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CS302: Paradigms of Programming Functional Programming with Haskell (Cont.)
Manas Thakur
Spring 2020
The best way to begin (and even finish!)
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CS302: Paradigms of Programming Functional Programming with Haskell - - PowerPoint PPT Presentation
CS302: Paradigms of Programming Functional Programming with Haskell - - PowerPoint PPT Presentation
CS302: Paradigms of Programming Functional Programming with Haskell (Cont.) Manas Thakur Spring 2020 The best way to begin (and even finish!) 2 Types types types What is a type? What is it useful for? What is type checking? Di
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Types types types
- What is a type?
- What is it useful for?
- What is type checking?
- Difference between a strongly and a weakly typed language?
- Why shouldn’t we always use the most general type?
- Static vs dynamic typing?
- Untyped languages?
- Haskell tries to offer the best of all worlds: Type inference!
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Duck typing! If it walks like a duck and it quacks like a duck, then it must be a duck.
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Abstract Data Types
- Type with operations
- What’s abstract about it?
- Hides the representation details.
- Recall our Point example from Lab2.
- Definition of Bool in Haskell:
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data Bool = False | True
Data declaration Data constructors
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Examples of ADTs
- What are constructors in OO languages?
- Check the types of Circle and Rectangle.
- Now you can use these types in functions:
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data Shape = Circle Float Float Float | Rectangle Float Float Float Float area :: Shape -> Float area (Circle _ _ r) = pi * r * r area (Rectangle ...
- Why won’t area :: Circle -> Float work?
- Same reason why foo :: True -> Int won’t work!
Notice pattern matching! Named constructors!
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Type Parameters
- Maybe is a very useful type for handling failures.
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data Maybe a = Nothing | Just a
Type parameter
head :: [a] -> a head [] = error “Empty list” head (x:_) = x safeHead :: [a] -> Maybe a safeHead [] = Nothing safeHead (x:_) = Just x safediv :: Int -> Int -> Maybe Int safediv _ 0 = Nothing safediv m n = Just (m `div` n) Can’t return this!
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Type Classes
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- Check the type of Haskell’s built-in sort function:
> import Data.List > :t sort > sort :: Ord a => [a] -> [a]
- It sorts lists containing elements of type a such that a belongs
to the type class Ord.
- What’s the problem with the following types for +:
(+) :: Int -> Int -> Int (+) :: Float -> Float -> Float (+) :: a -> a -> a
Too specific Too general
- We would like to define (+) for only number-like types.
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Type Classes (Cont.)
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- Check the type of + now:
- Here is the declaration of the type class Num from Haskell:
> :t (+) > + :: Num a => a -> a -> a class (Eq a, Show a) => Num a where (+),(-),(*) :: a -> a -> a negate :: a -> a abs, signum :: a -> a fromInteger :: Integer -> a
- Class Num is a subclass of both Eq and Show.
- +, -, *, negate, … are predefined functions in Num.
a is a type variable
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Recursive Types
- What does this type describe?
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data Nat = Zero | Succ Nat
- Does this remind of something from Lab1?
- Church numerals!
nat2int :: Nat -> Int nat2int Zero = 0 nat2int (Succ n) = 1 + nat2int n add :: Nat -> Nat -> Nat add m n = int2nat (nat2int m + nat2int n) CQ
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The best way to finish (and even begin!)
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On roll for the last week
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- 1. Type Inference
- 2. Proving Program
Properties
- 3. Monads