Reading Disadvantages of Scala type system versus Haskell?, I have to ask: what is it, specifically, that makes Haskell's type system more powerful than other languages' type systems (C, C++, Java). Apparently, even Scala can't perform some of the same powers as Haskell's type system. What is it, specifically, that makes Haskell's type system (Hindley–Milner type inference) so powerful? Can you give an example?
6 Answers
What is expressiveness? To my understanding it is what constraint the type system allow us to put on our code, or in other words what properties of code which we can prove. The more expressive a type system is, the more information we can embed at the type level (which can be used at compile time by the type-checker to check our code).
Here are some properties of Haskell's type system that other languages don't have.
- Purity.
Purity allows Haskell to distinguish pure code and IO capable code - Paramtricity.
Haskell enforces parametricity for parametrically polymorphic functions so they must obey some laws. (Some languages does let you to express polymorphic function types but they don't enforce parametricity, for example Scala lets you to pattern match on a specific type even if the argument is polymorphic) - ADT
- Extensions
Haskell's base type system is a weaker version of λ2 which itself isn't really impressive. But with these extensions it become really powerful (even able to express dependent types with singleton):- existential types
- rank-n types (full λ2)
- type families
- data kinds (allows "typed" programming at type level)
- GADT ...
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