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Scheme & Functional Programming

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This document explores the foundational elements of Scheme and functional programming. It covers essential topics such as data types, variable declaration, and the use of functions. You'll learn about defining variables, using control structures like `if` and `let`, and creating anonymous functions (lambdas). The text delves into list operations, including constructing, filtering, and appending lists, along with practical examples for calculating sums and applying functions. Ideal for beginners looking to deepen their understanding of functional programming principles.

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Scheme & Functional Programming

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  1. Scheme & Functional Programming

  2. (+ 23 41) >> 64 (- 1000 334) >> 666 (* 25 4 12) >> 1200 (+ (* 3 5) (- 10 6)) >> 19

  3. Data Types • #t for true and #f for false • Characters: #\a is ‘a’, #\space is ‘ ’ • Strings “Hello World!” • define variables: (define greeting “Hello World!”)

  4. (define num 2) (* 5 num) >> 10 (define (square x) (* x x)) (square 9) >> 81 (square (+ 5 4)) >> 81 (square (square 3)) >> 81

  5. (define (abs x) (if (< x 0) (- x) x)) • and, or, not (and (> x 5) (< x 10))

  6. (define (factorial n) (if (= n 1) 1 (* n (factorial (- n 1)))))

  7. Local variables: let • (let (list of bindings) (what to compute)) (let ((x 2) (y 3)) (* x y)) • Problem: can’t use x later in bindingslist • let* (let* ((x 2 ) (y (- x 2)) (*x y))

  8. Functions as arguments Want to calculate: b Σ f(n) n=a for any functions f and next: (define (sum f a next b) (if (> a b) 0 (+ (f a) (sum f (next a) next b)))) • if (inc a) is a+1, and (cube x) is x3 what is (sum cube 1 inc 5)

  9. lambda Functions • Remember anonymous functions in Python? That was a functional-programming feature. • (sum cube 1 inc 5) • (sum (lambda (x) (* x x x)) 1 (lambda (x) (+ 1 x)) 5)

  10. filter • (filter <function> <list>) • (filter positive? (list 1 -1 2 -2 3 -3))

  11. Lists (define one-through-four (list 1 2 3 4))> one-through-four> (1 2 3 4)

  12. Head (car) and Tail (cdr) (car one-through-four)1(cdr one-through-four)(2 3 4)(car (cdr one-through-four))2

  13. Construct a list (cons) (cons 10 one-through-four)(10 1 2 3 4)(cons 5 one-through-four)(5 1 2 3 4)

  14. append • Can append two lists into one • This is different than cons

  15. Empty List Keyword null is an empty list. Check for empty list:  (if (null? items)

  16. Quoting (define a 1)(define b 2)(list a b)(1 2)(list 'a 'b)(a b)(list 'a b)(a 2)

  17. Put it in a file • I know what you’re thinking….How do I make a comment? (Semicolon for in-lines) ; Hello World (define (hello) (begin (display “Hello World!”) (newline)))

  18. Scheme is interpreted… • but we can load a file all at once: • (load “hello.ss”)

  19. Practice • Sum up a list • “double up” a list – for example, (doubleUp (list 1 2 3 4)) should give(1 1 2 2 3 3 4 4) • zipUp two lists - do pairings, for example, (zipUp (list 1 2 3) (list 4 5 6)) should give ((1 4) (2 5) (3 6))

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