Operators

Operators in Prolog are simply a notational convenience. For example, the expression

2 + 1
could also be written +(2,1). It should be noticed that this expression represents the structure 
   +
 /   \
2     1
and not the number 3. The addition would only be performed if the structure was passed as an argument to an appropriate procedure (such as eval/2 — see Section [*]).

The Prolog syntax caters for operators of three main kinds — infix, prefix and postfix. An infix operator appears between its two arguments, while a prefix operator precedes its single argument and a postfix operator is written after its single argument.

Each operator has a precedence, which is a number from 1 to 1200. The precedence is used to disambiguate expressions where the structure of the term denoted is not made explicit through parenthesization. The general rule is that the operator with the highest precedence is the principal functor. Thus if `+' has a higher precedence than `/', then a+b/c and a+(b/c) are equivalent and denote the term +(a,/(b,c)). Note that the infix form of the term /(+(a,b),c) must be written with explicit parentheses, (a+b)/c.

If there are two operators in the subexpression having the same highest precedence, the ambiguity must be resolved from the types of the operators. The possible types for an infix operator are

xfx xfy yfx
With an operator of type `xfx', it is a requirement that both of the two subexpressions which are the arguments of the operator must be of lower precedence than the operator itself, i.e. their principal functors must be of lower precedence, unless the subexpression is explicitly bracketed (which gives it zero precedence). With an operator of type `xfy', only the first or left-hand subexpression must be of lower precedence; the second can be of the same precedence as the main operator; and vice versa for an operator of type `yfx'.

For example, if the operators `+' and `–' both have type `yfx' and are of the same precedence, then the expression ``a–b+c'' is valid, and means ``(a–b)+c'', i.e. ``+(–(a,b),c)''. Note that the expression would be invalid if the operators had type `xfx', and would mean ``a–(b+c)'', i.e. ``–(a,+(b,c))'', if the types were both `xfy'.

The possible types for a prefix operator are

fx fy
and for a postfix operator they are
xf yf
The meaning of the types should be clear by analogy with those for infix operators. As an example, if `not' were declared as a prefix operator of type `fy', then
not not P
would be a permissible way to write not(not(P)). If the type were `fx', the preceding expression would not be legal, although
not P
would still be a permissible form for not(P).

In SB-Prolog, a functor named name is declared as an operator of type type and precedence precedence by calling the evaluable predicate op:

| ?- op(precedence, type, name).
op/3 (L) The argument name can also be a list of names of operators of the same type and precedence.

It is possible to have more than one operator of the same name, so long as they are of different kinds, i.e. infix, prefix or postfix. An operator of any kind may be redefined by a new declaration of the same kind. This applies equally to operators which are provided as standard in SB-Prolog, namely the ones shown in Table [*].

Table: Operator Priorities
:– op( 1200, xfx, [ :–, –> ]).
:– op( 1200, fx, [ :– ]).
:– op( 1198, xfx, [ ::– ]).
:– op( 1150, fy, [ mode, public, dynamic ]).
:– op( 1100, xfy, [ ; ]).
:– op( 1050, xfy, [ –> ]).
:– op( 1000, xfy, [ ',' ]). /* See note below */
:– op( 900, fy, [ not, \  +, spy, nospy ]).
:– op( 700, xfx, [ =, is, =.., ==, \  = =, @<, @>, @= <, @> =,
      =:=, = \  =, <, >, = <, > =, ?=, \  = ]).
:– op( 661, xfy, [ `.' ]).
:– op( 500, yfx, [ +, –, / \, \/ ]).
:– op( 500, fx, [ +, – ]).
:– op( 400, yfx, [ *, /, //, «, » ]).
:– op( 300, xfx, [ mod ]).
:– op( 200, xfy, [ ˆ ]).


Operator declarations are most usefully placed in directives at the top of your program files. In this case the directive should be a command as shown above. Another common method of organization is to have one file just containing commands to declare all the necessary operators. This file is then always consulted first.

Note that a comma written literally as a punctuation character can be used as though it were an infix operator of precedence 1000 and type `xfy':

X,Y ','(X,Y)
represent the same compound term. But note that a comma written as a quoted atom is not a standard operator.

Note also that the arguments of a compound term written in standard syntax must be expressions of precedence below 1000. Thus it is necessary to parenthesize the expression P :– Q in

assert((P :- Q))
The following syntax restrictions serve to remove potential ambiguity associated with prefix operators.