Use reified constraints to make 3 numbers consecutive

Question

Here's an outline of my SWI-Prolog program:

:- use_module(library(clpfd)).

consec1(L) :-
   L=[L1,L2,L3,L4,L5,L6,L7,L8,L9],
   L ins 1..9,
   ...,
   abs(L5-L4)#=1,
   all_different(L),
   labeling([],L)

abs(L5-L4)#=1 makes L5 and L4 next to each other. If I wanted to make three numbers next to each other e.g. L3, L4 and L5, how could I use reified constraints to do this?

E.g. L3=4,L5=5,L4=6 or L4=7,L5=8,L3=9

Answer 1

This implements consecutive in the sense you gave in the comments. For a list of N values, we need space enough to make all the values fit in between, and all values need to be different.

consecutive([]).  % debatable case
consecutive(Xs) :-
   Xs = [_|_],
   length(Xs, N),
   all_different(Xs),
   max_of(Max, Xs),
   min_of(Min, Xs),
   Max-Min #= N-1.

max_of(Max, [Max]).
max_of(Max0, [E|Es]) :-
   Max0 #= max(E,Max1),
   max_of(Max1, Es).

min_of(Min, [Min]).
min_of(Min0, [E|Es]) :-
   Min0 #= min(E, Min1),
   min_of(Min1, Es).