src/Pure/Isar/calculation.ML
author skalberg
Thu Mar 03 12:43:01 2005 +0100 (2005-03-03)
changeset 15570 8d8c70b41bab
parent 15531 08c8dad8e399
child 15801 d2f5ca3c048d
permissions -rw-r--r--
Move towards standard functions.
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(*  Title:      Pure/Isar/calculation.ML
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    ID:         $Id$
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    Author:     Markus Wenzel, TU Muenchen
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Support for calculational proofs.
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*)
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signature CALCULATION =
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sig
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  val print_global_rules: theory -> unit
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  val print_local_rules: Proof.context -> unit
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  val trans_add_global: theory attribute
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  val trans_del_global: theory attribute
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  val trans_add_local: Proof.context attribute
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  val trans_del_local: Proof.context attribute
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  val sym_add_global: theory attribute
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  val sym_del_global: theory attribute
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  val sym_add_local: Proof.context attribute
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  val sym_del_local: Proof.context attribute
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  val symmetric_global: theory attribute
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  val symmetric_local: Proof.context attribute
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  val also: thm list option -> (Proof.context -> thm list -> unit)
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    -> Proof.state -> Proof.state Seq.seq
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  val finally: thm list option -> (Proof.context -> thm list -> unit)
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    -> Proof.state -> Proof.state Seq.seq
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  val moreover: (Proof.context -> thm list -> unit) -> Proof.state -> Proof.state
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  val ultimately: (Proof.context -> thm list -> unit) -> Proof.state -> Proof.state
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  val setup: (theory -> theory) list
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end;
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structure Calculation: CALCULATION =
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struct
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(** global and local calculation data **)
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(* theory data kind 'Isar/calculation' *)
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fun print_rules prt x (trans, sym) =
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  [Pretty.big_list "transitivity rules:" (map (prt x) (NetRules.rules trans)),
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    Pretty.big_list "symmetry rules:" (map (prt x) sym)]
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  |> Pretty.chunks |> Pretty.writeln;
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structure GlobalCalculationArgs =
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struct
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  val name = "Isar/calculation";
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  type T = thm NetRules.T * thm list
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  val empty = (NetRules.elim, []);
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  val copy = I;
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  val prep_ext = I;
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  fun merge ((trans1, sym1), (trans2, sym2)) =
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    (NetRules.merge (trans1, trans2), Drule.merge_rules (sym1, sym2));
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  val print = print_rules Display.pretty_thm_sg;
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end;
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structure GlobalCalculation = TheoryDataFun(GlobalCalculationArgs);
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val print_global_rules = GlobalCalculation.print;
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(* proof data kind 'Isar/calculation' *)
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structure LocalCalculationArgs =
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struct
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  val name = "Isar/calculation";
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  type T = (thm NetRules.T * thm list) * (thm list * int) option;
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  fun init thy = (GlobalCalculation.get thy, NONE);
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  fun print ctxt (rs, _) = print_rules ProofContext.pretty_thm ctxt rs;
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end;
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structure LocalCalculation = ProofDataFun(LocalCalculationArgs);
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val get_local_rules = #1 o LocalCalculation.get o Proof.context_of;
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val print_local_rules = LocalCalculation.print;
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(* access calculation *)
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fun get_calculation state =
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  (case #2 (LocalCalculation.get (Proof.context_of state)) of
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    NONE => NONE
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  | SOME (thms, lev) => if lev = Proof.level state then SOME thms else NONE);
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fun put_calculation thms state =
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  Proof.map_context
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    (LocalCalculation.put (get_local_rules state, SOME (thms, Proof.level state))) state;
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fun reset_calculation state =
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  Proof.map_context (LocalCalculation.put (get_local_rules state, NONE)) state;
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(** attributes **)
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(* add/del rules *)
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fun global_att f (x, thm) = (GlobalCalculation.map (f thm) x, thm);
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fun local_att f (x, thm) = (LocalCalculation.map (apfst (f thm)) x, thm);
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val trans_add_global = global_att (apfst o NetRules.insert);
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val trans_del_global = global_att (apfst o NetRules.delete);
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val trans_add_local = local_att (apfst o NetRules.insert);
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val trans_del_local = local_att (apfst o NetRules.delete);
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val sym_add_global = global_att (apsnd o Drule.add_rule) o ContextRules.elim_query_global NONE;
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val sym_del_global = global_att (apsnd o Drule.del_rule) o ContextRules.rule_del_global;
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val sym_add_local = local_att (apsnd o Drule.add_rule) o ContextRules.elim_query_local NONE;
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val sym_del_local = local_att (apsnd o Drule.del_rule) o ContextRules.rule_del_local;
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(* symmetry *)
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fun gen_symmetric get_sym = Drule.rule_attribute (fn x => fn th =>
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  (case Seq.chop (2, Method.multi_resolves [th] (get_sym x)) of
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    ([th'], _) => th'
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  | ([], _) => raise THM ("symmetric: no unifiers", 1, [th])
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  | _ => raise THM ("symmetric: multiple unifiers", 1, [th])));
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val symmetric_global = gen_symmetric (#2 o GlobalCalculation.get);
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val symmetric_local = gen_symmetric (#2 o #1 o LocalCalculation.get);
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(* concrete syntax *)
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val trans_attr =
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 (Attrib.add_del_args trans_add_global trans_del_global,
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  Attrib.add_del_args trans_add_local trans_del_local);
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val sym_attr =
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 (Attrib.add_del_args sym_add_global sym_del_global,
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  Attrib.add_del_args sym_add_local sym_del_local);
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(** proof commands **)
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fun assert_sane final =
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  if final then Proof.assert_forward else Proof.assert_forward_or_chain;
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(* maintain calculation register *)
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val calculationN = "calculation";
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fun maintain_calculation false calc state =
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      state
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      |> put_calculation calc
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      |> Proof.put_thms (calculationN, calc)
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  | maintain_calculation true calc state =
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      state
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      |> reset_calculation
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      |> Proof.reset_thms calculationN
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      |> Proof.simple_note_thms "" calc
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      |> Proof.chain;
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(* 'also' and 'finally' *)
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fun err_if state b msg = if b then raise Proof.STATE (msg, state) else ();
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fun calculate final opt_rules print state =
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  let
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    val strip_assums_concl = Logic.strip_assums_concl o Thm.prop_of;
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    val eq_prop = op aconv o pairself (Pattern.eta_contract o strip_assums_concl);
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    fun projection ths th = Library.exists (Library.curry eq_prop th) ths;
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    fun combine ths =
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      (case opt_rules of SOME rules => rules
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      | NONE =>
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          (case ths of [] => NetRules.rules (#1 (get_local_rules state))
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          | th :: _ => NetRules.retrieve (#1 (get_local_rules state)) (strip_assums_concl th)))
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      |> Seq.of_list |> Seq.map (Method.multi_resolve ths) |> Seq.flat
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      |> Seq.filter (not o projection ths);
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    val facts = Proof.the_facts (assert_sane final state);
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    val (initial, calculations) =
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      (case get_calculation state of
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        NONE => (true, Seq.single facts)
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      | SOME calc => (false, Seq.map single (combine (calc @ facts))));
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  in
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    err_if state (initial andalso final) "No calculation yet";
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    err_if state (initial andalso isSome opt_rules) "Initial calculation -- no rules to be given";
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    calculations |> Seq.map (fn calc => (print (Proof.context_of state) calc;
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        state |> maintain_calculation final calc))
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  end;
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fun also print = calculate false print;
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fun finally print = calculate true print;
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(* 'moreover' and 'ultimately' *)
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fun collect final print state =
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  let
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    val facts = Proof.the_facts (assert_sane final state);
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    val (initial, thms) =
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      (case get_calculation state of
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        NONE => (true, [])
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      | SOME thms => (false, thms));
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    val calc = thms @ facts;
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  in
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    err_if state (initial andalso final) "No calculation yet";
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    print (Proof.context_of state) calc;
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    state |> maintain_calculation final calc
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  end;
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fun moreover print = collect false print;
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fun ultimately print = collect true print;
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(** theory setup **)
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val setup =
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 [GlobalCalculation.init, LocalCalculation.init,
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  Attrib.add_attributes
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   [("trans", trans_attr, "declaration of transitivity rule"),
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    ("sym", sym_attr, "declaration of symmetry rule"),
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    ("symmetric", (Attrib.no_args symmetric_global, Attrib.no_args symmetric_local),
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      "resolution with symmetry rule")],
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  #1 o PureThy.add_thms
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   [(("", transitive_thm), [trans_add_global]),
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    (("", symmetric_thm), [sym_add_global])]];
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end;