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### Closure-converted types as indexed-types
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After some brainstorming, Roman and I (= Manuel) came to the conclusion that we can save ourselves a lot of bookkeeping if we can represent closure-converted types by indexed types (i.e., keeping track of which original types correspond to which converted types). The idea is to use a class
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```wiki
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class CC a where
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data CConv a -- closure converted 'a'
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to :: a -> CConv a
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fr :: CConv a -> a
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```
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The most interesting instance is that for functions, which reads
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```wiki
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data Clo a b = forall e. Clo (c -> a -> b) e
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class (CC a, CC b) => CC (a -> b) where
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data CConv (a -> b) = CCArrow (Clo a b)
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to f = Clo (\_ -> f) ()
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fr (Clo f e) = f e
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```
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After some brainstorming, Roman and I (= Manuel) came to the conclusion that we can save ourselves a lot of bookkeeping if we can represent closure-converted types by indexed types (i.e., keeping track of which original types correspond to which converted types). The details are under [indexed closure conversion](data-parallel/closure-conversion/indexed).
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### From the Skype discussion, 16 Mar 07
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