Complete graph traversal algorithm in Prolog

Question

Given a table, I want to explore all possible transition between the elements in the table. ex: for a table with size 3 [0,1,2], the output of the algorithm should be 0->1, 1->0, 0->2, 2->1, 1->2, 2->0. I guess this can be regarded as traversing a complete graph.

I have an implementation of an algorithm doing this in Python:

def test1(n):
 theList=[]
 theList.append(0)
 for x in range(0,n+1):
 for y in range(n,x+1,-1):
 theList.append(y)
 theList.append(x)
 if x!=n:
 theList.append(x+1)
 for x in range(n,0,-1):
 theList.append(x-1)
 return theList

This code always start at element 0, and return a list of all the transitions.

But I need my algorithm i Prolog. So I have done an attempt to port the Python-code to Prolog. My main focus has been on writing readable and maintainable code. But I guess there is great room for improvement wrt. performance of the Prolog code:

:- use_module(library(clpfd)).
:- use_module(library(between)).
:- use_module(library(lists)).
dynappend( List, X ) :-
 (
 foreach( Item, List ),
 param(X,T)
 do
 var( Item ), var(T) ->
 Item = X ,
 T = 1
 ;
 true
 ). 
s3(List,N):-
 LSize is N*(N+1)+1,
 length(List,LSize),
 dynappend( List, 0 ),
 (
 for(X1, 0, N ),
 param( N, List )
 do
 X1T is X1+2,
 ( between:numlist( X1T, N, YList ) -> true ; YList=[] ) , 
 lists:reverse(YList,RYList),
 (
 foreach(Y, RYList ),
 param( X1, List )
 do
 dynappend( List, Y ),
 dynappend( List, X1 )
 ),
 ( X1 #\= N -> X1T2 is X1+1, dynappend( List, X1T2 ) ; true )
 ),
 N1 is N-1,
 numlist( 0, N1, XList ), 
 lists:reverse(XList,RXList),
 (
 foreach(X2, RXList ),
 param(List)
 do
 dynappend( List, X2 )
 ).

Running the code:

| ?- s3(L, 2).
L = [0,2,0,1,2,1,0] ? 
yes

Any suggestions for improvements of the Prolog code?

• CapelliC: if you get the habit to use 'yield' in Python, you will end with much more Prolog like code, very similar to what @Mat shows
• Aseem Bansal: If someone suggests that a question belongs to codereview.SE please flag/ask a moderator to move it next time. Make a comment to move the question if you can't see the flag button and someone else will flag it. Posting the same question on both sites isn't considered good. Just wait a bit.

Answer 1

Consider describing what a transition is:

list_transition(List, (E1->E2)) :-
 select(E1, List, Rest),
 member(E2, Rest).

Example query:

?- list_transition([0,1,2], T).
T = (0->1) ;
T = (0->2) ;
T = (1->0) ;
T = (1->2) ;
T = (2->0) ;
T = (2->1) ;
false.

And to get all transitions:

?- findall(T, list_transition([0,1,2], T), Transitions).
Transitions = [ (0->1), (0->2), (1->0), (1->2), (2->0), (2->1)].