src/Provers/order.ML
author ballarin
Tue, 18 Sep 2007 18:51:07 +0200
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Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
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(*
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  Title:	Transitivity reasoner for partial and linear orders
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  Id:		$Id$
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  Author:	Oliver Kutter
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  Copyright:	TU Muenchen
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*)
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(* TODO: reduce number of input thms *)
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(*
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The package provides tactics partial_tac and linear_tac that use all
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premises of the form
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  t = u, t ~= u, t < u, t <= u, ~(t < u) and ~(t <= u)
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to
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1. either derive a contradiction,
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   in which case the conclusion can be any term,
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2. or prove the conclusion, which must be of the same form as the
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   premises (excluding ~(t < u) and ~(t <= u) for partial orders)
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The package is not limited to the relation <= and friends.  It can be
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instantiated to any partial and/or linear order --- for example, the
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divisibility relation "dvd".  In order to instantiate the package for
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a partial order only, supply dummy theorems to the rules for linear
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orders, and don't use linear_tac!
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*)
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signature ORDER_TAC =
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sig
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  (* Theorems required by the reasoner *)
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  type less_arith
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  val empty : thm -> less_arith
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  val update : string -> thm -> less_arith -> less_arith
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  (* Tactics *)
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  val partial_tac:
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    (theory -> term -> (term * string * term) option) -> less_arith -> int -> tactic
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  val linear_tac:
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    (theory -> term -> (term * string * term) option) -> less_arith -> int -> tactic
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end;
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structure Order_Tac: ORDER_TAC =
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struct
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(* Record to handle input theorems in a convenient way. *)
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type less_arith =
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  {
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    (* Theorems for partial orders *)
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    less_reflE: thm,  (* x < x ==> P *)
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    le_refl: thm,  (* x <= x *)
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    less_imp_le: thm, (* x < y ==> x <= y *)
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    eqI: thm, (* [| x <= y; y <= x |] ==> x = y *)
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    eqD1: thm, (* x = y ==> x <= y *)
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    eqD2: thm, (* x = y ==> y <= x *)
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    less_trans: thm,  (* [| x < y; y < z |] ==> x < z *)
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    less_le_trans: thm,  (* [| x < y; y <= z |] ==> x < z *)
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    le_less_trans: thm,  (* [| x <= y; y < z |] ==> x < z *)
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    le_trans: thm,  (* [| x <= y; y <= z |] ==> x <= z *)
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    le_neq_trans : thm, (* [| x <= y ; x ~= y |] ==> x < y *)
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    neq_le_trans : thm, (* [| x ~= y ; x <= y |] ==> x < y *)
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    not_sym : thm, (* x ~= y ==> y ~= x *)
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    (* Additional theorems for linear orders *)
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    not_lessD: thm, (* ~(x < y) ==> y <= x *)
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    not_leD: thm, (* ~(x <= y) ==> y < x *)
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    not_lessI: thm, (* y <= x  ==> ~(x < y) *)
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    not_leI: thm, (* y < x  ==> ~(x <= y) *)
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    (* Additional theorems for subgoals of form x ~= y *)
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    less_imp_neq : thm, (* x < y ==> x ~= y *)
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    eq_neq_eq_imp_neq : thm (* [| x = u ; u ~= v ; v = z|] ==> x ~= z *)
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  }
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fun empty dummy_thm =
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    {less_reflE= dummy_thm, le_refl= dummy_thm, less_imp_le= dummy_thm, eqI= dummy_thm,
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      eqD1= dummy_thm, eqD2= dummy_thm,
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      less_trans= dummy_thm, less_le_trans= dummy_thm, le_less_trans= dummy_thm,
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      le_trans= dummy_thm, le_neq_trans = dummy_thm, neq_le_trans = dummy_thm,
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      not_sym = dummy_thm,
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      not_lessD= dummy_thm, not_leD= dummy_thm, not_lessI= dummy_thm, not_leI= dummy_thm,
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      less_imp_neq = dummy_thm, eq_neq_eq_imp_neq = dummy_thm}
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fun change thms f =
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  let
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    val {less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq} = thms;
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    val (less_reflE', le_refl', less_imp_le', eqI', eqD1', eqD2', less_trans',
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      less_le_trans', le_less_trans', le_trans', le_neq_trans', neq_le_trans',
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      not_sym', not_lessD', not_leD', not_lessI', not_leI', less_imp_neq',
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      eq_neq_eq_imp_neq') =
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     f (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq)
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  in {less_reflE = less_reflE', le_refl= le_refl',
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      less_imp_le = less_imp_le', eqI = eqI', eqD1 = eqD1', eqD2 = eqD2',
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      less_trans = less_trans', less_le_trans = less_le_trans',
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      le_less_trans = le_less_trans', le_trans = le_trans', le_neq_trans = le_neq_trans',
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      neq_le_trans = neq_le_trans', not_sym = not_sym',
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      not_lessD = not_lessD', not_leD = not_leD', not_lessI = not_lessI',
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      not_leI = not_leI',
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      less_imp_neq = less_imp_neq', eq_neq_eq_imp_neq = eq_neq_eq_imp_neq'}
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  end;
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fun update "less_reflE" thm thms =
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    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq) =>
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    (thm, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
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  | update "le_refl" thm thms =
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    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq) =>
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    (less_reflE, thm, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
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  | update "less_imp_le" thm thms =
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    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   130
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   131
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   132
    (less_reflE, le_refl, thm, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   133
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   134
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   135
  | update "eqI" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   136
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   137
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   138
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   139
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   140
    (less_reflE, le_refl, less_imp_le, thm, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   141
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   142
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   143
  | update "eqD1" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   144
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   145
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   146
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   147
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   148
    (less_reflE, le_refl, less_imp_le, eqI, thm, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   149
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   150
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   151
  | update "eqD2" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   152
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   153
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   154
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   155
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   156
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, thm, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   157
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   158
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   159
  | update "less_trans" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   160
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   161
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   162
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   163
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   164
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, thm,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   165
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   166
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   167
  | update "less_le_trans" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   168
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   169
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   170
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   171
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   172
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   173
      thm, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   174
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   175
  | update "le_less_trans" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   176
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   177
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   178
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   179
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   180
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   181
      less_le_trans, thm, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   182
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   183
  | update "le_trans" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   184
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   185
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   186
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   187
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   188
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   189
      less_le_trans, le_less_trans, thm, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   190
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   191
  | update "le_neq_trans" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   192
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   193
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   194
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   195
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   196
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   197
      less_le_trans, le_less_trans, le_trans, thm, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   198
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   199
  | update "neq_le_trans" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   200
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   201
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   202
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   203
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   204
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   205
      less_le_trans, le_less_trans, le_trans, le_neq_trans, thm,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   206
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   207
  | update "not_sym" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   208
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   209
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   210
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   211
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   212
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   213
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   214
      thm, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   215
  | update "not_lessD" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   216
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   217
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   218
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   219
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   220
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   221
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   222
      not_sym, thm, not_leD, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   223
  | update "not_leD" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   224
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   225
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   226
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   227
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   228
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   229
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   230
      not_sym, not_lessD, thm, not_lessI, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   231
  | update "not_lessI" thm thms =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   232
    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   233
      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   234
      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   235
      eq_neq_eq_imp_neq) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   236
    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, thm, not_leI, less_imp_neq, eq_neq_eq_imp_neq))
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  | update "not_leI" thm thms =
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    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq) =>
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    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, thm, less_imp_neq, eq_neq_eq_imp_neq))
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  | update "less_imp_neq" thm thms =
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    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq) =>
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    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, thm, eq_neq_eq_imp_neq))
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  | update "eq_neq_eq_imp_neq" thm thms =
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    change thms (fn (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq,
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      eq_neq_eq_imp_neq) =>
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    (less_reflE, le_refl, less_imp_le, eqI, eqD1, eqD2, less_trans,
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      less_le_trans, le_less_trans, le_trans, le_neq_trans, neq_le_trans,
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      not_sym, not_lessD, not_leD, not_lessI, not_leI, less_imp_neq, thm));
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(* Extract subgoal with signature *)
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fun SUBGOAL goalfun i st =
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  goalfun (List.nth(prems_of st, i-1),  i, Thm.theory_of_thm st) st
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                             handle Subscript => Seq.empty;
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(* Internal datatype for the proof *)
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datatype proof
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  = Asm of int 
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  | Thm of proof list * thm; 
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exception Cannot;
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 (* Internal exception, raised if conclusion cannot be derived from
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     assumptions. *)
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exception Contr of proof;
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  (* Internal exception, raised if contradiction ( x < x ) was derived *)
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fun prove asms = 
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  let fun pr (Asm i) = List.nth (asms, i)
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  |       pr (Thm (prfs, thm)) = (map pr prfs) MRS thm
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  in pr end;
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(* Internal datatype for inequalities *)
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datatype less 
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   = Less  of term * term * proof 
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   | Le    of term * term * proof
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   | NotEq of term * term * proof; 
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(* Misc functions for datatype less *)
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fun lower (Less (x, _, _)) = x
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  | lower (Le (x, _, _)) = x
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  | lower (NotEq (x,_,_)) = x;
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fun upper (Less (_, y, _)) = y
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  | upper (Le (_, y, _)) = y
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  | upper (NotEq (_,y,_)) = y;
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fun getprf   (Less (_, _, p)) = p
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|   getprf   (Le   (_, _, p)) = p
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|   getprf   (NotEq (_,_, p)) = p;
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(* ************************************************************************ *)
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(*                                                                          *)
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(* mkasm_partial                                                            *)
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(*                                                                          *)
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(* Tuple (t, n) (t an assumption, n its index in the assumptions) is        *)
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(* translated to an element of type less.                                   *)
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(* Partial orders only.                                                     *)
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(*                                                                          *)
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(* ************************************************************************ *)
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fun mkasm_partial decomp (less_thms : less_arith) sign (t, n) =
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  case decomp sign t of
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    SOME (x, rel, y) => (case rel of
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      "<"   => if (x aconv y) then raise Contr (Thm ([Asm n], #less_reflE less_thms)) 
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               else [Less (x, y, Asm n)]
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    | "~<"  => []
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    | "<="  => [Le (x, y, Asm n)]
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    | "~<=" => [] 
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    | "="   => [Le (x, y, Thm ([Asm n], #eqD1 less_thms)),
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                Le (y, x, Thm ([Asm n], #eqD2 less_thms))]
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    | "~="  => if (x aconv y) then 
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                  raise Contr (Thm ([(Thm ([(Thm ([], #le_refl less_thms)) ,(Asm n)], #le_neq_trans less_thms))], #less_reflE less_thms))
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               else [ NotEq (x, y, Asm n),
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                      NotEq (y, x,Thm ( [Asm n], #not_sym less_thms))] 
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    | _     => error ("partial_tac: unknown relation symbol ``" ^ rel ^
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                 "''returned by decomp."))
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  | NONE => [];
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(* ************************************************************************ *)
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(*                                                                          *)
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(* mkasm_linear                                                             *)
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(*                                                                          *)
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(* Tuple (t, n) (t an assumption, n its index in the assumptions) is        *)
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(* translated to an element of type less.                                   *)
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(* Linear orders only.                                                      *)
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(*                                                                          *)
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(* ************************************************************************ *)
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fun mkasm_linear decomp (less_thms : less_arith) sign (t, n) =
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  case decomp sign t of
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    SOME (x, rel, y) => (case rel of
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      "<"   => if (x aconv y) then raise Contr (Thm ([Asm n], #less_reflE less_thms)) 
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               else [Less (x, y, Asm n)]
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    | "~<"  => [Le (y, x, Thm ([Asm n], #not_lessD less_thms))]
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    | "<="  => [Le (x, y, Asm n)]
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    | "~<=" => if (x aconv y) then 
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                  raise (Contr (Thm ([Thm ([Asm n], #not_leD less_thms)], #less_reflE less_thms))) 
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               else [Less (y, x, Thm ([Asm n], #not_leD less_thms))] 
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    | "="   => [Le (x, y, Thm ([Asm n], #eqD1 less_thms)),
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                Le (y, x, Thm ([Asm n], #eqD2 less_thms))]
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    | "~="  => if (x aconv y) then 
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                  raise Contr (Thm ([(Thm ([(Thm ([], #le_refl less_thms)) ,(Asm n)], #le_neq_trans less_thms))], #less_reflE less_thms))
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               else [ NotEq (x, y, Asm n),
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                      NotEq (y, x,Thm ( [Asm n], #not_sym less_thms))] 
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    | _     => error ("linear_tac: unknown relation symbol ``" ^ rel ^
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                 "''returned by decomp."))
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  | NONE => [];
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(* ************************************************************************ *)
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(*                                                                          *)
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(* mkconcl_partial                                                          *)
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(*                                                                          *)
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(* Translates conclusion t to an element of type less.                      *)
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(* Partial orders only.                                                     *)
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(*                                                                          *)
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(* ************************************************************************ *)
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   373
fun mkconcl_partial decomp (less_thms : less_arith) sign t =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   374
  case decomp sign t of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   375
    SOME (x, rel, y) => (case rel of
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   376
      "<"   => ([Less (x, y, Asm ~1)], Asm 0)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   377
    | "<="  => ([Le (x, y, Asm ~1)], Asm 0)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   378
    | "="   => ([Le (x, y, Asm ~1), Le (y, x, Asm ~1)],
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   379
                 Thm ([Asm 0, Asm 1], #eqI less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   380
    | "~="  => ([NotEq (x,y, Asm ~1)], Asm 0)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   381
    | _  => raise Cannot)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   382
  | NONE => raise Cannot;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   383
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   384
(* ************************************************************************ *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   385
(*                                                                          *)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   386
(* mkconcl_linear                                                           *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   387
(*                                                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   388
(* Translates conclusion t to an element of type less.                      *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   389
(* Linear orders only.                                                      *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   390
(*                                                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   391
(* ************************************************************************ *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   392
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   393
fun mkconcl_linear decomp (less_thms : less_arith) sign t =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   394
  case decomp sign t of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   395
    SOME (x, rel, y) => (case rel of
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   396
      "<"   => ([Less (x, y, Asm ~1)], Asm 0)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   397
    | "~<"  => ([Le (y, x, Asm ~1)], Thm ([Asm 0], #not_lessI less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   398
    | "<="  => ([Le (x, y, Asm ~1)], Asm 0)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   399
    | "~<=" => ([Less (y, x, Asm ~1)], Thm ([Asm 0], #not_leI less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   400
    | "="   => ([Le (x, y, Asm ~1), Le (y, x, Asm ~1)],
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   401
                 Thm ([Asm 0, Asm 1], #eqI less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   402
    | "~="  => ([NotEq (x,y, Asm ~1)], Asm 0)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   403
    | _  => raise Cannot)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   404
  | NONE => raise Cannot;
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   405
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   406
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   407
(*** The common part for partial and linear orders ***)
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   408
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   409
(* Analysis of premises and conclusion: *)
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   410
(* decomp (`x Rel y') should yield (x, Rel, y)
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   411
     where Rel is one of "<", "<=", "~<", "~<=", "=" and "~=",
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   412
     other relation symbols cause an error message *)
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   413
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   414
fun gen_order_tac mkasm mkconcl decomp (less_thms : less_arith) =
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   415
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   416
let
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   417
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   418
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   419
(*                                                                     *)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   420
(* mergeLess                                                           *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   421
(*                                                                     *)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   422
(* Merge two elements of type less according to the following rules    *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   423
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   424
(* x <  y && y <  z ==> x < z                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   425
(* x <  y && y <= z ==> x < z                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   426
(* x <= y && y <  z ==> x < z                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   427
(* x <= y && y <= z ==> x <= z                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   428
(* x <= y && x ~= y ==> x < y                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   429
(* x ~= y && x <= y ==> x < y                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   430
(* x <  y && x ~= y ==> x < y                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   431
(* x ~= y && x <  y ==> x < y                                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   432
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   433
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   434
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   435
fun mergeLess (Less (x, _, p) , Less (_ , z, q)) =
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   436
      Less (x, z, Thm ([p,q] , #less_trans less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   437
|   mergeLess (Less (x, _, p) , Le (_ , z, q)) =
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   438
      Less (x, z, Thm ([p,q] , #less_le_trans less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   439
|   mergeLess (Le (x, _, p) , Less (_ , z, q)) =
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   440
      Less (x, z, Thm ([p,q] , #le_less_trans less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   441
|   mergeLess (Le (x, z, p) , NotEq (x', z', q)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   442
      if (x aconv x' andalso z aconv z' ) 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   443
      then Less (x, z, Thm ([p,q] , #le_neq_trans less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   444
      else error "linear/partial_tac: internal error le_neq_trans"
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   445
|   mergeLess (NotEq (x, z, p) , Le (x' , z', q)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   446
      if (x aconv x' andalso z aconv z') 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   447
      then Less (x, z, Thm ([p,q] , #neq_le_trans less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   448
      else error "linear/partial_tac: internal error neq_le_trans"
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   449
|   mergeLess (NotEq (x, z, p) , Less (x' , z', q)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   450
      if (x aconv x' andalso z aconv z') 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   451
      then Less ((x' , z', q))
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   452
      else error "linear/partial_tac: internal error neq_less_trans"
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   453
|   mergeLess (Less (x, z, p) , NotEq (x', z', q)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   454
      if (x aconv x' andalso z aconv z') 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   455
      then Less (x, z, p)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   456
      else error "linear/partial_tac: internal error less_neq_trans"
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   457
|   mergeLess (Le (x, _, p) , Le (_ , z, q)) =
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   458
      Le (x, z, Thm ([p,q] , #le_trans less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   459
|   mergeLess (_, _) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   460
      error "linear/partial_tac: internal error: undefined case";
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   461
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   462
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   463
(* ******************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   464
(* tr checks for valid transitivity step                                *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   465
(* ******************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   466
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   467
infix tr;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   468
fun (Less (_, y, _)) tr (Le (x', _, _))   = ( y aconv x' )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   469
  | (Le   (_, y, _)) tr (Less (x', _, _)) = ( y aconv x' )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   470
  | (Less (_, y, _)) tr (Less (x', _, _)) = ( y aconv x' )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   471
  | (Le (_, y, _))   tr (Le (x', _, _))   = ( y aconv x' )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   472
  | _ tr _ = false;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   473
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   474
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   475
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   476
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   477
(* transPath (Lesslist, Less): (less list * less) -> less              *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   478
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   479
(* If a path represented by a list of elements of type less is found,  *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   480
(* this needs to be contracted to a single element of type less.       *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   481
(* Prior to each transitivity step it is checked whether the step is   *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   482
(* valid.                                                              *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   483
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   484
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   485
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   486
fun transPath ([],lesss) = lesss
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   487
|   transPath (x::xs,lesss) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   488
      if lesss tr x then transPath (xs, mergeLess(lesss,x))
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   489
      else error "linear/partial_tac: internal error transpath";
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   490
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   491
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   492
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   493
(* less1 subsumes less2 : less -> less -> bool                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   494
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   495
(* subsumes checks whether less1 implies less2                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   496
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   497
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   498
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   499
infix subsumes;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   500
fun (Less (x, y, _)) subsumes (Le (x', y', _)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   501
      (x aconv x' andalso y aconv y')
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   502
  | (Less (x, y, _)) subsumes (Less (x', y', _)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   503
      (x aconv x' andalso y aconv y')
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   504
  | (Le (x, y, _)) subsumes (Le (x', y', _)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   505
      (x aconv x' andalso y aconv y')
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   506
  | (Less (x, y, _)) subsumes (NotEq (x', y', _)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   507
      (x aconv x' andalso y aconv y') orelse (y aconv x' andalso x aconv y')
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   508
  | (NotEq (x, y, _)) subsumes (NotEq (x', y', _)) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   509
      (x aconv x' andalso y aconv y') orelse (y aconv x' andalso x aconv y')
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   510
  | (Le _) subsumes (Less _) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   511
      error "linear/partial_tac: internal error: Le cannot subsume Less"
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   512
  | _ subsumes _ = false;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   513
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   514
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   515
(*                                                                     *)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   516
(* triv_solv less1 : less ->  proof option                     *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   517
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   518
(* Solves trivial goal x <= x.                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   519
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   520
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   521
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   522
fun triv_solv (Le (x, x', _)) =
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   523
    if x aconv x' then  SOME (Thm ([], #le_refl less_thms))
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   524
    else NONE
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   525
|   triv_solv _ = NONE;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   526
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   527
(* ********************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   528
(* Graph functions                                                       *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   529
(* ********************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   530
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   531
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   532
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   533
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   534
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   535
(* General:                                                            *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   536
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   537
(* Inequalities are represented by various types of graphs.            *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   538
(*                                                                     *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   539
(* 1. (Term.term * (Term.term * less) list) list                       *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   540
(*    - Graph of this type is generated from the assumptions,          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   541
(*      it does contain information on which edge stems from which     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   542
(*      assumption.                                                    *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   543
(*    - Used to compute strongly connected components                  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   544
(*    - Used to compute component subgraphs                            *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   545
(*    - Used for component subgraphs to reconstruct paths in components*)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   546
(*                                                                     *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   547
(* 2. (int * (int * less) list ) list                                  *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   548
(*    - Graph of this type is generated from the strong components of  *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   549
(*      graph of type 1.  It consists of the strong components of      *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   550
(*      graph 1, where nodes are indices of the components.            *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   551
(*      Only edges between components are part of this graph.          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   552
(*    - Used to reconstruct paths between several components.          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   553
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   554
(* ******************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   555
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   556
   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   557
(* *********************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   558
(* Functions for constructing graphs                           *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   559
(* *********************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   560
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   561
fun addEdge (v,d,[]) = [(v,d)]
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   562
|   addEdge (v,d,((u,dl)::el)) = if v aconv u then ((v,d@dl)::el)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   563
    else (u,dl):: (addEdge(v,d,el));
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   564
    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   565
(* ********************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   566
(*                                                                       *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   567
(* mkGraphs constructs from a list of objects of type less a graph g,    *) 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   568
(* by taking all edges that are candidate for a <=, and a list neqE, by  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   569
(* taking all edges that are candiate for a ~=                           *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   570
(*                                                                       *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   571
(* ********************************************************************* *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   572
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   573
fun mkGraphs [] = ([],[],[])
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   574
|   mkGraphs lessList = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   575
 let
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   576
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   577
fun buildGraphs ([],leqG,neqG,neqE) = (leqG, neqG, neqE)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   578
|   buildGraphs (l::ls, leqG,neqG, neqE) = case l of 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   579
  (Less (x,y,p)) =>    
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   580
       buildGraphs (ls, addEdge (x,[(y,(Less (x, y, p)))],leqG) , 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   581
                        addEdge (x,[(y,(Less (x, y, p)))],neqG), l::neqE) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   582
| (Le (x,y,p)) =>
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   583
      buildGraphs (ls, addEdge (x,[(y,(Le (x, y,p)))],leqG) , neqG, neqE) 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   584
| (NotEq  (x,y,p)) => 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   585
      buildGraphs (ls, leqG , addEdge (x,[(y,(NotEq (x, y, p)))],neqG), l::neqE) ;
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   586
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   587
  in buildGraphs (lessList, [], [], []) end;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   588
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   589
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   590
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   591
(*                                                                         *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   592
(* adjacent g u : (''a * 'b list ) list -> ''a -> 'b list                  *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   593
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   594
(* List of successors of u in graph g                                      *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   595
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   596
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   597
 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   598
fun adjacent eq_comp ((v,adj)::el) u = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   599
    if eq_comp (u, v) then adj else adjacent eq_comp el u
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   600
|   adjacent _  []  _ = []  
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   601
  
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   602
     
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   603
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   604
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   605
(* transpose g:                                                            *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   606
(* (''a * ''a list) list -> (''a * ''a list) list                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   607
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   608
(* Computes transposed graph g' from g                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   609
(* by reversing all edges u -> v to v -> u                                 *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   610
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   611
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   612
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   613
fun transpose eq_comp g =
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   614
  let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   615
   (* Compute list of reversed edges for each adjacency list *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   616
   fun flip (u,(v,l)::el) = (v,(u,l)) :: flip (u,el)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   617
     | flip (_,nil) = nil
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   618
   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   619
   (* Compute adjacency list for node u from the list of edges
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   620
      and return a likewise reduced list of edges.  The list of edges
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   621
      is searches for edges starting from u, and these edges are removed. *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   622
   fun gather (u,(v,w)::el) =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   623
    let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   624
     val (adj,edges) = gather (u,el)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   625
    in
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   626
     if eq_comp (u, v) then (w::adj,edges)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   627
     else (adj,(v,w)::edges)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   628
    end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   629
   | gather (_,nil) = (nil,nil)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   630
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   631
   (* For every node in the input graph, call gather to find all reachable
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   632
      nodes in the list of edges *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   633
   fun assemble ((u,_)::el) edges =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   634
       let val (adj,edges) = gather (u,edges)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   635
       in (u,adj) :: assemble el edges
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   636
       end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   637
     | assemble nil _ = nil
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   638
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   639
   (* Compute, for each adjacency list, the list with reversed edges,
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   640
      and concatenate these lists. *)
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   641
   val flipped = foldr (op @) nil (map flip g)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   642
 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   643
 in assemble g flipped end    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   644
      
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   645
(* *********************************************************************** *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   646
(*                                                                         *)      
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   647
(* scc_term : (term * term list) list -> term list list                    *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   648
(*                                                                         *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   649
(* The following is based on the algorithm for finding strongly connected  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   650
(* components described in Introduction to Algorithms, by Cormon, Leiserson*)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   651
(* and Rivest, section 23.5. The input G is an adjacency list description  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   652
(* of a directed graph. The output is a list of the strongly connected     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   653
(* components (each a list of vertices).                                   *)          
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   654
(*                                                                         *)   
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   655
(*                                                                         *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   656
(* *********************************************************************** *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   657
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   658
fun scc_term G =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   659
     let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   660
  (* Ordered list of the vertices that DFS has finished with;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   661
     most recently finished goes at the head. *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   662
  val finish : term list ref = ref nil
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   663
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   664
  (* List of vertices which have been visited. *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   665
  val visited : term list ref = ref nil
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   666
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   667
  fun been_visited v = exists (fn w => w aconv v) (!visited)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   668
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   669
  (* Given the adjacency list rep of a graph (a list of pairs),
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   670
     return just the first element of each pair, yielding the 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   671
     vertex list. *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   672
  val members = map (fn (v,_) => v)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   673
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   674
  (* Returns the nodes in the DFS tree rooted at u in g *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   675
  fun dfs_visit g u : term list =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   676
      let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   677
   val _ = visited := u :: !visited
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   678
   val descendents =
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   679
       foldr (fn ((v,l),ds) => if been_visited v then ds
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   680
            else v :: dfs_visit g v @ ds)
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   681
        nil (adjacent (op aconv) g u)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   682
      in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   683
   finish := u :: !finish;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   684
   descendents
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   685
      end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   686
     in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   687
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   688
  (* DFS on the graph; apply dfs_visit to each vertex in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   689
     the graph, checking first to make sure the vertex is
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   690
     as yet unvisited. *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   691
  app (fn u => if been_visited u then ()
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   692
        else (dfs_visit G u; ()))  (members G);
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   693
  visited := nil;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   694
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   695
  (* We don't reset finish because its value is used by
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   696
     foldl below, and it will never be used again (even
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   697
     though dfs_visit will continue to modify it). *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   698
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   699
  (* DFS on the transpose. The vertices returned by
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   700
     dfs_visit along with u form a connected component. We
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   701
     collect all the connected components together in a
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   702
     list, which is what is returned. *)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   703
  Library.foldl (fn (comps,u) =>  
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   704
      if been_visited u then comps
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   705
      else ((u :: dfs_visit (transpose (op aconv) G) u) :: comps))  (nil,(!finish))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   706
end;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   707
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   708
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   709
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   710
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   711
(* dfs_int_reachable g u:                                                  *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   712
(* (int * int list) list -> int -> int list                                *) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   713
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   714
(* Computes list of all nodes reachable from u in g.                       *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   715
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   716
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   717
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   718
fun dfs_int_reachable g u = 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   719
 let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   720
  (* List of vertices which have been visited. *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   721
  val visited : int list ref = ref nil
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   722
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   723
  fun been_visited v = exists (fn w => w = v) (!visited)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   724
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   725
  fun dfs_visit g u : int list =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   726
      let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   727
   val _ = visited := u :: !visited
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   728
   val descendents =
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   729
       foldr (fn ((v,l),ds) => if been_visited v then ds
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   730
            else v :: dfs_visit g v @ ds)
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   731
        nil (adjacent (op =) g u)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   732
   in  descendents end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   733
 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   734
 in u :: dfs_visit g u end;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   735
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   736
    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   737
fun indexComps components = 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   738
    ListPair.map (fn (a,b) => (a,b)) (0 upto (length components -1), components);
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   739
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   740
fun indexNodes IndexComp = 
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   741
    List.concat (map (fn (index, comp) => (map (fn v => (v,index)) comp)) IndexComp);
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   742
    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   743
fun getIndex v [] = ~1
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   744
|   getIndex v ((v',k)::vs) = if v aconv v' then k else getIndex v vs; 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   745
    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   746
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   747
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   748
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   749
(*                                                                         *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   750
(* dfs eq_comp g u v:                                                       *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   751
(* ('a * 'a -> bool) -> ('a  *( 'a * less) list) list ->                   *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   752
(* 'a -> 'a -> (bool * ('a * less) list)                                   *) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   753
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   754
(* Depth first search of v from u.                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   755
(* Returns (true, path(u, v)) if successful, otherwise (false, []).        *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   756
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   757
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   758
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   759
fun dfs eq_comp g u v = 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   760
 let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   761
    val pred = ref nil;
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   762
    val visited = ref nil;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   763
    
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   764
    fun been_visited v = exists (fn w => eq_comp (w, v)) (!visited)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   765
    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   766
    fun dfs_visit u' = 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   767
    let val _ = visited := u' :: (!visited)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   768
    
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   769
    fun update (x,l) = let val _ = pred := (x,l) ::(!pred) in () end;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   770
    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   771
    in if been_visited v then () 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   772
    else (app (fn (v',l) => if been_visited v' then () else (
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   773
       update (v',l); 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   774
       dfs_visit v'; ()) )) (adjacent eq_comp g u')
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   775
     end
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   776
  in 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   777
    dfs_visit u; 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   778
    if (been_visited v) then (true, (!pred)) else (false , [])   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   779
  end;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   780
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   781
  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   782
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   783
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   784
(* completeTermPath u v g:                                                 *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   785
(* Term.term -> Term.term -> (Term.term * (Term.term * less) list) list    *) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   786
(* -> less list                                                            *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   787
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   788
(* Complete the path from u to v in graph g.  Path search is performed     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   789
(* with dfs_term g u v.  This yields for each node v' its predecessor u'   *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   790
(* and the edge u' -> v'.  Allows traversing graph backwards from v and    *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   791
(* finding the path u -> v.                                                *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   792
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   793
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   794
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   795
  
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   796
fun completeTermPath u v g  = 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   797
  let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   798
   val (found, tmp) =  dfs (op aconv) g u v ;
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   799
   val pred = map snd tmp;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   800
   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   801
   fun path x y  =
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   802
      let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   803
 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   804
      (* find predecessor u of node v and the edge u -> v *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   805
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   806
      fun lookup v [] = raise Cannot
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   807
      |   lookup v (e::es) = if (upper e) aconv v then e else lookup v es;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   808
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   809
      (* traverse path backwards and return list of visited edges *)   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   810
      fun rev_path v = 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   811
       let val l = lookup v pred
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   812
           val u = lower l;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   813
       in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   814
        if u aconv x then [l]
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   815
        else (rev_path u) @ [l] 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   816
       end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   817
     in rev_path y end;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   818
       
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   819
  in 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   820
  if found then (if u aconv v then [(Le (u, v, (Thm ([], #le_refl less_thms))))]
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   821
  else path u v ) else raise Cannot
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   822
end;  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   823
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   824
      
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   825
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   826
(*                                                                         *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   827
(* findProof (sccGraph, neqE, ntc, sccSubgraphs) subgoal:                  *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   828
(*                                                                         *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   829
(* (int * (int * less) list) list * less list *  (Term.term * int) list    *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   830
(* * ((term * (term * less) list) list) list -> Less -> proof              *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   831
(*                                                                         *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   832
(* findProof constructs from graphs (sccGraph, sccSubgraphs) and neqE a    *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   833
(* proof for subgoal.  Raises exception Cannot if this is not possible.    *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   834
(*                                                                         *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   835
(* *********************************************************************** *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   836
     
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   837
fun findProof (sccGraph, neqE, ntc, sccSubgraphs) subgoal =
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   838
let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   839
   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   840
 (* complete path x y from component graph *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   841
 fun completeComponentPath x y predlist = 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   842
   let         
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   843
	  val xi = getIndex x ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   844
	  val yi = getIndex y ntc 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   845
	  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   846
	  fun lookup k [] =  raise Cannot
23577
c5b93c69afd3 avoid polymorphic equality;
wenzelm
parents: 22578
diff changeset
   847
	  |   lookup k ((h: int,l)::us) = if k = h then l else lookup k us;	  
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   848
	  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   849
	  fun rev_completeComponentPath y' = 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   850
	   let val edge = lookup (getIndex y' ntc) predlist
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   851
	       val u = lower edge
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   852
	       val v = upper edge
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   853
	   in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   854
             if (getIndex u ntc) = xi then 
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   855
	       (completeTermPath x u (List.nth(sccSubgraphs, xi)) )@[edge]
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   856
	       @(completeTermPath v y' (List.nth(sccSubgraphs, getIndex y' ntc)) )
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   857
	     else (rev_completeComponentPath u)@[edge]
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   858
	          @(completeTermPath v y' (List.nth(sccSubgraphs, getIndex y' ntc)) )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   859
           end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   860
   in  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   861
      if x aconv y then 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   862
        [(Le (x, y, (Thm ([], #le_refl less_thms))))]
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   863
      else ( if xi = yi then completeTermPath x y (List.nth(sccSubgraphs, xi))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   864
             else rev_completeComponentPath y )  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   865
   end;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   866
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   867
(* ******************************************************************* *) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   868
(* findLess e x y xi yi xreachable yreachable                          *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   869
(*                                                                     *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   870
(* Find a path from x through e to y, of weight <                      *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   871
(* ******************************************************************* *) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   872
 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   873
 fun findLess e x y xi yi xreachable yreachable = 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   874
  let val u = lower e 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   875
      val v = upper e
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   876
      val ui = getIndex u ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   877
      val vi = getIndex v ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   878
            
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   879
  in 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   880
      if ui mem xreachable andalso vi mem xreachable andalso 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   881
         ui mem yreachable andalso vi mem yreachable then (
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   882
       
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   883
  (case e of (Less (_, _, _)) =>  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   884
       let
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   885
        val (xufound, xupred) =  dfs (op =) sccGraph xi (getIndex u ntc)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   886
	    in 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   887
	     if xufound then (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   888
	      let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   889
	       val (vyfound, vypred) =  dfs (op =) sccGraph (getIndex v ntc) yi  
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   890
	      in 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   891
	       if vyfound then (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   892
	        let 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   893
	         val xypath = (completeComponentPath x u xupred)@[e]@(completeComponentPath v y vypred)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   894
	         val xyLesss = transPath (tl xypath, hd xypath)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   895
	        in 
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   896
		 if xyLesss subsumes subgoal then SOME (getprf xyLesss) 
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   897
                 else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   898
	       end)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   899
	       else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   900
	      end)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   901
	     else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   902
	    end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   903
       |  _   => 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   904
         let val (uvfound, uvpred) =  dfs (op =) sccGraph (getIndex u ntc) (getIndex v ntc) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   905
             in 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   906
	      if uvfound then (
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   907
	       let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   908
	        val (xufound, xupred) = dfs (op =) sccGraph xi (getIndex u ntc)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   909
	       in
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   910
		if xufound then (
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   911
		 let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   912
		  val (vyfound, vypred) =  dfs (op =) sccGraph (getIndex v ntc) yi
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   913
		 in 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   914
		  if vyfound then (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   915
		   let
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   916
		    val uvpath = completeComponentPath u v uvpred
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   917
		    val uvLesss = mergeLess ( transPath (tl uvpath, hd uvpath), e)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   918
		    val xypath = (completeComponentPath  x u xupred)@[uvLesss]@(completeComponentPath v y vypred)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   919
		    val xyLesss = transPath (tl xypath, hd xypath)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   920
		   in 
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   921
		    if xyLesss subsumes subgoal then SOME (getprf xyLesss)
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   922
                    else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   923
		   end )
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   924
		  else NONE   
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   925
	         end)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   926
		else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   927
	       end ) 
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   928
	      else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   929
	     end )
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   930
    ) else NONE
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   931
end;  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   932
   
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   933
         
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   934
in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   935
  (* looking for x <= y: any path from x to y is sufficient *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   936
  case subgoal of (Le (x, y, _)) => (
19617
7cb4b67d4b97 avoid raw equality on type thm;
wenzelm
parents: 19250
diff changeset
   937
  if null sccGraph then raise Cannot else ( 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   938
   let 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   939
    val xi = getIndex x ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   940
    val yi = getIndex y ntc
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   941
    (* searches in sccGraph a path from xi to yi *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   942
    val (found, pred) = dfs (op =) sccGraph xi yi
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   943
   in 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   944
    if found then (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   945
       let val xypath = completeComponentPath x y pred 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   946
           val xyLesss = transPath (tl xypath, hd xypath) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   947
       in  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   948
	  (case xyLesss of
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   949
	    (Less (_, _, q)) => if xyLesss subsumes subgoal then (Thm ([q], #less_imp_le less_thms))  
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   950
				else raise Cannot
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   951
	     | _   => if xyLesss subsumes subgoal then (getprf xyLesss) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   952
	              else raise Cannot)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   953
       end )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   954
     else raise Cannot 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   955
   end 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   956
    )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   957
   )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   958
 (* looking for x < y: particular path required, which is not necessarily
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   959
    found by normal dfs *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   960
 |   (Less (x, y, _)) => (
19617
7cb4b67d4b97 avoid raw equality on type thm;
wenzelm
parents: 19250
diff changeset
   961
  if null sccGraph then raise Cannot else (
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   962
   let 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   963
    val xi = getIndex x ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   964
    val yi = getIndex y ntc
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   965
    val sccGraph_transpose = transpose (op =) sccGraph
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   966
    (* all components that can be reached from component xi  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   967
    val xreachable = dfs_int_reachable sccGraph xi
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   968
    (* all comonents reachable from y in the transposed graph sccGraph' *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   969
    val yreachable = dfs_int_reachable sccGraph_transpose yi
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   970
    (* for all edges u ~= v or u < v check if they are part of path x < y *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   971
    fun processNeqEdges [] = raise Cannot 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   972
    |   processNeqEdges (e::es) = 
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   973
      case  (findLess e x y xi yi xreachable yreachable) of (SOME prf) => prf  
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   974
      | _ => processNeqEdges es
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   975
        
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   976
    in 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   977
       processNeqEdges neqE 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   978
    end
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   979
  )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   980
 )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   981
| (NotEq (x, y, _)) => (
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   982
  (* if there aren't any edges that are candidate for a ~= raise Cannot *)
19617
7cb4b67d4b97 avoid raw equality on type thm;
wenzelm
parents: 19250
diff changeset
   983
  if null neqE then raise Cannot
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   984
  (* if there aren't any edges that are candidate for <= then just search a edge in neqE that implies the subgoal *)
19617
7cb4b67d4b97 avoid raw equality on type thm;
wenzelm
parents: 19250
diff changeset
   985
  else if null sccSubgraphs then (
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   986
     (case (Library.find_first (fn fact => fact subsumes subgoal) neqE, subgoal) of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   987
       ( SOME (NotEq (x, y, p)), NotEq (x', y', _)) =>
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   988
          if  (x aconv x' andalso y aconv y') then p 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   989
	  else Thm ([p], #not_sym less_thms)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
   990
     | ( SOME (Less (x, y, p)), NotEq (x', y', _)) => 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   991
          if x aconv x' andalso y aconv y' then (Thm ([p], #less_imp_neq less_thms))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
   992
          else (Thm ([(Thm ([p], #less_imp_neq less_thms))], #not_sym less_thms))
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   993
     | _ => raise Cannot) 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   994
   ) else (
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   995
   
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   996
   let  val xi = getIndex x ntc 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
   997
        val yi = getIndex y ntc
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   998
	val sccGraph_transpose = transpose (op =) sccGraph
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
   999
        val xreachable = dfs_int_reachable sccGraph xi
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1000
	val yreachable = dfs_int_reachable sccGraph_transpose yi
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1001
	
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1002
	fun processNeqEdges [] = raise Cannot  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1003
  	|   processNeqEdges (e::es) = (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1004
	    let val u = lower e 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1005
	        val v = upper e
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1006
		val ui = getIndex u ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1007
		val vi = getIndex v ntc
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1008
		
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1009
	    in  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1010
	        (* if x ~= y follows from edge e *)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1011
	    	if e subsumes subgoal then (
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1012
		     case e of (Less (u, v, q)) => (
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1013
		       if u aconv x andalso v aconv y then (Thm ([q], #less_imp_neq less_thms))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1014
		       else (Thm ([(Thm ([q], #less_imp_neq less_thms))], #not_sym less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1015
		     )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1016
		     |    (NotEq (u,v, q)) => (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1017
		       if u aconv x andalso v aconv y then q
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1018
		       else (Thm ([q],  #not_sym less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1019
		     )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1020
		 )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1021
                (* if SCC_x is linked to SCC_y via edge e *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1022
		 else if ui = xi andalso vi = yi then (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1023
                   case e of (Less (_, _,_)) => (
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1024
		        let val xypath = (completeTermPath x u (List.nth(sccSubgraphs, ui)) ) @ [e] @ (completeTermPath v y (List.nth(sccSubgraphs, vi)) )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1025
			    val xyLesss = transPath (tl xypath, hd xypath)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1026
			in  (Thm ([getprf xyLesss], #less_imp_neq less_thms)) end)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1027
		   | _ => (   
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1028
		        let 
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1029
			    val xupath = completeTermPath x u  (List.nth(sccSubgraphs, ui))
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1030
			    val uxpath = completeTermPath u x  (List.nth(sccSubgraphs, ui))
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1031
			    val vypath = completeTermPath v y  (List.nth(sccSubgraphs, vi))
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1032
			    val yvpath = completeTermPath y v  (List.nth(sccSubgraphs, vi))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1033
			    val xuLesss = transPath (tl xupath, hd xupath)     
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1034
			    val uxLesss = transPath (tl uxpath, hd uxpath)			    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1035
			    val vyLesss = transPath (tl vypath, hd vypath)			
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1036
			    val yvLesss = transPath (tl yvpath, hd yvpath)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1037
			    val x_eq_u =  (Thm ([(getprf xuLesss),(getprf uxLesss)], #eqI less_thms))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1038
			    val v_eq_y =  (Thm ([(getprf vyLesss),(getprf yvLesss)], #eqI less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1039
			in 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1040
                           (Thm ([x_eq_u , (getprf e), v_eq_y ], #eq_neq_eq_imp_neq less_thms)) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1041
			end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1042
			)       
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1043
		  ) else if ui = yi andalso vi = xi then (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1044
		     case e of (Less (_, _,_)) => (
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1045
		        let val xypath = (completeTermPath y u (List.nth(sccSubgraphs, ui)) ) @ [e] @ (completeTermPath v x (List.nth(sccSubgraphs, vi)) )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1046
			    val xyLesss = transPath (tl xypath, hd xypath)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1047
			in (Thm ([(Thm ([getprf xyLesss], #less_imp_neq less_thms))] , #not_sym less_thms)) end ) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1048
		     | _ => (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1049
		        
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1050
			let val yupath = completeTermPath y u (List.nth(sccSubgraphs, ui))
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1051
			    val uypath = completeTermPath u y (List.nth(sccSubgraphs, ui))
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1052
			    val vxpath = completeTermPath v x (List.nth(sccSubgraphs, vi))
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1053
			    val xvpath = completeTermPath x v (List.nth(sccSubgraphs, vi))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1054
			    val yuLesss = transPath (tl yupath, hd yupath)     
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1055
			    val uyLesss = transPath (tl uypath, hd uypath)			    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1056
			    val vxLesss = transPath (tl vxpath, hd vxpath)			
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1057
			    val xvLesss = transPath (tl xvpath, hd xvpath)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1058
			    val y_eq_u =  (Thm ([(getprf yuLesss),(getprf uyLesss)], #eqI less_thms))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1059
			    val v_eq_x =  (Thm ([(getprf vxLesss),(getprf xvLesss)], #eqI less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1060
			in
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1061
			    (Thm ([(Thm ([y_eq_u , (getprf e), v_eq_x ], #eq_neq_eq_imp_neq less_thms))], #not_sym less_thms))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1062
		        end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1063
		       )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1064
		  ) else (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1065
                       (* there exists a path x < y or y < x such that
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1066
                          x ~= y may be concluded *)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1067
	        	case  (findLess e x y xi yi xreachable yreachable) of 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1068
		              (SOME prf) =>  (Thm ([prf], #less_imp_neq less_thms))  
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
  1069
                             | NONE =>  (
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1070
		               let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1071
		                val yr = dfs_int_reachable sccGraph yi
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1072
	                        val xr = dfs_int_reachable sccGraph_transpose xi
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1073
		               in 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1074
		                case  (findLess e y x yi xi yr xr) of 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1075
		                      (SOME prf) => (Thm ([(Thm ([prf], #less_imp_neq less_thms))], #not_sym less_thms)) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1076
                                      | _ => processNeqEdges es
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1077
		               end)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1078
		 ) end) 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1079
     in processNeqEdges neqE end)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1080
  )    
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1081
end;
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1082
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1083
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1084
(* ******************************************************************* *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1085
(*                                                                     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1086
(* mk_sccGraphs components leqG neqG ntc :                             *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1087
(* Term.term list list ->                                              *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1088
(* (Term.term * (Term.term * less) list) list ->                       *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1089
(* (Term.term * (Term.term * less) list) list ->                       *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1090
(* (Term.term * int)  list ->                                          *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1091
(* (int * (int * less) list) list   *                                  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1092
(* ((Term.term * (Term.term * less) list) list) list                   *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1093
(*                                                                     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1094
(*                                                                     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1095
(* Computes, from graph leqG, list of all its components and the list  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1096
(* ntc (nodes, index of component) a graph whose nodes are the         *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1097
(* indices of the components of g.  Egdes of the new graph are         *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1098
(* only the edges of g linking two components. Also computes for each  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1099
(* component the subgraph of leqG that forms this component.           *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1100
(*                                                                     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1101
(* For each component SCC_i is checked if there exists a edge in neqG  *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1102
(* that leads to a contradiction.                                      *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1103
(*                                                                     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1104
(* We have a contradiction for edge u ~= v and u < v if:               *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1105
(* - u and v are in the same component,                                *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1106
(* that is, a path u <= v and a path v <= u exist, hence u = v.        *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1107
(* From irreflexivity of < follows u < u or v < v. Ex false quodlibet. *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1108
(*                                                                     *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1109
(* ******************************************************************* *)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1110
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1111
fun mk_sccGraphs _ [] _ _ = ([],[])
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1112
|   mk_sccGraphs components leqG neqG ntc = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1113
    let
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1114
    (* Liste (Index der Komponente, Komponente *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1115
    val IndexComp = indexComps components;
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1116
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1117
       
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1118
    fun handleContr edge g = 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1119
       (case edge of 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1120
          (Less  (x, y, _)) => (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1121
	    let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1122
	     val xxpath = edge :: (completeTermPath y x g )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1123
	     val xxLesss = transPath (tl xxpath, hd xxpath)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1124
	     val q = getprf xxLesss
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1125
	    in 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1126
	     raise (Contr (Thm ([q], #less_reflE less_thms ))) 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1127
	    end 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1128
	  )
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1129
        | (NotEq (x, y, _)) => (
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1130
	    let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1131
	     val xypath = (completeTermPath x y g )
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1132
	     val yxpath = (completeTermPath y x g )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1133
	     val xyLesss = transPath (tl xypath, hd xypath)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1134
	     val yxLesss = transPath (tl yxpath, hd yxpath)
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1135
             val q = getprf (mergeLess ((mergeLess (edge, xyLesss)),yxLesss )) 
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1136
	    in 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1137
	     raise (Contr (Thm ([q], #less_reflE less_thms )))
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1138
	    end  
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1139
	 )
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1140
	| _ =>  error "trans_tac/handleContr: invalid Contradiction");
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1141
 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1142
   	
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1143
    (* k is index of the actual component *)   
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1144
       
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1145
    fun processComponent (k, comp) = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1146
     let    
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1147
        (* all edges with weight <= of the actual component *)  
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1148
        val leqEdges = List.concat (map (adjacent (op aconv) leqG) comp);
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1149
        (* all edges with weight ~= of the actual component *)  
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1150
        val neqEdges = map snd (List.concat (map (adjacent (op aconv) neqG) comp));
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1151
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1152
       (* find an edge leading to a contradiction *)   
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
  1153
       fun findContr [] = NONE
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1154
       |   findContr (e::es) = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1155
		    let val ui = (getIndex (lower e) ntc) 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1156
			val vi = (getIndex (upper e) ntc) 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1157
		    in 
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
  1158
		        if ui = vi then  SOME e
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1159
		        else findContr es
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1160
		    end; 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1161
		   
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1162
		(* sort edges into component internal edges and 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1163
		   edges pointing away from the component *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1164
		fun sortEdges  [] (intern,extern)  = (intern,extern)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1165
		|   sortEdges  ((v,l)::es) (intern, extern) = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1166
		    let val k' = getIndex v ntc in 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1167
		        if k' = k then 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1168
			    sortEdges es (l::intern, extern)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1169
			else sortEdges  es (intern, (k',l)::extern) end;
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1170
		
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1171
		(* Insert edge into sorted list of edges, where edge is
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1172
                    only added if
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1173
                    - it is found for the first time
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1174
                    - it is a <= edge and no parallel < edge was found earlier
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1175
                    - it is a < edge
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1176
                 *)
23577
c5b93c69afd3 avoid polymorphic equality;
wenzelm
parents: 22578
diff changeset
  1177
          	 fun insert (h: int,l) [] = [(h,l)]
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1178
		 |   insert (h,l) ((k',l')::es) = if h = k' then (
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1179
		     case l of (Less (_, _, _)) => (h,l)::es
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1180
		     | _  => (case l' of (Less (_, _, _)) => (h,l')::es
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1181
	                      | _ => (k',l)::es) )
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1182
		     else (k',l'):: insert (h,l) es;
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1183
		
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1184
		(* Reorganise list of edges such that
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1185
                    - duplicate edges are removed
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1186
                    - if a < edge and a <= edge exist at the same time,
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1187
                      remove <= edge *)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1188
    		 fun reOrganizeEdges [] sorted = sorted: (int * less) list
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1189
		 |   reOrganizeEdges (e::es) sorted = reOrganizeEdges es (insert e sorted); 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1190
	
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1191
                 (* construct the subgraph forming the strongly connected component
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1192
		    from the edge list *)    
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1193
		 fun sccSubGraph [] g  = g
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1194
		 |   sccSubGraph (l::ls) g = 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1195
		          sccSubGraph ls (addEdge ((lower l),[((upper l),l)],g))
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1196
		 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1197
		 val (intern, extern) = sortEdges leqEdges ([], []);
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1198
                 val subGraph = sccSubGraph intern [];
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1199
		  
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1200
     in  
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
  1201
         case findContr neqEdges of SOME e => handleContr e subGraph
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1202
	 | _ => ((k, (reOrganizeEdges (extern) [])), subGraph)
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1203
     end; 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1204
  
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1205
    val tmp =  map processComponent IndexComp    
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1206
in 
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1207
     ( (map fst tmp), (map snd tmp))  
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1208
end; 
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1209
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1210
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1211
(** Find proof if possible. **)
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1212
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1213
fun gen_solve mkconcl sign (asms, concl) =
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1214
 let 
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1215
  val (leqG, neqG, neqE) = mkGraphs asms
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1216
  val components = scc_term leqG   
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1217
  val ntc = indexNodes (indexComps components)
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1218
  val (sccGraph, sccSubgraphs) = mk_sccGraphs components leqG neqG ntc
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1219
 in
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1220
   let 
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1221
   val (subgoals, prf) = mkconcl decomp less_thms sign concl
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1222
   fun solve facts less =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
  1223
      (case triv_solv less of NONE => findProof (sccGraph, neqE, ntc, sccSubgraphs) less
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15103
diff changeset
  1224
      | SOME prf => prf )
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1225
  in
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1226
   map (solve asms) subgoals
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1227
  end
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1228
 end;
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1229
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1230
in
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1231
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1232
    SUBGOAL (fn (A, n, sign) =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1233
     let
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1234
      val rfrees = map Free (rename_wrt_term A (Logic.strip_params A))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1235
      val Hs = map (fn H => subst_bounds (rfrees, H)) (Logic.strip_assums_hyp A)
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1236
      val C = subst_bounds (rfrees, Logic.strip_assums_concl A)
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1237
      val lesss = List.concat (ListPair.map (mkasm decomp less_thms sign) (Hs, 0 upto (length Hs - 1)))
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1238
      val prfs = gen_solve mkconcl sign (lesss, C);
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1239
      val (subgoals, prf) = mkconcl decomp less_thms sign C;
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1240
     in
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1241
      METAHYPS (fn asms =>
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1242
	let val thms = map (prove asms) prfs
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1243
	in rtac (prove thms prf) 1 end) n
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1244
     end
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1245
     handle Contr p => METAHYPS (fn asms => rtac (prove asms p) 1) n
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1246
	  | Cannot  => no_tac
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1247
	  )
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1248
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1249
end;
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1250
14445
4392cb82018b Bug-fixes for transitivity reasoner.
ballarin
parents: 14398
diff changeset
  1251
(* partial_tac - solves partial orders *)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1252
val partial_tac = gen_order_tac mkasm_partial mkconcl_partial;
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1253
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1254
(* linear_tac - solves linear/total orders *)
24639
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1255
val linear_tac = gen_order_tac mkasm_linear mkconcl_linear;
9b73bc9b05a1 Defunctorised transitivity reasoner; locale interpretation requires dynamic instances.
ballarin
parents: 23577
diff changeset
  1256
14398
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1257
       
c5c47703f763 Efficient, graph-based reasoner for linear and partial orders.
ballarin
parents:
diff changeset
  1258
end;