(*  Title:      Pure/Isar/calculation.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

    License:    GPL (GNU GENERAL PUBLIC LICENSE)

Support for calculational proofs.

*)

signature CALCULATION =

sig

  val print_global_rules: theory -> unit

  val print_local_rules: Proof.context -> unit

  val trans_add_global: theory attribute

  val trans_del_global: theory attribute

  val trans_add_local: Proof.context attribute

  val trans_del_local: Proof.context attribute

  val sym_add_global: theory attribute

  val sym_del_global: theory attribute

  val sym_add_local: Proof.context attribute

  val sym_del_local: Proof.context attribute

  val symmetric_global: theory attribute

  val symmetric_local: Proof.context attribute

  val also: thm list option -> (Proof.context -> thm list -> unit)

    -> Proof.state -> Proof.state Seq.seq

  val finally: thm list option -> (Proof.context -> thm list -> unit)

    -> Proof.state -> Proof.state Seq.seq

  val moreover: (Proof.context -> thm list -> unit) -> Proof.state -> Proof.state

  val ultimately: (Proof.context -> thm list -> unit) -> Proof.state -> Proof.state

  val setup: (theory -> theory) list

end;

structure Calculation: CALCULATION =

struct

(** global and local calculation data **)

(* theory data kind 'Isar/calculation' *)

fun print_rules prt x (trans, sym) =

  [Pretty.big_list "transitivity rules:" (map (prt x) (NetRules.rules trans)),

    Pretty.big_list "symmetry rules:" (map (prt x) sym)]

  |> Pretty.chunks |> Pretty.writeln;

structure GlobalCalculationArgs =

struct

  val name = "Isar/calculation";

  type T = thm NetRules.T * thm list

  val empty = (NetRules.elim, []);

  val copy = I;

  val prep_ext = I;

  fun merge ((trans1, sym1), (trans2, sym2)) =

    (NetRules.merge (trans1, trans2), Drule.merge_rules (sym1, sym2));

  val print = print_rules Display.pretty_thm_sg;

end;

structure GlobalCalculation = TheoryDataFun(GlobalCalculationArgs);

val print_global_rules = GlobalCalculation.print;

(* proof data kind 'Isar/calculation' *)

structure LocalCalculationArgs =

struct

  val name = "Isar/calculation";

  type T = (thm NetRules.T * thm list) * (thm list * int) option;

  fun init thy = (GlobalCalculation.get thy, None);

  fun print ctxt (rs, _) = print_rules ProofContext.pretty_thm ctxt rs;

end;

structure LocalCalculation = ProofDataFun(LocalCalculationArgs);

val get_local_rules = #1 o LocalCalculation.get o Proof.context_of;

val print_local_rules = LocalCalculation.print;

(* access calculation *)

fun get_calculation state =

  (case #2 (LocalCalculation.get (Proof.context_of state)) of

    None => None

  | Some (thms, lev) => if lev = Proof.level state then Some thms else None);

fun put_calculation thms state =

  Proof.map_context

    (LocalCalculation.put (get_local_rules state, Some (thms, Proof.level state))) state;

fun reset_calculation state =

  Proof.map_context (LocalCalculation.put (get_local_rules state, None)) state;

(** attributes **)

(* add/del rules *)

fun global_att f (x, thm) = (GlobalCalculation.map (f thm) x, thm);

fun local_att f (x, thm) = (LocalCalculation.map (apfst (f thm)) x, thm);

val trans_add_global = global_att (apfst o NetRules.insert);

val trans_del_global = global_att (apfst o NetRules.delete);

val trans_add_local = local_att (apfst o NetRules.insert);

val trans_del_local = local_att (apfst o NetRules.delete);

val sym_add_global = global_att (apsnd o Drule.add_rule) o ContextRules.elim_query_global None;

val sym_del_global = global_att (apsnd o Drule.del_rule) o ContextRules.rule_del_global;

val sym_add_local = local_att (apsnd o Drule.add_rule) o ContextRules.elim_query_local None;

val sym_del_local = local_att (apsnd o Drule.del_rule) o ContextRules.rule_del_local;

(* symmetry *)

fun gen_symmetric get_sym = Drule.rule_attribute (fn x => fn th =>

  (case Seq.chop (2, Method.multi_resolves [th] (get_sym x)) of

    ([th'], _) => th'

  | ([], _) => raise THM ("symmetric: no unifiers", 1, [th])

  | _ => raise THM ("symmetric: multiple unifiers", 1, [th])));

val symmetric_global = gen_symmetric (#2 o GlobalCalculation.get);

val symmetric_local = gen_symmetric (#2 o #1 o LocalCalculation.get);

(* concrete syntax *)

val trans_attr =

 (Attrib.add_del_args trans_add_global trans_del_global,

  Attrib.add_del_args trans_add_local trans_del_local);

val sym_attr =

 (Attrib.add_del_args sym_add_global sym_del_global,

  Attrib.add_del_args sym_add_local sym_del_local);

(** proof commands **)

fun assert_sane final =

  if final then Proof.assert_forward else Proof.assert_forward_or_chain;

(* maintain calculation register *)

val calculationN = "calculation";

fun maintain_calculation false calc state =

      state

      |> put_calculation calc

      |> Proof.put_thms (calculationN, calc)

  | maintain_calculation true calc state =

      state

      |> reset_calculation

      |> Proof.reset_thms calculationN

      |> Proof.simple_note_thms "" calc

      |> Proof.chain;

(* 'also' and 'finally' *)

fun err_if state b msg = if b then raise Proof.STATE (msg, state) else ();

fun calculate final opt_rules print state =

  let

    val strip_assums_concl = Logic.strip_assums_concl o Thm.prop_of;

    val eq_prop = op aconv o pairself (Pattern.eta_contract o strip_assums_concl);

    fun projection ths th = Library.exists (Library.curry eq_prop th) ths;

    fun combine ths =

      (case opt_rules of Some rules => rules

      | None =>

          (case ths of [] => NetRules.rules (#1 (get_local_rules state))

          | th :: _ => NetRules.retrieve (#1 (get_local_rules state)) (strip_assums_concl th)))

      |> Seq.of_list |> Seq.map (Method.multi_resolve ths) |> Seq.flat

      |> Seq.filter (not o projection ths);

    val facts = Proof.the_facts (assert_sane final state);

    val (initial, calculations) =

      (case get_calculation state of

        None => (true, Seq.single facts)

      | Some calc => (false, Seq.map single (combine (calc @ facts))));

  in

    err_if state (initial andalso final) "No calculation yet";

    err_if state (initial andalso is_some opt_rules) "Initial calculation -- no rules to be given";

    calculations |> Seq.map (fn calc => (print (Proof.context_of state) calc;

        state |> maintain_calculation final calc))

  end;

fun also print = calculate false print;

fun finally print = calculate true print;

(* 'moreover' and 'ultimately' *)

fun collect final print state =

  let

    val facts = Proof.the_facts (assert_sane final state);

    val (initial, thms) =

      (case get_calculation state of

        None => (true, [])

      | Some thms => (false, thms));

    val calc = thms @ facts;

  in

    err_if state (initial andalso final) "No calculation yet";

    print (Proof.context_of state) calc;

    state |> maintain_calculation final calc

  end;

fun moreover print = collect false print;

fun ultimately print = collect true print;

(** theory setup **)

val setup =

 [GlobalCalculation.init, LocalCalculation.init,

  Attrib.add_attributes

   [("trans", trans_attr, "declaration of transitivity rule"),

    ("sym", sym_attr, "declaration of symmetry rule"),

    ("symmetric", (Attrib.no_args symmetric_global, Attrib.no_args symmetric_local),

      "resolution with symmetry rule")],

  #1 o PureThy.add_thms

   [(("", transitive_thm), [trans_add_global]),

    (("", symmetric_thm), [sym_add_global])]];

end;