wenzelm@6778
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(* Title: Pure/Isar/calculation.ML
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wenzelm@6778
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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 also: thm list option -> (thm list -> unit) -> Proof.state -> Proof.state Seq.seq
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val finally: thm list option -> (thm list -> unit) -> Proof.state -> Proof.state Seq.seq
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val moreover: (thm list -> unit) -> Proof.state -> Proof.state
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val ultimately: (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 rs = Pretty.writeln (Pretty.big_list "calculation rules:"
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(map Display.pretty_thm (NetRules.rules rs)));
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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
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val empty = NetRules.init_elim;
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val copy = I;
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val prep_ext = I;
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val merge = NetRules.merge;
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fun print _ = print_rules;
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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 * int) option;
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fun init thy = (GlobalCalculation.get thy, None);
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fun print _ (rs, _) = print_rules 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_st;
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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_st 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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LocalCalculation.put_st (get_local_rules state, Some (thms, Proof.level state)) state;
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fun reset_calculation state =
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LocalCalculation.put_st (get_local_rules state, None) state;
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(** attributes **)
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(* trans add/del *)
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fun mk_att f g (x, thm) = (f (g thm) x, thm);
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val trans_add_global = mk_att GlobalCalculation.map NetRules.insert;
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val trans_del_global = mk_att GlobalCalculation.map NetRules.delete;
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val trans_add_local = mk_att LocalCalculation.map (Library.apfst o NetRules.insert);
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val trans_del_local = mk_att LocalCalculation.map (Library.apfst o NetRules.delete);
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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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(** proof commands **)
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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.simple_have_thms calculationN calc
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|> Proof.reset_facts
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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_have_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 facts = Proof.the_facts state;
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val eq_prop = op aconv o pairself (#prop o Thm.rep_thm);
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fun differ thms thms' = not (Library.equal_lists eq_prop (thms, thms'));
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fun combine thms =
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let
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val ths = thms @ facts;
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val rs = get_local_rules state;
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val rules =
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(case ths of [] => NetRules.rules rs
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| th :: _ => NetRules.may_unify rs (Logic.strip_assums_concl (#prop (Thm.rep_thm th))));
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val ruleq = Seq.of_list (if_none opt_rules [] @ rules);
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in Seq.map Library.single (Seq.flat (Seq.map (Method.multi_resolve ths) ruleq)) end;
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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 thms => (false, Seq.filter (differ thms) (combine thms)))
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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 is_some opt_rules) "Initial calculation -- no rules to be given";
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calculations |> Seq.map (fn calc => (print calc; 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 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 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 = [GlobalCalculation.init, LocalCalculation.init,
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Attrib.add_attributes [("trans", trans_attr, "declare transitivity rule")]];
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end;
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