Jeff Cheah - Scheme Learning Notes

Scheme is a programming language, and it’s a dialect of a programming language called Lisp. Lisp is one of the two oldest programming languages that is still widely used today.

Expression

Scheme is composed of expression, which is a construct that returns a value.

Primitive Expression

Primitive is just a set of values of different data types. For example:

; Number
1       ; integer
2.0     ; real
3/4     ; rational

; Symbol
x
abc

; Boolean
#t      ; true
true    ; true
#f      ; false
false   ; false

; String
"hello"

; Character
#\c     ; character 'c'
#\A     ; character 'A'

Combination

Expressions can be combined with operators to form a combination. A combination is surrounded by brackets, and it’s also known as s-expression.

The most common combination is a call expression, which includes an operator and followed by 0 or more operands. Nesting and line breaks are allowed in call expressions.

(+ (* 3
      (+ (* 2 4)
         (+ 3 5)))
   (+ (- 10 7)
      6))           ; 57
(quotient 10 2)     ; 5
(not #t)            ; #f

Special Forms

A special form is a combination that is not a call expression, it has the same syntax but comes with special rules.

Comparison Operator

(>= 3 2)                ; #f
(< 5 12)                ; #t

If expression

If expression are expressed in following form:

(if <predicate> <consequent> <alternative>)

The interpreter starts by evaluating the <predicate> part, if it evaluates to a true value, <consequent> will be evaluated, otherwise <alternative> will be evaluated and the resulting value will be returned.

Boolean Operator

(and <e1> ... <en>)

Short circuiting is supported in Scheme, which means expression <e>’s will be evaluated from left to right. If any <e> evaluates to false, false value is returned and the rest of the <e>’s will not be evaluated. If no false value is found, the value of the last element is returned.

(or <e1> ... <en>)

Or operator is similar to and operator, the interpreter evaluates the <e>’s from left to right. The difference is that once an <e> evaluates to true, the value is returned and the rest of the <e>’s will not be evaluated. If no true value is found, a false value is returned.

(not <e>)

Not expression evaluates to true when the expression <e> evaluates to false, and false otherwise.

Definition

A definition binds a value to a symbol.

(define a 1)
(* a 2)       ; 2

Procedures can also be defined using define, in a slightly different form.

(define (<name> <formal parameters>) <body>)

For example, a square procedure can be defined as following

(define (square x) (* x x))
(square 12)     ; 144

Lambda Expression

Lambda is a special kind of procedure. It behaves exactly like a procedure that is created using define, except that it has no name.

(lambda (<formal parameters>) <body>)

Lambda expression can be used for procedure definition, the following expressions are equivalent.

(define (square x) (* x x))
(define square (lambda (x) (* x x)))

Lambda expression can also be used as the operator in a call expression.

((lambda (x) (* x x)) 6)      ; 36

Scheme Learning Notes