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haskell_type_system [2015/04/21 16:35] nikolaj |
haskell_type_system [2015/04/21 16:37] nikolaj |
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| The type system derives which fmap to use from the fact that we apply the construction to a list. | The type system derives which fmap to use from the fact that we apply the construction to a list. | ||
| - | The following example is the functor whose object map maps each type to a type which additionally contains the term '$\text{Nothing}$': | + | The following example is the functor whose object map maps each type to a type, where each of the old terms have a clone with the prefix '$\text{Just}$', and there is more over an additional term called nothing '$\text{Nothing}$': |
| <code/Haskell> | <code/Haskell> | ||
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| 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 === | ||
