# Code (Week 9)

## Table of Contents

## 1 Existentially quantified types

{-# LANGUAGE ExistentialQuantification #-} {-# LANGUAGE GADTs, StandaloneDeriving #-} module ExistsEx where data M where MC :: a -> M -- we can create values of type M. As the content type xs :: [M] xs = [ MC 4, MC True, MC even] -- we can never do anything with values of type M, as we -- can't 'unpack' them. The following function raises a type -- error, as the type of x can't be known statically -- unpack (MC x) = x data MS where MSC :: Show a => a -> MS deriving instance (Show MS) -- note that the function 'even' can't be in the list now, -- because it's type is not in the class Show ys :: [MS] ys = [ MSC 4, MSC True] -- we still can't define unpack, but we can take x and apply -- show to it: now, it's clear what the result type of the -- function is, independent of the actual type of x unpackAndShow :: MS -> String unpackAndShow (MSC x) = show x -- we can also bundle the value of type 'a' explicitly with a -- function which knows what to do with it data MP where MPC :: a -> (a -> String) -> MP -- For the values whose type is in the Show class, we just provide the -- their show function, for 'even' we provide a costumised zs :: [MP] zs = [ MPC 4 show , MPC True show, MPC even (\_ -> "the function \'even\'")] unpackAndShowMP :: MP -> String unpackAndShowMP (MPC x f) = f x

Shape example:

module Shapes where class ShapeC a where perimeter :: a -> Double area :: a -> Double data Shape = forall a. ShapeC a => Shape a data Circle = Circle Double data Rectangle = Rectangle Double Double -- add this instance so we can apply methods directly instance ShapeC Shape where perimeter (Shape shape) = perimeter shape area (Shape shape) = area shape -- additional instances can be defined anywhere instance ShapeC Circle where perimeter (Circle r) = 2 * pi * r area (Circle r) = pi * r * r instance ShapeC Rectangle where perimeter (Rectangle x y) = 2*(x + y) area (Rectangle x y) = x * y -- smart constructors circle :: Double -> Shape circle r | r > 0 = Shape (Circle r) | otherwise = error "Circle with non-positive radius" rectangle :: Double -> Double -> Shape rectangle x y | x > 0 && y > 0 = Shape (Rectangle x y) | otherwise = error "Rectangle with non-positive side length" shapes :: [Shape] shapes = [circle 12, circle 10, rectangle 5 6]