op, infix, prefix, and postfix operators, precedence in Prolog
Syntax:

:- op(+Precedence, +Type, :Name).

The Prolog built-in predicate op serves to define the Type and Precedence of infix and postfix, and prefix operators in Prolog terms. Prolog terms normally begin with the functor (e.g. likes, in likes(mary, pizza)) but exceptions exist - for example, arithmetic expressions are written in the usual infix way (i.e. as X + 1, rather than +(X, 1)), and negation can be written without parentheses, as a prefix operator: not P.

The table below lists the predefined infix operators in SWI-Prolog. You may wish to add infix operators of your own. For example, you might wish to define an infix and. This can be done as follows:

:- op(700, xfy, and).

This declares and to be an operator with precedence 700 and type xfy.

Note two things: (1) the fact that these things are referred two as operators does not mean that an operation is performed when they are encountered. This is not usually the case; and (2) the declaration of an operator only affects the external appearance of the operator in your program - internally, the standard representation is used - for example X + 1 really is internally represented by Prolog as though it was +(X, 1).

Precedence is an integer between 0 and 1200. Precedence 0 removes the declaration. Type is one of: xf, yf, xfx, xfy, yfx, yfy, fy or fx. The f indicates the position of the functor, while x and y indicate the position of the arguments. Thus xfx, xfy, and yfx all indicate an infix operator. y should be interpreted as "in this position a term with precedence equal to or less than the precedence of the functor should occur". For x the precedence of the argument must be strictly less than that of the functor. The precedence of a term is 0, unless its principal functor is an operator, in which case the precedence is the precedence of this operator. A term enclosed in brackets (…) has precedence 0.

To see how this works, consider the arithmetic expression a - b - c. In normal maths, this is interpreted as (a - b) - c, rather than a - (b - c). To achieve this, the binary infix operator - must be declared as type yfx so that the first argument has precedence over the second. Then, internally, a - b - c will be represented as -(-(a, b), c) rather than -(a, -(b, c)).

Built-in Operators (SWI-Prolog)

Prec.TypeOperator
1200xfx-->, :-
1200 fx:-, ?-
1150 fxdynamic, discontiguous, initialization, module_transparent, multifile, thread_local, volatile
1100xfy;, |
1050xfy->, op*->
1000xfy,
954xfy\
900 fy\+
900 fx~
700xfx<, =, =.., =@=, =:=, =<, ==, =\=, >, >=, @<, @=<, @>, @>=, \=, \==, is
600xfy:
500 yfx+, -, /\, \/, xor
500 fx+, -, ?, \
400 yfx*, /, //, rdiv, <<, >>, mod, rem
200xfx**
200xfy^

Note that all operators can be redefined by the user, most commonly accidentally and with disastrous results.