Operators, Functions and Modules1 Pattern Matching & Recursion.

Operators, Functions and Modules 1

Pattern Matching&

Recursion


add2 0 b = badd2 a 0 = a add2 a b = a + b

A pattern can be

A literal 0 ‘a’ True False

A variable any argument value will match this

Wild card “_” any argument value will match this

A tuple pattern (p1, p2, …, pn) matches a tuple with matching values

A constructor

Here is a simple use of patterns in defining a function

add2 :: Int -> Int -> Int


A problemThe following table shows the weekly sales in a company,

Week 0 1 2 3 4 5 6

Sales 15 5 7 18 7 0 5

We want to know that given a week n,

What is the total sales from week 0 to week n

What is the maximum weekly sales from week 0 to week n

Function to calculate total sales given a particular week:

We will first represent the table of weekly data,sales :: Int -> Intsales 0 = 15sales 1 = 5sales 2 = 7sales 3 = 18sales 4 = 7sales 5 = 0sales 6 = 5


totalSales :: Int -> Int

totalSales n | n = = 0 = sales 0 | otherwise = totalSales (n-1) + sales n

We have used recursion in the definition of our functions. This type of recursion is called primitive recursion.

The first clause is called the base case and the second clause is called the recursive case.totalSales 4 = totalSales 3 + sales 4 = (totalSales 2 + sales 3) + sales 4 = ((totalSales 1 + sales 2) + sales 3 )+ sales 4 = (((totalSales 0 + sales 1) + sales 2) + sales 3 )+ sales 4 = ((((sales 0 + sales 1) + sales 2) + sales 3 ) + sales 4 = 15+5 + 7+18+7+0+5=57

Definition of totalSales (using guards):


maxSales 4

= maxi (sales 4) maxSales 3

= maxi 7 (maxi (sales 3) maxSales 2)

= maxi 7 (maxi 18 (maxi (sales 2) maxSales 1))

= maxi 7 (maxi 18 (maxi 7 (maxi (sales 1) maxSales 0)))

= maxi 7 (maxi 18 (maxi 7 (maxi 5 sales 0)))

= maxi 7 (maxi 18 (maxi 7 (maxi 5 15)))

= maxi 7 (maxi 18 (maxi 7 15))

= maxi 7 (maxi 18 15)

= maxi 7 18

= 18

Function to calculate maximum sales(using guards):maxSales :: Int -> Int

maxSales n

| n = = 0 = sales 0

| otherwise = maxi (sales n) maxSales (n-1)


Pattern matching could have been used for defining these functions. Pattern matching may be used when we have a number of equations. Each equation can become a pattern. Let’s now define totalSales and maxSales using patterns.

totalSales 0 = sales 0totalSales n = totalSales (n-1) + sales n

maxSales 0 = sales 0maxSales n = maxi (sales n) (maxSales (n-1))

The underscore “_” (known as don’t care) can be used as a pattern and we use it when we do not care about the value it matches with.

isZero :: Int -> BoolisZero 0 = TrueisZero _ = FalsePrelude> isZero ‘A’


More Types


The ASCII code of the characters can also be used for representing them. For instance, ‘\65’ is equivalent to ‘A’.

Character

Type Char is a Haskell built-in type. Characters are put inside single quotes.

‘a’ to ‘z’, ‘A’ to ‘Z’, ‘0’ to ‘9’

Some characters are represented using a backslash “\” before them.

Examples are:tab ‘\t’, newline ‘\n’, backslash ‘\\’

single quote ‘\’’, double quote ‘\”’

ASCII codes 65 to 90 represent A-Z

ASCII codes 97 to 122 represent a-z

ASCII codes 48 to 57 represent 0-9


Prelude> ord ‘r’114Prelude> ‘\114’rPrelude> chr (114)rHere is a function for converting a lower case letter to capital.offset :: Intoffset = ord ‘A’ – ord ‘a’toCapital :: Char -> ChartoCapital ch = chr (ord ch + offset)

Here, we did not have to define offset. We could have simply said:toCapital ch = chr (ord ch + (ord ‘A’ – ‘ord ‘a’))It is however good practice to define offset as ewe have.

There are two useful built in conversion functions.chr :: Int -> Charord :: Char -> Int


Other functions

toLowr:: Char -> Char

toLowr ch = chr (ord ch - offset)

isDigit :: Char -> Bool

isDigit ch = (‘0’ <= ch) && (ch <= ‘9’)

isChar :: Char -> Bool

isChar ch = not (isDigit ch)


The operator ++ used above is the concatenation operator.Prelude>putStr “Massey University”Massey UniversityPrelude> putStr “\99u\116”cutPrelude>putStr “oranges\napples\npears”

Strings:

A string is a special list consisting of characters. Type String = [Char]

Here are some strings:

“Haskell is a functional programming language.”

”\72el\108o\t world”

“Haskell “ ++ “ programming”

orangesapplespears


Floating Point Numbers

Type Float is used for calculations involving floating point numbers.

Examples of floating point numbers:

110.3421

345.365

4.0

-2.09

Type Float is not used very much. Floating point arithmetic is not

very precise in Haskell because of the limited space allowed for the

internal representation of floating point numbers. A type like Double

may be used for more precision.


Float ->Float -> Float

+, *, -, /, ** (example: x ** y )

Float ->Float

cos, sin, tan, abs, sqrt (square root)

Float ->Int -> Float

^ (example: x^n)

Float ->Int

ceiling, floor, round, truncate

Integer ->Float

fromInteger

Float

pi (the constant pi)

An example: sin (pi/2) * pi

Some built-in floating point operations:


Using Integer and Float answer :: Integer answer=42

Main> answer + 2.8ERROR - Unresolved overloading*** Type : Fractional Int => Int*** Expression : answer + 2.8Prelude> answer + truncate 2.844Prelude> fromInteger answer + 2.844.8Prelude> floor 2.82Prelude> ceiling 2.83Prelude> round 2.83Prelude> truncate 2.82


Function to compute average of weekly sales

meanSales :: Integer -> Float

meanSales n =

fromInteger (totalSales n) / fromInteger (n+1)

Operators, Functions and Modules1 Pattern Matching & Recursion.

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