haskell-98-tutorial.pdf

of expressions include atomic values such as the integer 5 , the character ’a’ , and the function

integers), Char (characters), Integer->Integer (functions mapping Integer to Integer ), as well

as the structured types [Integer] (homogeneous lists of integers) and (Char,Integer) (character,

The \ :: " can be read \has type."

inc can be dened by the single equation:

ration (x4.4.1), with whichwe can declare an explicit typing for inc :

For pedagogical purposes, when we wish to indicate that an expression e

duces," to another expression or value e

) e

so the expression ’a’+’b’ is ill-typed. The main advantage of statically typed languages is well-

it is enforced byHaskell’s lexical syntax. In fact, the case of the other characters matters, too: foo ,

integers (e.g. [1,2,3] ), lists of characters ( [’a’,’b’,’c’] ), even lists of lists of integers, etc., are

all members of this family. (Note, however, that [2,’b’] is not avalid example, since there is no

single typethatcontains both 2 and ’b’ .)

[Identiers suchas a above are called type variables, and are uncapitalized to distinguish them

from specic types suchas Int . Furthermore, since Haskell has only universally quantied types,

ply write [a] in the example above. In other words, all type variables are implicitly universally

explaining the principles of polymorphism. The list [1,2,3] in Haskell is actually shorthand for

the list 1:(2:(3:[])) , where [] is the empty list and : is the inx operator that adds its rst

write this list as 1:2:3:[] .

empty list is 0, and the length of a list whose rst element is x and remainder is xs is 1 plus the

length of xs ." (Note the naming convention used here; xs is the plural of x , and should be read

x:xs . In a function application these patterns are matched against actual parameters in a fairly

one element, binding x to the rst element and xs to the rest of the list). If the match succeeds,

containing elements of anytype, for example [Integer] , [Char] ,or [[Integer]] .

) 3

length [[1],[2],[3]] ) 3

Here are two other useful polymorphic functions on lists that will be used later. Function head

Unlike length , these functions are not dened for all possible values of their argument. A runtime

others in the sense that the set of values they dene is larger. For example, the type [a] is more

substitution for a . With regard to this generalization ordering, Haskell’s type system possesses two

all instances of the expression". For example, the principal type of head is [a]->a ; [b]->a , a->a ,

or even a are correct types, but too general, whereas something like [Integer]->Integer is too

of examples ( x 4.2.1).

The type being dened here is Bool , and it has exactly twovalues: True and False . Type Bool is

Because of the single constructor, a type like Point is often called a tuple type, since it is essentially