Arithmetic operations in the head of a clause - prolog

Question

I am a writing Prolog predicate that would compare some point (myPosition(2,2)) in Cartesian coordinate system with some other point in the neighbourhood. As a result, it should show the direction (north, east, south, west) that we should choose to get from myPosition(2,2) to that point. Here is the code of my .pl file:
myPosition(2,2).
turn_to_east(X+1,Y) :-
myPosition(X,Y),
write('East.').
turn_to_west(X-1,Y) :-
myPosition(X,Y),
write('West.').
turn_to_north(X,Y+1) :-
myPosition(X,Y),
write('North.').
turn_to_south(X,Y-1) :-
myPosition(X,Y),
write('South.').
turn_to_the_point(X,Y) :- turn_to_east(X,Y).
turn_to_the_point(X,Y) :- turn_to_west(X,Y).
turn_to_the_point(X,Y) :- turn_to_north(X,Y).
turn_to_the_point(X,Y) :- turn_to_south(X,Y).
Then, when I upload the file to SWI-Prolog and write:
turn_to_the_point(1,2).
I get just:
false.
Why can't I get the answer 'West.' or any other?

Answer 1

The reason is that by default Prolog does not interpret +, - and other arithmetic operators. 1+1 is simply 1+1 (this is syntactical sugar for +(1,1)), not 2. This could be useful if you for instance would like to define your own expression evaluator, and you see + as the boolean sum, or something completely different.
There is however one way to collapse such expression such that it derives 2 out of 1+1 using the (is)/2 predicate. For instance:
turn_to_east(NX,Y) :-
myPosition(X,Y),
NX is X+1,
write('East.').
Given you query turn_to_east/2 with turn_to_east(1,2), NX = 1. Now you fetch the myPosition/2 data: X = 2 and Y = 2. Prolog does an equivalence check in the meantime and sees that the Y-coordinate of turn_to_east/2 is the same as the one of myPosition. Next it collapses 2+1 to 3 and sees that this is not equivalent to NX = 1 so this predicate fails. But if you had queried turn_to_east(3,1) it would have succeeded and thus write East..
If you modify your entire theory with the above discussed concept, like:
myPosition(2,2).
turn_to_east(NX,Y) :-
myPosition(X,Y),
NX is X+1,
write('East.').
turn_to_west(NX,Y) :-
myPosition(X,Y),
NX is X-1,
write('West.').
turn_to_north(X,NY) :-
myPosition(X,Y),
NY is Y+1,
write('North.').
turn_to_south(X,NY) :-
myPosition(X,Y),
NY is Y-1,
write('South.').
turn_to_the_point(X,Y) :- turn_to_east(X,Y).
turn_to_the_point(X,Y) :- turn_to_west(X,Y).
turn_to_the_point(X,Y) :- turn_to_north(X,Y).
turn_to_the_point(X,Y) :- turn_to_south(X,Y).
It answers the query correctly:
?- turn_to_the_point(1,2).
West.
true ;
false.
A note in general is that predicates better not have side-effects like write/1 stuff: this is not only for Prolog, almost all programming languages advice to split a program into calculation and interaction. Perhaps a better way to solve this, is to see the direction as an parameter:
myPosition(2,2).
turn_to_point(NX,Y,east) :-
myPosition(X,Y),
NX is X+1.
turn_to_point(NX,Y,west) :-
myPosition(X,Y),
NX is X-1.
turn_to_point(X,NY,north) :-
myPosition(X,Y),
NY is Y+1.
turn_to_point(X,NY,south) :-
myPosition(X,Y),
NY is Y-1.
turn_to_the_point(X,Y) :-
turn_to_point(X,Y,D),
write(D).
In that case the turn_to_the_point/2 predicate is clearly an interaction predicate whereas its turn_to_the_point/3 variant does computations.