Functional Programming Concepts Creating New Functions procedures Composition

Functional Programming Concepts • Creating New Functions (procedures) • Composition • Currying • Lazy Evaluation • Polymorphism CSE 341 -- S. Tanimoto Functional Programming 1

Composition and Currying in Functional Languages Q. How can two functions be combined to create a new function? A. By composition. h(x) = g(f(x)) Q. How can a function and one value be combined to create a new function? A. By currying. h(x) = f(a, x) h 2(x, y) = f 2(a, x, y) CSE 341 -- S. Tanimoto Functional Programming 2

Composition in Scheme (define (compose-unary-fns f g) (lambda (x) (f (g x))) ) (define tripler (lambda (x) (* 3 x))) (define squarer (lambda (x) (* x x))) (define triple-squarer (compose-unary-fns tripler squarer) ) (triple-squarer 5) => 75 CSE 341 -- S. Tanimoto Functional Programming 3

Currying in Scheme (define (curry-binary-fn f firstarg) (lambda (x) (f firstarg x)) ) (define cons-with-john (curry-binary-fn cons ’john) ) (cons-with-john 21) => (21. JOHN) CSE 341 -- S. Tanimoto Functional Programming 4

Currying in Miranda Q. How does Miranda support currying? A. Any function that takes multiple arguments can be curried. mult x y = x * y triple = mult 3 Here mult is being curried with 3 producing a new function triple. Miranda defines a function of n arguments to be equivalent to a function of one argument that returns another function, that function taking n-1 arguments. CSE 341 -- S. Tanimoto Functional Programming 5

Lazy Evaluation Q. What is lazy evaluation? A. It's a policy of only evaluating forms whose values are needed by a consumer, such as a print request. If Scheme fully supported lazy evaluation, then (CAR (LIST 1 (+ 2 3) (* 4 5) (/ 6 7))) would not result in any arithmetic actually being performed, since only the element 1 needs to be returned. CSE 341 -- S. Tanimoto Functional Programming 6

Lazy Evaluation - Scheme? Q. Does Scheme support lazy evaluation? A. Only in some limited ways. . . The special forms IF and COND, and the macros AND and OR perform lazy evaluation of their arguments. (or (= n 2) (= n 3) (= n 5) (= n 7) (= n 11) ‘not-a-small-prime) If n is 2, then only the first comparison is performed. CSE 341 -- S. Tanimoto Functional Programming 7

Lazy Evaluation - Efficiency? Q. Does lazy evaluation always lead to more efficient computation? A. No. Consider the Miranda code double x = x + x double 11*13 This evaluates as 11*13 + 11*13 = 143 + 143 = 186 But with applicative order evaluation we would have double 11*13 = double 143 = 143 + 143 = 186 which performs less arithmetic. Also, lazy evaluation usually incurs extra overhead. CSE 341 -- S. Tanimoto Functional Programming 8

Lazy Evaluation and Infinite Data Structures Q. Are there any other benefits of lazy evaluation? A. Yes, it permits creation and manipulation of "infinite" data structures. In Miranda, the list (1, 2, 3, . . . ) is written [1. . ] and can be used in expressions. hd (tl (map triple [1. . ]))) || returns 9 If you told Miranda to compute the length of [1. . ], however, it would loop indefinitely. CSE 341 -- S. Tanimoto Functional Programming 9

Polymorphism Q. What is polymorphism? A. The property of a programming language feature or entity being able to support multiple types of data. Q. What is usually meant by function polymorphism? A. The ability for one function to accept arguments whose types can vary from one call to another. In Scheme, for example, CONS is polymorphic: (cons 1 2) ; numeric arguments (cons ’a ’b) ; symbolic arguments Note: CONS is not overloaded; it's polymorphic. CSE 341 -- S. Tanimoto Functional Programming 10

Polymorphism Q. Is there another way for a function to exhibit polymorphism? A. Yes, it can return different types of values. For example, the Scheme function given by (define (check-for-positive n) (if (< n 0) 'negative n) ) may return either a number or a symbol, depending on the value of n. CSE 341 -- S. Tanimoto Functional Programming 11

Polymorphic Variables Q. What is a polymorphic variable? A. It’s a variable that can hold values of more than one type. In Scheme, symbols often serve as polymorphic variables: (define x 5) (set! x ’apple) (set! x ’(peaches and pears)) CSE 341 -- S. Tanimoto Functional Programming 12

Polymorphism in Java Q. Does Java support polymorphism? A. Yes, via the use of the built-in, general class Object. public class Widget extends Object { private String name; public void set. Name(String n) {name = n; } } public Widget test(Widget w) { Widget w 2 = (Widget) w. clone(); w 2. set. Name(“The cloned Widget”); return w 2; } CSE 341 -- S. Tanimoto Functional Programming 13