Rank2Types.md

+
+
+
+# Rank-2 Types
+
+
+## Brief Explanation
+
+
+
+Functions may have polymorphic arguments, subject to three restrictions:
+
+
+1. Such functions must have explicit type signatures, using `forall` to bind polymorphic type variables, e.g.
+
+  ```wiki
+  g :: (forall a. a -> a) -> (Bool, Char)
+  ```
+1. In the definition of the function, polymorphic arguments
+
+  1. must be matched on the left-hand side, and
+  1. can only be matched by a variable or wildcard (`_`) pattern.  The variable then has the polymorphic type of the corresponding argument, e.g.
+
+    ```wiki
+    g f = (f True, f 'a')
+    ```
+1. When such a function is used, it must be applied to at least as many arguments to include the polymorphic ones (so it's a good idea to put those first).  Each expression must have a generalized type at least as general as that declared for the corresponding argument, e.g.
+
+  ```wiki
+  g id
+  g undefined
+  ```
+
+
+The more general [RankNTypes](rank-n-types) relax restrictions 2(1) and 3.
+
+
+## References
+
+
+- [PolymorphicComponents](polymorphic-components) do the same thing for data constructors.
+
+## Tickets
+
+
+
+<table><tr><th>[\#60](https://gitlab.haskell.org//haskell/prime/issues/60)</th>
+<td>add RankNTypes or Rank2Types</td></tr></table>
+
+
+
+## Pros
+
+
+- simple type inference
+- offered by GHC and Hugs for years
+- enables [ runST](http://www.haskell.org/ghc/docs/latest/html/libraries/base/Control-Monad-ST.html) and similar devices
+- used in cheap deforestation
+- useful with non-regular (or nested) types
+- useful with [PolymorphicComponents](polymorphic-components)
+
+## Cons
+
+
+- functions with rank-2 types are not first class
+- can be awkward in comparison with [RankNTypes](rank-n-types)