Operators
KEY 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 data 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 is - see 2.3). 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 the use of brackets. The general rule is that it is the operator with the HIGHEST precedence that is the principal functor. Thus if '+' has a higher precedence than '/', then a+b/c 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 brackets, i.e. (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 Emas 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). 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 Emas Prolog, namely: :- op( 1200, xfx, [ :-, --> ]). :- op( 1200, fx, [ :-, ?- ]). :- op( 1100, xfy, [ ; ]). :- op( 1050, xfy, [ -> ]). :- op( 1000, xfy, [ ',' ]). /* See note below */ :- op( 900, fy, [ not, \+, spy, nospy ]). :- op( 700, xfx, [ =, is, =.., ==, \==, @<, @>, @=<, @>=, =:=, =\=, <, >, =<, >= ]). :- op( 500, yfx, [ +, -, /\, \/ ]). :- op( 500, fx, [ +, - ]). :- op( 400, yfx, [ *, /, <<, >> ]). :- op( 300, xfx, [ mod ]). :- op( 200, xfy, [ ^ ]). Operator declarations are most usefuly 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 organisation 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', i.e. 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 bracket the expression "P:-Q" in assert((P:-Q)) Note carefully the following syntax restrictions, which serve to remove potential ambiguity associated with prefix operators. 1. In a term written in standard syntax, the principal functor and its following "(" must NOT be separated by any intervening spaces, newlines etc. Thus point (X,Y,Z) is invalid syntax. 2. If the argument of a prefix operator starts with a "(", this "(" must be separated from the operator by at least one space or other non-printable character. Thus :-(p;q),r. (where ':-' is the prefix operator) is invalid syntax, and must be written as e.g. :- (p;q),r. 3. If a prefix operator is written without an argument, as an ordinary atom, the atom is treated as an expression of the same precedence as the prefix operator, and must therefore be bracketed where necessary. Thus the brackets are necessary in X = (?-)