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haskell_type_system [2015/04/21 16:36] nikolaj |
haskell_type_system [2015/10/10 20:18] nikolaj |
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| == Function types == | == Function types == | ||
| Type theoretically (on the kind level): | Type theoretically (on the kind level): | ||
| - | ${\large\frac{a,b\ :\ \star}{a\to b\ :\ \star}}$ | + | ${\large\frac{a\ :\ \star \hspace{.5cm} b\ :\ \star}{a\to b\ :\ \star}}$ |
| Haskell syntax: | Haskell syntax: | ||
| Line 36: | Line 36: | ||
| Type theoretically: | Type theoretically: | ||
| - | ${\large\frac{x\ :\ a\hspace{.5cm} g\ :\ b}{\lambda x.g\ :\ a\to b}}$ | + | ${\large\frac{x\ :\ a \hspace{.5cm} g\ :\ b}{\lambda x.g\ :\ a\to b}}$ |
| <code/Haskell> | <code/Haskell> | ||
| Line 159: | Line 159: | ||
| For all types $a$, the constructor $(\to)\,a$ is the object map of $\mathrm{Hom}_\mathrm{Hask}(a,-)$. | For all types $a$, the constructor $(\to)\,a$ is the object map of $\mathrm{Hom}_\mathrm{Hask}(a,-)$. | ||
| - | In fact, all of the functors mentioned can be made into monads, and they are known as list, maybe and reader monad. | + | In fact, all of the functors mentioned can be made into [[monad_._haskell|monads]], and they are known as list, maybe and reader monad. |
| === Reference === | === Reference === | ||
