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A polymorphic type for handling optional values and errors

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In Language:Haskell, maybe types are modeled by the following type constructor:

-- The Maybe type constructor
data Maybe a = Nothing | Just a
 deriving (Read, Show, Eq)

Nothing represents the lack of a value (or an error). Just represent the presence of a value. Functionality may use arbitrary pattern matching to process values of Maybe types, but there is a fold function for maybes:

-- A fold function for maybes
maybe :: b -> (a -> b) -> Maybe a -> b
maybe b _ Nothing = b
maybe _ f (Just a) = f a

Thus, maybe inspects the maybe value passed as the third and final argument and applies the first or the second argument for the cases Nothing or Just, respectively. Let us illustrate a maybe-like fold by means of looking up entries in a map. Let's say that we maintain a map of abbreviations from which to lookup abbreviations for expansion. We would like to keep a term, as is, if it does not appear in the map. Thus:

> let abbreviations = [("FP","Functional programming"),("LP","Logic programming")]
> lookup "FP" abbreviations 
Just "Functional programming"
> lookup "OOP" abbreviations 
Nothing
> let lookup' x m = maybe x id (lookup x m)
> lookup' "FP" abbreviations 
"Functional programming"
> lookup' "OOP" abbreviations 
"OOP"

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