% mem( X, L ) is true if X is a member of L
% it's true that member is built-in to some versions of prolog
mem( X, [X|_] ).
mem( X, [_|R] ) :- mem( X, R ).

% len( L, N ) is true iff L is a list of length N:
len( [], 0 ).
len( [_|R], N ) :- len( R, M ), N is M+1.

% app( A, B, L ) is true iff L is the concatentation of A and B
app( [], L , L ).
app( [F|R1], L, [F|R2] ) :- app( R1, L , R2 ).

% lastof( X, L ) is true iff X is the last element of L
lastof( X, [X] ).
lastof( X, [_|R] ) :- lastof( X, R ).

% sum( L, N ) is true iff N is the sum of L's (all-numeric) elements
sum( [], 0 ).
sum( [F|R], N ) :- sum( R, M ), N is M+F.

% nextto(X,Y,L) is true if X is next to Y in L
nextto( X, Y, [X,Y|_] ).
nextto( X, Y, [Y,X|_] ).
nextto( X, Y, [_|R] ) :- nextto( X, Y, R ).


%  start( L1, L2 ) is true if L1 is the start of L2 (both are lists)
start( [], _ ).
start( [F|R], [F|R2] ) :- start( R , R2 ).


%  sublist( S, L ) is true if S is a sublist of L (both are lists) 
sublist( [], _ ).
sublist( [F|R1], [F|R] ) :- start( R1, R ).
sublist( S, [_|R] ) :- sublist( S, R ).