I have come across an unfamiliar bit of Prolog syntax in Lee Naish's paper Higher-order logic programming in Prolog. Here is the first code sample from the paper:
% insertion sort (simple version)
isort([], []).
isort(A.As, Bs) :-
isort(As, Bs1),
isort(A, Bs1, Bs).
% insert number into sorted list
insert(N, [], [N]).
insert(N, H.L, N.H.L) :-
N =< H.
insert(N, H.LO, H.L) :-
N > H,
insert(N, LO, L).
My confusion is with A.As in isort(A.As, Bs) :-. From the context, it appears to be an alternate cons syntax for lists, the equivalent of isort([A|As], Bs) :-.
As well N.H.L appears to be a more convenient way to say [N|[H|L]].
But SWI Prolog won't accept this unusual syntax (unless I'm doing something wrong).
Does anyone recognize it? is my hypothesis correct? Which Prolog interpreter accepts that as valid syntax?
The dot operator was used for lists in the very first Prolog system of 1972, written in Algol-W, sometimes called Prolog 0. It is inspired by similar notation in LISP systems. The following exemple is from the paper The birth of Prolog by Alain Colmerauer and Philippe Roussel – the very creators of Prolog.
+ELEMENT(*X, *X.*Y).
+ELEMENT(*X, *Y.*Z) -ELEMENT(*X, *Z).
At that time, [] used to be NIL. All remaining the same in the next version Prolog I written in Fortran by Battani & Meloni.
Then DECsystem 10 Prolog used cases to distinguish atoms and variables and introduced the square bracket notation replacing nil and X.Xs with [] and [X,..Xs] which in later versions of DECsystem 10 received [X|Xs] as an alternative. In ISO Prolog, there is only [X|Xs], .(X,Xs), and as canonical syntax '.'(X,Xs).
Please note that the dot has many different rôles in ISO Prolog. It serves already as
end token when followed by a % or a layout character like SPACE, NEWLINE, TAB.
decimal point in a floating point number, like 3.14159
graphic token char forming graphic tokens as =..
So if you are now declaring . as an infix operator, you have to be very careful. Both with what you write and what Prolog systems will read. A single additional space can change the meaning of a term. Consider two lists of numbers in both notations:
[1,2.3,4]. [5].
1 .2.3.4.[]. 5.[].
Please note that you have to add a space after 1. In this context, an additional white space in front of a number may change the meaning of your terms. Like so:
[1|2.3]. [4]. 5. [].
1 .2.3. 4.[]. 5. [].
Here is another example which might be even more convincing:
[1,-2].
1.(-2).[].
Negative numbers require round brackets within dot-lists.
Today, there is only YAP and XSB left that still offer infix . by default – and they do it differently. And XSB does not even recognize above dot syntax: you need round brackets around some of the nonnegative numbers.
You wrote that N.H.L appears to be a more convenient way to say [N|[H|L]]. There is a simple rule-of-thumb to simplify such expressions in ISO Prolog: Whenever you see within a list the tokens | and [ immediately after each other, you can replace them by , (and remove the corresponding ] on the right side). So you can now write: [N,H|L] which does not look that bad.
You can use that rule also in the other direction. If we have a list [1,2,3,4,5] we can use | as a "razor blade" like so: [1,2,3|[4,5]].
Another remark, since you are reading Naish's paper: In the meantime, it is well understood that only call/N is needed! And ISO Prolog supports call/1, call/2 up to call/8.