I am having problems getting a list of lists into

Question

I am writing a solution to working out distances between numbers in a list using recursion, but have been struggling with getting the intended output. I am trying to get a list of lists into a single list, but attempts at using flatten and append/2 aren't working. I have tried for hours, and keep going around in circles, can someone tell me what i'm doing wrong please?

:- use_module(library(clpfd)).

difference([],_,[]).
differwnce([L|Ls],X,[DST|Ds]) :-
   DST #= abs(X - L),
   difference(Ls,X,Ds).

differences[],[]).
differences([L|Ls], [DST|Tail]) :-
   difference(Ls,X,DST),
   differences(Ls, Tail).

Here is the intended input and output:-

?- differences([1,2,4,9],Ds).
Ds = [1,3,8,2,7,5].

Current Output:

Ds = [[1,3,8],[2,7],[5],[]].

Answer 1

Why not use the library predicate append/2 like so?

?- append([[1,3,8],[2,7],[5],[]], Xs).
Xs = [1,3,8,2,7,5].

Answer 2

seq([]) --> [].
seq([E|Es]) --> [E], seq(Es).

seqq([]) --> [].
seqq([Es|Ess]) -->
  seq(Es),
  seqq(Ess).

?- phrase(seqq([[1,3,8],[2,7],[5],[]]), Es).
Es = [1,3,8,2,7,5].

Answer 3

You can convert your distances/3 predicate into a distances/4 predicate that returns a list tail for the elements that will follow, effectively using an open list:

:- use_module(library(clpfd)).

distances([], _, Tail, Tail).
distances([BN| Bs], B, [DST| Ds], Tail) :-
   DST #= abs(B - BN),
   distances(Bs, B, Ds, Tail).

triangle([], []).
triangle([BN| Bs], Ds) :-
    distances(Bs, BN, Ds, Tail),
    triangle(Bs, Tail).

Sample call:

?- triangle([1,2,4,9], Ds).
Ds = [1, 3, 8, 2, 7, 5].

To better understand this solution consider the results of the following query:

?- distances([2,4,9], 1, Ds, Tail).
Ds = [1, 3, 8| Tail].

This solution is more efficient than calling predicates such as append/2 or flatten/3 at the end.

P.S. If you still need a distances/3 predicate to use elsewhere, you can define it easily:

distances(Bs, B, Ds) :-
    distances(Bs, B, Ds, []).