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Scheme Documentation



We use comments to leave notes about the code to the reader. Comments are not actually run by Scheme, they are just there to help us read the code.

We can make single line comments with ; .

; Use single line comments to clarify parts of code.
; This program adds 1 and 2 and stores the result in x
(define x (+ 1 2)); done

Basic Data Types

Data can be a string, number, a boolean, or something else.
A string is a text element. A number can be number, integer, rational, real, and/or complex. A boolean is an element that returns either #t (True) or #f (False). There are additional variable types.
The example code below shows how we can check the type of data
(string? "hi")  ; Returns #t (True) indicating "hi" is a string
(integer? 2)    ; Returns #t (True) indicating 2 is an integer
(boolean? #f)   ; Returns #t (True) indicating #f is a boolean


Variables have an associated 'type' based on their characteristics.

We use variables to store values that can be used to control commands in our code. We can also alter these values throughout the code.

; Make a variable to store text
(define name "Zach")

; Create variables that are numbers
(define num_one 3) ; num_one now have the value 3
(define num_two 4) ; num_two now has the value 4
(define sum (+ num_one num_2)) ; sum now has the value 7
(set! num_one 20)  ; num_one now has the value 20


We use mathematical, comparison, and logical operators in our codes to compare and alter values and make decisions.

Comparison Operators

Use comparison operators to compare elements in order to make decisions in your code. Comparison operators return booleans (#t/#f).

; For numbers use below
(> x y)           ; is x greater than y
(>= x y)          ; is x greater than or equal to y
(< x y)           ; is x less than y
(<= x y)          ; is x less than or equal to y
(= x y)           ; is x equal to y

; For strings use below
(string>? x y)           ; is x greater than y
(string>=? x y)          ; is x greater than or equal to y

Logical Operators

Use logical operators to check multiple conditions at once or one condition out of multiple.

; And Operator
(and x y)                 ; Returns x and y

; Or Operator
(or x y)                  ; Returns x or y

; Not operator
(not x)                   ; Returns not x

; You can combine many booleans!
(and x (or y z))

Mathematical Operators

Use mathematical operators to alter values.

+   Addition
-   Subtraction
*   Multiplication
/   Division
remainder Remainder of division
quotient  Quotient of division
(+ a b)
(* a b)

; Division
(/ 5 2)               ; Returns 5/2
(/ 5.0 2)             ; Returns 2.5
(/ 6 2.0))            ; Returns 3.

; Quotient
(quotient 13 5)       ; Returns 2

; Remainder
(remainder 13 5)      ; Returns 3

; Absolute value
(abs -2)              ; Returns 2

; Square root
(sqrt 9)              ; Returns 3

; Raising to a power
(expt x y)            ; Returns x^y

; Rounding, rounds to even when the number is halfway between two integers
(round 1.7)           ; Returns 2
(round 3.1)           ; Returns 3
(round 1.5)           ; Returns 2
(round 2.5)           ; Returns 2

Random Numbers

; Random integer in [0, n)
(random n)
; Returns random number in [0, 10)
(random 10)


Strings are pieces of text. We can gain much information about strings and alter them in many ways using various methods.

; We can take a substring of a string.
(substring string  a b) ; returns the substring of string beginning at a and ending right before b
(substring "example 1 3") ; returns ex

Control Structures


Loops help us repeat commands which makes our code much shorter. Scheme doesnn't really have loops but we can do something similar

Scheme doesn't have traditional for or while loops, but when you want to repeat something, you can do something like below.

; This will print the numbers 1 to 10 each on it's own line
(let loop ((i 1))
   (if (= i 10)
     (begin (display i) (display "\n"))
     (begin (display i) (display "\n")
            (loop (+ i 1)))))

If Statements

Use an if statement to instruct the computer to do something only when a condition is true. If the condition is false, the following command will be skipped.

(if (BOOLEAN_EXPRESSION) (do something) )
; x will only be doubled if x is positive
(if (> x 0) (set! x (* x 2)))

If/Else Statements

We can tell the computer how to make decisions using if/else statements.

(if (BOOLEAN_EXPRESSION) (do something) (do something else) )
; if x is positive x is doubled, else x is set to 1
(if (> x 0) (set! x (* x 2)) (set! x 1))


We can use cond similarly to linking if and else if statements. cond executes the body of the first condition that is met. Only the last condition may represent else.

    ; this will show equal
    (define x 7)

    (cond ((> x 7) 'greater)
          ((< x 7) 'less)