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Type witness

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A '''type witness''' is a value that represents one of a range of possible types. When implemented as [[generalised algebraic datatype]]s (GADTs), type witness can be used to perform dynamic casts.
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A '''type witness''' is a value that represents one of a range of possible [[type]]s. When implemented as [[generalised algebraic datatype]]s (GADTs), type witness can be used to perform dynamic casts.
   
Types <tt>a</tt> and <tt>b</tt> may or may not be the same type. We wish to perform the cast <tt>a -> Maybe b</tt>, or more generally, <tt>p a -> Maybe (p b)</tt> for any <tt>p</tt>, depending on whether <tt>a</tt> and <tt>b</tt> are the same type. This can be done with GADTs if we have "witnesses" for the two types:
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Types <tt>a</tt> and <tt>b</tt> may or may not be the same [[type]]. We wish to perform the cast <tt>a -> Maybe b</tt>, or more generally, <tt>p a -> Maybe (p b)</tt> for any <tt>p</tt>, depending on whether <tt>a</tt> and <tt>b</tt> are the same type. This can be done with GADTs if we have "witnesses" for the two types:
   
 
dynamicCast :: Witness a -> Witness b -> p a -> Maybe (p b)
 
dynamicCast :: Witness a -> Witness b -> p a -> Maybe (p b)
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dynamicCast _ _ _ = Nothing
 
dynamicCast _ _ _ = Nothing
   
If we wish to add type constructors such as the list constructor, that can be done by composing type constructors:
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If we wish to add [[type]] [[constructor]]s such as the list constructor, that can be done by composing type constructors:
   
 
data Witness a where
 
data Witness a where

Revision as of 21:25, 24 February 2006

A type witness is a value that represents one of a range of possible types. When implemented as generalised algebraic datatypes (GADTs), type witness can be used to perform dynamic casts.

Types a and b may or may not be the same type. We wish to perform the cast a -> Maybe b, or more generally, p a -> Maybe (p b) for any p, depending on whether a and b are the same type. This can be done with GADTs if we have "witnesses" for the two types:

dynamicCast :: Witness a -> Witness b -> p a -> Maybe (p b)

A simple witness type might be defined over the Int, Bool and Char types like so:

data Witness a where
  IntWitness :: Witness Int
  BoolWitness :: Witness Bool
  CharWitness :: Witness Char
dynamicCast IntWitness IntWitness pa = Just pa
dynamicCast BoolWitness BoolWitness pa = Just pa
dynamicCast CharWitness CharWitness pa = Just pa
dynamicCast _ _ _ = Nothing

If we wish to add type constructors such as the list constructor, that can be done by composing type constructors:

data Witness a where
  IntWitness :: Witness Int
  BoolWitness :: Witness Bool
  CharWitness :: Witness Char
  ListWitness :: Witness a -> Witness [a] 
data Compose p q a = MkCompose (p (q a))
dynamicCast IntWitness IntWitness pa = Just pa
dynamicCast BoolWitness BoolWitness pa = Just pa
dynamicCast CharWitness CharWitness pa = Just pa
dynamicCast (ListWitness wa) (ListWitness wb) pla = do
  MkCompose plb <- dynamicCast wa wb (MkCompose pla)
  return plb
dynamicCast _ _ _ = Nothing

By using more complex composition types in addition to Compose, it is possible for witnesses to allow type constructors of more complex kinds.