Categories for the Working Hacker Philip Wadler University of - - PowerPoint PPT Presentation

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Categories for the Working Hacker Philip Wadler University of - - PowerPoint PPT Presentation

Jul 21, 2023 448 likes •830 views

Categories for the Working Hacker Philip Wadler University of Edinburgh QCon SF, 15 Nov 2017 Products in Java public class Product<A,B> { private A fst; private B snd; public Product(A fst, B snd) { this.fst = fst; this.snd = snd; }

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Categories for the Working Hacker

Philip Wadler University of Edinburgh QCon SF, 15 Nov 2017

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Products in Java

public class Product<A,B> { private A fst; private B snd; public Product(A fst, B snd) { this.fst = fst; this.snd = snd; } public A getFst() { return this.fst; } public B getSnd() { return this.snd; } }

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Products in Java

public class Test { public Product<Integer,String> pair = new Product(1, “two”); public Integer one = pair.getFst(); public String two = pair.getSnd(); }

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Products in Haskell

data Product a b = Pair { fst :: a, snd :: b }

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Products in Haskell

pair :: Product Int String pair = Pair 1 “two”

  • ne :: Int
  • ne = fst pair

two :: String two = snd pair

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Sums in Java

public interface Sum<A,B> { public <C> C caseExpr(Function<A,C> f, Function<B,C> g); } public class Left<A,B> implements Sum<A,B> { private A x; public Left(A x) { this.x = x; } public <C> C caseExpr(Function<A,C> f, Function<B,C> g) { return f.apply(x); } } public class Right<A,B> implements Sum<A,B> { private B y; public Right(B y) { this.y = y; } public <C> C caseExpr(Function<A,C> f, Function<B,C> g) { return g.apply(y); } }

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Sums in Java

public class ErrInt extends Sum<String,Integer> { public ErrInt err = new Left(“error”); public ErrInt one = new Right(1); public ErrInt add(ErrInt that) { return this.caseExpr( e -> new Left(e), m -> that.caseExpr( e -> new Left(e), n -> new Right(m+n) ) ); public ErrInt test = one.add(err); }

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Sums in Haskell

data Sum a b = Left a | Right b

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Sums in Haskell

type ErrInt = Sum String Int err = Left “error”

  • ne = Right 1

add :: ErrInt -> ErrInt -> ErrInt add (Left e) that = Left e add this (Left e) = Left e add (Right m) (Right n) = Right (m+n) test = add one err

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Exponentials in Java

public class Test { public Function<Integer,Integer> add (Integer n) { return x -> x + n; } public Function<Integer,Integer> incr = add(1); public Integer three = incr.apply(2); }

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Exponentials in Haskell

add :: Int -> (Int -> Int) add n = \x -> n + x incr :: Int -> Int incr = add 1 three :: Int three = incr 2

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Exponentials in Haskell

add :: Int -> Int -> Int add n x = n + x incr :: Int -> Int incr = add 1 three :: Int three = incr 2

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Further Reading

  • Saunders MacLane, Categories for the Working

Mathematician

  • Benjamin Pierce, Basic Category Theory for Computer

Scientists

  • Bartosz Milewski, Programming Cafe (blog)

Bartosz Milewski's Programming Cafe