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copied!<p><em>Throughout this answer I'm going to talk about Haskell 98 and SML.</em></p> <p>Both type systems have the same foundations really, <a href="http://en.wikipedia.org/wiki/System_F">System F</a>. This means you have basic parametric polymorphism</p> <pre><code>foo :: a -> b -> a foo : 'a -> 'b -> 'c </code></pre> <p>SML provides functors and modules and Haskell type classes, but both of these are really built on top of a core calculus.</p> <p>The most interesting difference is that Haskell is System Fw, which is a souped up version of System F. In particular, it provides a richer notion of kinds (the types of types) allowing for things like</p> <pre><code>data Foo f a = Foo (f a) </code></pre> <p>Notice here that <code>f</code> is a function from a type onto another type, it's kind in other words is <code>* -> *</code>. In fact, Haskell 98 + Type families + PolyKinds + DataKinds extends this further by allowing arbitrary type functions. This gives you something like simply typed lambda calculus with types. For example, here's a church encoding of type level lists</p> <pre class="lang-hs prettyprint-override"><code>{-# LANGUAGE TypeFamilies, EmptyDataDecls #-} -- So we can box things up to partially apply them type family Eval e type instance Eval (Car a b) = a type instance Eval (Cdr a b) = b type instance Eval (Cons a b f) = Eval (f a b) data Car a b data Cdr a b data Cons a b (f :: * -> * -> *) type First p = Eval (p Car) type Second p = Eval (p Cdr) foo :: First (Cons (First (Cons Int Bool)) String) foo = 1 </code></pre> <p>This isn't expressible in SML's core type system, however with functors, one can hack around this.</p>

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