What are Operators? - 1. Operators. What are Operators? - 2. Properties. » Position» Precedence class» associativity. » x + y * z. » +(x, *(y, z)).

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1 What are Operators? - 1 Functors Introduce operators to improve the readability of programs Operators syntactic sugar Based on Clocksin & Mellish Sections 2.3, 5.5 O-1 O-2 The arithmetic expression:» x + y * z What are Operators? - 2 Would normally be written in Prolog as» +(x, *(y, z)). Operators do not cause any arithmetic to be carried out Properties An operator has three properties» Position» Precedence class» associativity The is operator is used to do arithmetic A programmer (you) can define their own operators O-3 O-4

2 Position - 1 Operators written in between their arguments are called infix operators» +» *» / Operators written before their arguments are called prefix operators» -» + Operators written after their arguments are called postfix operators»! Position - 2 In Prolog we associate a special atom with an operator to specify its position Specifiers for infix operators are:» xfx» xfy» yfx» yfy Specifiers for prefix operators are:» fx» fy Specifiers for postfix operators are:» xf» yf O-5 O-6 Position - 3 It may help to picture the letter f as the operator and the x and y represent the arguments. For infix operators f is in the middle with x/y on either side» xfx, xfy, yfx, yfy For prefix operators the f comes before the argument» fx, fy For postfix operators the f comes after the argument» xf, xy If we are given the expression» =(x, *(y, z)) Precedence - 1 It is very clear multiplication must be done before the addition because the * structure is an argument of the + structure If we are given the expression» x + y * z It is clear the multiplication should be done first because we were taught * is done before + in elementary school What about the expression» X <==> y >==< z Which is done first the <==> operator or the >==< operator? O-7 O-8

3 Precedence - 2 Precedence gives us rules to determine the order in which operators are applied. Precedence class is an integer On most Prolog systems the integers range from 1 to 1200 An operator with a precedence class of 1 has the highest precedence An operator with a precedence class of 1200 has the lowest precedence Higher precedence means do first. Can always use ( ) to force the order of using operators Precedence - Examples Which has a precedence with the highest numeric value?? * or + + :- or + :- ; or, ; is or / is O-9 O-10 Precedence - 3 Precedence of some built-in operators Operator Precedence :- 1200? is 700 > * 400 Pages of Clocksin and Mellish (5 th ed) gives a listing of the predicates defining the standard operators in Prolog Associativity Defines which operands belong to which operator when several operators are used in sequence The x and y in the position specifiers enables associativity information to be conveyed. y means that the argument can contain operators of the same or lower precedence class x means that the operators in the argument must have a strictly lower precedence class O-11 O-12

4 If <=> is declared yfx We look at the expression» a <==> b <==> c Associativity - Example There are two interpretations» a <==> ( b <==> c ) Which is correct?? If <=> is declared yfx We look at the expression» a <==> b <==> c Associativity - Example There are two interpretations» a <==> ( b <==> c ) Which is correct?? What if we wanted the second interpretation to be correct what do we do?? O-13 O-14 If <=> is declared yfx We look at the expression» a <==> b <==> c Associativity - Example There are two interpretations» a <==> ( b <==> c ) Associativity - Another Example How do we declare not so that not not a is legal? Which is correct?? What if we wanted the second interpretation to be correct what do we do??» Declare <==> as xfy O-15 O-16

5 Associativity - Another Example How do we declare not so that not not a is legal? fy It is illegal if not is declared fx (unless you use brackets)» not (not a) Declaring an Operator In order to declare an operator the built-in predicate op is used op takes 3 arguments:» Name is the atom we want to be an operator» Prec is the precedence class of the operator (an integer)» Spec is an atom representing the position/associativity specifier The operator is declared by providing the following goal:»?- op(prec, Spec, Name). If the operator declaration is legal the goal will succeed. O-17 O-18 Given Associativity - Binary Operators A oper B Can define oper as a binary operator with... op ( 100, xfy, oper ). -- right associative op ( 100, yfx, oper ). -- left associative op ( 100, xfx, oper ). -- evaluate both operands first op ( 100, yfy, oper ). -- not defined, ambiguous Examples of operator declarations :- op( 1200, xfx, :- ). :- op( 1200, fx,?- ). :- op( 1100, xfy, ; ). :- op( 700, xfx, is ). :- op( 700, xfx, >= ). :- op( 500, yfx, * ). :- op( 300, xfx, mod ). Pages of Clocksin and Mellish (5 th ed) gives a listing of the predicates defining the standard operators in Prolog O-19 O-20

6 Defining multiple Operators If a bunch of operators have the same specifiers and precedence we can define them all at once.?- op( 700, xfx, [ >, <, =<, >= ] ). Above defines >, <, =<, >= all at once Multiple Precedence Example We define the operators plays and and as follows» :- op( 300, xfx, plays ).» :- op( 200, xfy, and ). Example:» term1 = jimmy plays football and squash» term2 = susan plays tennis and basketball and volleyball Represent the above terms as Prolog structures. O-21 O-22 Multiple Precedence Example We define the operators plays and and as follows» :- op( 300, xfx, plays ).» :- op( 200, xfy, and ). Multiple Precedence Example We define the operators plays and and as follows» :- op( 300, xfx, plays ).» :- op( 200, xfy, and ). term1 = jimmy plays football and squash Represent the above term as a Prolog structure. term2 = susan plays tennis and basketball and volleyball Represent the above term as a Prolog structure. plays( jimmy, and( football, squash ) ) plays( susan, and (tennis, and ( basketball, volleyball ) ) ) O-23 O-24

7 Giving operators meaning - 1 Once we have created an operator we must define rules to give the operator meaning This is just like any other functor in Prolog Giving Meaning - An example We want to define some properties of animals using syntax that is similar to natural language First we define the operators:» :- op( 100, xfx, [ has, isa, flies ] ). Then we give the operators meaning:» Animal has hair :- Animal isa mammal.» Animal has feathers :- Animal isa bird.» owl isa bird.» cat isa mammal.» dog isa mammal. O-25 O-26 Member operator - Example Create an infix operator belongs_to that acts like the member predicate First define the operator: Member operator - Example Create an infix operator belongs_to that acts like the member predicate First define the operator:» :- op( 500, xfy, belongs_to ). Now define the clauses: O-27 O-28

8 Member operator - Example Create an infix operator belongs_to that acts like the member predicate First define the operator:» :- op( 500, xfy, belongs_to ). Now define the clauses:» X belongs_to [X _ ].» X belongs_to [ _ L ] :- X belongs_to L. O-29