%   Predicates in lambda Prolog that define some of `higher-order'
%   mapping operations.

module preds.
import List.

type  mappred            (A -> B -> o) -> list A -> list B -> o.
type  forevery, forsome  (A -> o) -> list A -> o.
type  sublist            (A -> o) -> list A -> list A -> o.

% Relates a binary predicate P and two lists if corresponding elements
% of the two lists are P-related.

mappred P nil nil.
mappred P (X :: L) (Y :: K) :- P X Y, mappred P L K.

% Relates a predicate and a list if every element in the list satisfies P. 

forevery P nil.
forevery P (X :: L) :- P X, forevery P L.

% Relates a predicate and a list if some element in the list satisfies P.

forsome P (X :: L) :- P X ; forsome P L.

% Relates a predicate with two lists if the second is a subkist of the
% first, all of whose elements are members of the first list.

sublist P (X::L) (X::K) :- P X, sublist P L K.
sublist P (X::L) K      :- sublist P L K.
sublist P nil nil.