CS 251 Fall 2019 CS 251 Fall 2019 Principles of Programming - - PowerPoint PPT Presentation

CS 251 Fall 2019 Principles of Programming Languages

Ben Wood

λ

CS 251 Fall 2019

Principles of Programming Languages

Ben Wood

λ

https://cs.wellesley.edu/~cs251/f19/

Higher-order Functions

+hof.rkt

Higher-order Functions 1

Topics

• Functions are first-class.
• Using first-class/higher-order functions
• Map and filter
• Next time: getting the semantics right

Higher-order Functions 2

First-class and higher order functions

Functions are fi first-cl clas ass val alue ues, can be used or created wherever we use or create any other values:

– Arguments to (higher order) function calls – Results of (higher order) function bodies – Stored in cons cells or other data structures – Bound (named) by variables – …

Hi Higher order functions take or return other functions. Powerful ways to:

– factor out common functionality – parameterize general patterns with specific behavior

Higher-order Functions 3

Function closures support lexical scope for nested functions.

Sneak peak:

– Function bodies can use any bindings in scope where function is defined, including from outside the function definition. – Distinct concept from first-class functions – Back to this powerful idea soon!

Higher-order Functions 4

Functions as arguments

(define (map-pair f pair) (cons (f (car pair)) (f (cdr pair))))

Elegant strategy for factoring out code for common patterns of data manipulation. Combines well with anonymous functions. [S [See code examples in ho hof.r f.rkt kt]

Higher-order Functions 5

A style point

(if x #t #f) (lambda (x) (f x))

(n-times (lambda (x) (cdr x)) 2 (list 1 2 3 4))

(n-times cdr 2 (list 1 2 3 4))

Higher-order Functions 6

✘ ✓

Map

(define (map f elems) (if (null? elems) null (cons (f (first elems)) (map f (rest elems)))))

Higher-order Functions 7

HO HOF HO HOF

v1 v2 vn

f f f

(f v1)

⋯ ⋯

(f v2) (f vn) argument list result list

Filter

(define (filter f elems) (if (null? elems) null (if (f (first elems)) (cons (first elems) (filter f (rest elems))) (filter f (rest elems)))))

Higher-order Functions 8

HO HOF HO HOF

#t #f #t

v1 v2 vn

f f f

⋯ ⋯

vn v1 argument list result list

Rewrite the list practice functions

• Which functions could be built using map/filter?
• For which functions does this feel more or less

elegant than your original implementation?

Higher-order Functions 9

Generalizing

Our examples of first-class functions so far:

– Take one function as an argument to another function – Process a number or a list

But first-class functions are useful anywhere for any kind of data

– Pass several functions as arguments – Put functions in data structures (tuples, lists, etc.) – Return functions as results – Write higher-order functions that traverse other data structures

Powerful idioms to:

– factor out and reuse common functionality – parameterize general patterns with specific behavior – clearly communicate high-level meaning/intent

Higher-order Functions 10