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Scheme Programming Language Cheatsheet

A concise cheat sheet covering the core syntax, data types, procedures, and control structures of the Scheme programming language, useful for quick reference and learning.

Basic Syntax and Data Types

Core Syntax

()

All Scheme code is enclosed in parentheses. This signifies a function call or a special form.

define

Used to define variables and procedures.

Example: (define x 10)

lambda

Creates anonymous functions (procedures).

Example: (lambda (x) (+ x 1))

Data Types

Numbers

Integers, decimals, fractions.

Example: 10, 3.14, 1/2

Booleans

#t (true) and #f (false).

Characters

Represented with #\.

Example: #\a, #\space

Strings

Sequences of characters enclosed in double quotes.

Example: "hello"

Symbols

Unique identifiers, often used as keys.

Example: 'symbol

Lists

Ordered collections of data.

Example: '(1 2 3)

Basic Procedures

+, -, *, /

Arithmetic operators.

Example: (+ 1 2) (evaluates to 3)

=

Numerical equality comparison.

Example: (= 1 1) (evaluates to #t)

cons

Constructs a new list by adding an element to the beginning of an existing list.

Example: (cons 1 '(2 3)) (evaluates to '(1 2 3))

car

Returns the first element of a list.

Example: (car '(1 2 3)) (evaluates to 1)

cdr

Returns the rest of the list after the first element.

Example: (cdr '(1 2 3)) (evaluates to '(2 3))

Control Structures

Conditional Execution

if

Basic conditional statement. (if condition then-expression else-expression)

Example: (if (= x 10) "x is 10" "x is not 10")

cond

Multi-way conditional. (cond (condition1 expression1) (condition2 expression2) ... (else expression))

Example:

(cond
  ((> x 0) "positive")
  ((< x 0) "negative")
  (else "zero"))

Iteration and Recursion

Recursion

Scheme primarily uses recursion for iteration. A function calls itself until a base case is reached.

Example:

(define (factorial n)
  (if (= n 0)
      1
      (* n (factorial (- n 1)))))

do

The do form provides a looping construct. (do ((variable initial update) ...) (termination-condition result) body ...)

Example:

(do ((i 0 (+ i 1))
     (sum 0 (+ sum i)))
    ((> i 10) sum)
  (display i) (newline))

Boolean Operations

and

Returns #t if all expressions are true.

Example: (and (> 5 3) (< 10 20))

or

Returns #t if at least one expression is true.

Example: (or (> 5 3) (> 10 20))

not

Negates a boolean value.

Example: (not (= 5 3))

Working with Lists

List Manipulation

list

Creates a list from given elements.

Example: (list 1 2 3) (evaluates to '(1 2 3))

append

Concatenates lists.

Example: (append '(1 2) '(3 4)) (evaluates to '(1 2 3 4))

reverse

Reverses the order of elements in a list.

Example: (reverse '(1 2 3)) (evaluates to '(3 2 1))

length

Returns the number of elements in a list.

Example: (length '(1 2 3)) (evaluates to 3)

Mapping and Filtering

map

Applies a function to each element of a list and returns a new list with the results.

Example: (map (lambda (x) (* x 2)) '(1 2 3)) (evaluates to '(2 4 6))

filter

Creates a new list containing only the elements that satisfy a given predicate (a function that returns #t or #f).

Example: (filter (lambda (x) (> x 1)) '(1 2 3)) (evaluates to '(2 3))

List Predicates

null?

Checks if a list is empty.

Example: (null? '()) (evaluates to #t)

list?

Checks if a value is a list.

Example: (list? '(1 2 3)) (evaluates to #t)

member

Checks if an element is a member of a list.

Example: (member 2 '(1 2 3)) (evaluates to '(2 3))

Input and Output

Basic I/O

display

Prints a value to the console.

Example: (display "Hello, world!")

newline

Prints a newline character to the console.

Example: (newline)

read

Reads a Scheme expression from the input.

Example: (read)

Formatted Output

format

Formatted output (implementation-dependent, check your Scheme system’s documentation).

Example (Racket): (format #t "The value of x is ~a" x)

File I/O

open-input-file

Opens a file for input.

Example: (define input-port (open-input-file "data.txt"))

open-output-file

Opens a file for output.

Example: (define output-port (open-output-file "output.txt"))

read-char

Reads a single character from an input port.

Example: (read-char input-port)

write-char

Writes a single character to an output port.

Example: (write-char #\a output-port)

close-input-port

Closes an input port.

Example: (close-input-port input-port)

close-output-port

Closes an output port.

Example: (close-output-port output-port)
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