2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
17 | Node of ('a foterm) list
19 type 'a substitution = (int * 'a foterm) list
21 type comparison = Lt | Eq | Gt | Incomparable
23 type rule = SuperpositionRight | SuperpositionLeft | Demodulation
24 type direction = Left2Right | Right2Left | Nodir
25 type position = int list
29 | Step of rule * int * int * direction * position * 'a substitution
30 (* rule, eq1, eq2, direction of eq2, position, substitution *)
33 | Equation of 'a foterm (* lhs *)
35 * 'a foterm (* type *)
36 * comparison (* orientation *)
37 | Predicate of 'a foterm
39 type varlist = int list
44 * varlist (* variable list *)
45 * 'a proof (* proof *)
47 type 'a passive_clause = int * 'a unit_clause (* weight * equation *)
53 let compare = Pervasives.compare
56 module M : Map.S with type key = int
59 type 'a bag = 'a unit_clause M.t
64 val eq : t -> t -> bool
65 val compare : t -> t -> int
67 val embed : t -> t foterm * int list
70 module Utils (B : Blob) = struct
71 let rec eq_foterm x y =
74 | Leaf t1, Leaf t2 -> B.eq t1 t2
75 | Var i, Var j -> i = j
76 | Node l1, Node l2 -> List.for_all2 eq_foterm l1 l2
80 let rec lexicograph f l1 l2 =
85 if c <> 0 then c else lexicograph f xs ys
90 let rec compare_foterm x y =
92 | Leaf t1, Leaf t2 -> B.compare t1 t2
93 | Var i, Var j -> i - j
94 | Node l1, Node l2 -> lexicograph compare_foterm l1 l2
95 | Leaf _, ( Node _ | Var _ ) -> ~-1
97 | Node _, Var _ -> ~-1
101 let eq_literal l1 l2 =
103 | Predicate p1, Predicate p2 -> eq_foterm p1 p2
104 | Equation (l1,r1,ty1,o1), Equation (l2,r2,ty2,o2) ->
105 o1 = o2 && eq_foterm l1 l2 && eq_foterm r1 r2 && eq_foterm ty1 ty2
109 let compare_literal l1 l2 =
111 | Predicate p1, Predicate p2 -> compare_foterm p1 p2
112 | Equation (l1,r1,ty1,o1), Equation (l2,r2,ty2,o2) ->
113 let c = Pervasives.compare o1 o2 in
114 if c <> 0 then c else
115 let c = compare_foterm l1 l2 in
116 if c <> 0 then c else
117 let c = compare_foterm r1 r2 in
118 if c <> 0 then c else
119 compare_foterm ty1 ty2
120 | Predicate _, Equation _ -> ~-1
121 | Equation _, Predicate _ -> 1
124 let eq_unit_clause (id1,_,_,_) (id2,_,_,_) = id1 = id2
125 let compare_unit_clause (id1,_,_,_) (id2,_,_,_) = Pervasives.compare id1 id2