Comments on: Type manipulation: Tricks of the trade http://blog.ezyang.com/2010/02/type-manipulation-tricks-of-the-trade/ Existential Pontification and Generalized Abstract Digressions Sun, 05 Feb 2012 23:02:11 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Edward Z. Yang http://blog.ezyang.com/2010/02/type-manipulation-tricks-of-the-trade/comment-page-1/#comment-183 Edward Z. Yang Sun, 14 Mar 2010 21:14:14 +0000 http://ezyang.scripts.mit.edu/blog/?p=194#comment-183 As zygoloid on #haskell points out, this inference is completely normal once you stop treating -> as infix: <pre> f a1 == (c1 -> c2) -> h c1 -> h c2 == (c1 -> c2) -> (h c1 -> h c2) == (->) (c1 -> c2) (h c1 -> h c2)</pre> So <code>f = (->) (c1 -> c2), and a1 = (h c1 -> h c2)</code> As zygoloid on #haskell points out, this inference is completely normal once you stop treating -> as infix:

   f a1
== (c1 -> c2) -> h c1 -> h c2
== (c1 -> c2) -> (h c1 -> h c2)
== (->) (c1 -> c2) (h c1 -> h c2)

So f = (->) (c1 -> c2), and a1 = (h c1 -> h c2)

]]> By: roy_hu http://blog.ezyang.com/2010/02/type-manipulation-tricks-of-the-trade/comment-page-1/#comment-176 roy_hu Sat, 13 Mar 2010 09:30:08 +0000 http://ezyang.scripts.mit.edu/blog/?p=194#comment-176 Great post, and very thought provoking. Most of the equations are solved by Hindley-Milner-style type unification. The type inference of fmap fmap fmap is a bit magical to me. How exactly does the compiler solve f a1 == (c1 -> c2) -> h c1 -> h c2 ? I don't think it's because the compiler has some built-in knowledge of functors, because you can define a new class Functor' and the type is inferenced the same way. Is there a general theory behind "higher-order type inference"? Great post, and very thought provoking. Most of the equations are solved by Hindley-Milner-style type unification. The type inference of fmap fmap fmap is a bit magical to me. How exactly does the compiler solve f a1 == (c1 -> c2) -> h c1 -> h c2 ? I don’t think it’s because the compiler has some built-in knowledge of functors, because you can define a new class Functor’ and the type is inferenced the same way. Is there a general theory behind “higher-order type inference”?

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