     |-> (Proof.refine o Method.Basic o K o Method.insert) |> Seq.hd
   122   end;
   123 
   124 val obtain = gen_obtain Attrib.local_attribute ProofContext.read_vars ProofContext.read_propp;
   125 val obtain_i = gen_obtain (K I) ProofContext.cert_vars ProofContext.cert_propp;
   126 
   127 end;