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Scheme & Functional Programming Cheat Sheet

Scheme & Functional Programming Cheat Sheet




Scheme & Functional Programming Cheat Sheet



Basic Syntax & Notation

Prefix Notation


;; Infix vs Prefix
;; Infix: 2 + 3 * 4
;; Prefix: (+ 2 (* 3 4))

;; All operations are functions
(+ 1 2 3 4) ;; → 10
(* 2 3 4) ;; → 24
(- 10 3) ;; → 7
(/ 20 4) ;; → 5



Basic Forms


;; Numbers
42, 3.14, -17, 1/3

;; Booleans
#t, #f

;; Characters
#\a, #\b, #\space, #\newline

;; Strings
"Hello World"

;; Symbols
'hello, 'world, '+






Core Procedures


Procedure
Description
Example


define
Create variables/procedures
(define x 5)


if
Conditional expression
(if (> x 0) "pos" "neg")


cond
Multiple conditions
(cond [(> x 0) "pos"] [else "neg"])


and
Logical AND
(and #t #f) → #f


or
Logical OR
(or #t #f) → #t


not
Logical NOT
(not #t) → #f


abs
Absolute value
(abs -5) → 5


odd?
Check if odd
(odd? 3) → #t


even?
Check if even
(even? 4) → #t







Defining Procedures


;; Basic procedure definition
(define (procedure-name param1 param2)
body-expression)

;; Example: Add procedure
(define (add x y)
(+ x y))

;; Usage
(add 5 3) ;; → 8

;; Lambda (anonymous functions)
(lambda (x y) (+ x y))
((lambda (x y) (+ x y)) 5 3) ;; → 8






The Fantastic Recursive Approach


Four Steps to Recursive Solutions:

Size-n Problem: What are we trying to solve?

Stopping Conditions: When do we stop recursing?

Size-m Problems: What smaller problems do we solve?

Construction: How do we build the solution from smaller parts?





Factorial Example


(define (factorial n)
;; 1. Size-n problem: factorial of n
(if (