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Functions not data structures

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Sometimes the best way to represent data is using a function.

Church encoding can be used to represent any algebraic data type using only functions.

Another example is the following, not very efficient, implementation of a FiniteMap:

type FiniteMap key elt = key -> Maybe elt
 
emptyFM :: FiniteMap key elt
emptyFM = \k' -> Nothing
 
addToFM :: (Eq key) => FiniteMap key elt -> key -> elt -> FiniteMap key elt
addToFM m k v = \k' -> if (k == k') then Just v else m k'
 
delFromFM :: (Eq k) => FiniteMap key elt -> key -> FiniteMap key elt
delFromFM  m k = \k' -> if (k == k') then Nothing else m k'
 
lookupFM :: (Eq k) => FiniteMap key elt -> key -> Maybe elt
lookupFM m k = m k

Runtime compilation uses functions not data structures to implement an interpretation layer.