# ​Parallel and Concurrent Haskell (3)

3.1 Algebraic Data Types: Product Type, Sum Type

Projection by Pattern Match:

fst :: (a , b )  -> a
fst  (x, _) = x

snd (_,y) = y

:t  ( , ) data constructor

( , ) :: a -> b -> (a,b) type constructor

Kind
:k (,) type constructor
(,) :: * -> * ->  *

Laziness

3.2 Sum Type

data Either a b = Left a | Right b
Left :: a -> Either a b
Right :: b -> Either a b

safeSqrt :: Either String Double -> Either String Double

safeSqrt (Left str) = Left str
safeSqrt (Right x) =
if x <0
then Left “Error”
else Right (sqrt x)

safeSqrt  sx =
case sx of
Left str -> Left str
Right str ->if x < 0
then Left “Error”
else Right (sqrt x)

data Bool = True | False
case x < 0 of
True -> …
False -> …

(<) :: Ord a => a -> a -> Bool

Note: Ord = Order

a + 0 = a

data X a = X a | Y Void

a + 0

a * 1 = a

type Y a = (a , () )

a * 0 = 0
type Z a = (a, Void) ~ Void

Note: (a, Void) is an impossible pair of 2 elements, because Void has no element, so (a, Void) is equivalent to Void.

2 = 1 + 1
2 = Bool
Bool = True | False

# Parallel & Concurrent Haskell (2)

Continued from : (Part 1)

2.2 Data Structure

Function (+) ::  D -> D -> D
inc  x  = 1 + x ~ (+) ::  1 + x

Section (Partial appl) : inc  = (+ 1)

Type ~ Set {values} : Integer Set / Boolean Set {0,1} / Empty Set “Void” { } / …

Type of Singleton (1 element) : Unit ( )

Declare a new Type : data

data () = ()
1st () = Type of Unit
2nd () = constructor of Unit

Haskell convention : Type name = constructor name

(To avoid having too many nsmes)

Define cares Ian product of Types (Sets):

data Product a b = P a b

Product : Type constructor
P : Data constructor (function with 2 args of types a, b)
P :: a -> b -> Product a b

Data Immutable : remember how it was constructed.

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

sqDist ‘ ‘ (P x y ) = x^2 + y^2
sqDist ‘ ‘ :: Num a =-> Product a a -> a

Built-in for “pair”:

data ( , ) a b =( , ) a b

eg.
( , ) 1 2 gives (1, 2)

All data (Types) are formed by only 2 methods : Product or Sum.

$\boxed {\text {Algebraic Data : by Product, Sum}}$

http://chimera.labs.oreilly.com/books/1230000000929/index.html
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# Parallel and Concurrent Haskell (1)

2016

1-1: Introduction

Everything in Haskell is PURE (function), including side effects (print, I/O such as open files, update data, …)

“Pure”: f (x) = a, regardless of ‘x’ value may change, always returns the result ‘a’

2.1 Function

f a b = function f, arg a & b

sqDist (x, y ) = x^2 + y^2
main = print $sqDist (3, 4) dist pt = sqrt$ sqDist pt

dist = sqrt . sqDist

Note: pronounce “.” as “AFTER

id  :: a -> a [Signature] # Polymorphic
id  x = x [Implementation]

flop :: (a, b) -> (b, a)
flop p = = (snd p,fst p)

flop’ (x,y) = (y,x)

Example:
print \$ flop (5, “Hello!”)

Currying
sqDist :: Double ->Double -> Double
Equivalent to: sqDist 1 arg but return a function (Double -> Double)
sqDist :: Double -> (Double -> Double)

sqDist x y = x^2 + y^2

Equiv: sqDist (x,y) # but difficult to partial application.

Partial Application (pass fewer args)
sqDist 0 = Double -> Double

sqdistfromzero
:: Double -> Double
sqdistfromzero = sqDist 0

2.2 Functions

Function (+) ::  D -> D -> D
inc  x  = 1 + x ~ (+) ::  1 + x

Section (Partial appl) : inc  = (+ 1)

To be continued … (Part 2)

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