CSEN403: Concepts of Programming LanguagesFunctional Programming II: Types and Currying

Nada Sharaf

Spring Semester 2019

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Type System of Haskell

Haskell is able to infer the functions typeI i.e. if you omit type specifications for a function, Haskell will still be

able to infer the type of any well-formed expression.Haskell is strongly typed.

I Programs with inconsistent types are rejectedI Example:

F You can not apply a function to a value with a wrong typeF You cannot write a function that produces values of different type

classes

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What is a type

A name for a group of related valuesTrue and False are of the same type: Bool

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Type Specification

e :: t

The expression e has a type tExamples:

I > :t TrueTrue :: Bool

I > :t ’a’’a’ :: Char

I > :t "Nada""Nada" :: String

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Type Classes

A class has different types inside it.=> is used to differentiate between the classes used and the actualtypesBefore the =>, constraints on types are places.After => actual type is placedExamples:

I > :t 11 :: Num a => a

1 is an instance of NumericI > :t (1,2)

(1,2) :: (Num a, Num b) => (b,a)

I > :t (1,2.5)(1,2.5) :: (Fractional a, Num b) => (b,a)

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Some Built-In Types

Integer unbounded integer numbersInt 32-bit integer numbers

Rational unbounded rational numbersFloat, Double single- and double-precision floating-point numbers

Bool Boolean values (True, False)Char characters, e.g., ‘a’

All types and type classes start with an upper case characterInt has a fixed capacity whereas Integer in theory has no bounds onsize

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Types for Functions

a->b

The input has type a

The output has type b

Example:> :t oddodd :: Integral a => a -> Bool

Example:> :t eveneven :: Integral a => a -> Bool

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Example

add (x,y) = x+y

> :t addadd :: (Int,Int) -> Int

If we want to restrict it to Int values onlyIn the file we have to restruct the type definition to overwrite theinferred one.add:: (Int,Int) -> Int

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Currying

add x y = x+y

You might believe that the function add has two inputs and oneoutput.This is not the case in Haskell.In Haskell, every function has one input and one outputInputs and outputs could howveer be in turn functionIn other words, the input of add is a numeric x

Its output is a function hence the term curried function.The output function in turn has one input y and an outputrepresenting the sum of x and y

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Currying Contd.

add x y = x+y

add:: Num a => a -> (a-> a)

The brackets are usually omitted

add:: Num a => a -> a-> a

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Polymorphic Functions

The type of function contains many (poly) types

> length [1,2,3]3

>length [1.5,6.2]2

>length [’a’,’b’,’c’,’d’]4

length :: [a] -> Int

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Defining New Names for Existing types

We use the keyword type

Type declarationtype MyString = [Char]

type Point = (Int, Int)

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Example

type Point = (Int, Int)

getX :: Point -> IntgetX (x,y) = x

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Type Declaration

Can have a parameter

type Point2 a = (a,a)

getX2 :: Point a -> agetX2 (x,y) = x

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New Types

Use the keyword data.You start to enumerate the possible templates of the values of thistypedata Fruit = Apple | Banana

Without the new data Fruit introduced, we can not use the valuesApple or BananaApple and Banana are called the constructorsThey are used to construct values of the new type Fruit/

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Example

color :: Fruit -> Stringcolor Apple = "red"color Banana = "yellow"

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Parameters

A constructor can have parametersExampledata Shape = Circle Float | Rect Float Float

To construct a value of the type Shape, you canI Use the constructor Circle followed by an floating point value

(representing the radius)I Use the constructor Rect followed by two floating point values

(representing the length and width)

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Example

area (Circle r) = 3.14*r*rarea (Rect l w) = l*w

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Deriving Show

data Shape = Circle Float | Rect Float Float deriving Show

To be able show/print values of this new typeFunctions: formCircle, formRectformCircle r = Circle rformRect l w = Rect l w

Similarly, to be able to check if two values of a new type are equal ornot, the new data type has to be deriving Eq

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Define a list of integers

data List = Empty | L Int List deriving Show

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Define a list of any elements

data List a = Empty | L a (List a) deriving Show

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Thank You!

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