dependent-sum- Dependent sum type

Safe HaskellSafe




type (:=) = (:~:) Source

Backwards compatibility alias; as of GHC 7.8, this is the same as `(:~:)`.

class GEq f where Source

A class for type-contexts which contain enough information to (at least in some cases) decide the equality of types occurring within them.


geq :: f a -> f b -> Maybe (a := b) Source

Produce a witness of type-equality, if one exists.

A handy idiom for using this would be to pattern-bind in the Maybe monad, eg.:

extract :: GEq tag => tag a -> DSum tag -> Maybe a
extract t1 (t2 :=> x) = do
    Refl <- geq t1 t2
    return x

Or in a list comprehension:

extractMany :: GEq tag => tag a -> [DSum tag] -> [a]
extractMany t1 things = [ x | (t2 :=> x) <- things, Refl <- maybeToList (geq t1 t2)]

(Making use of the DSum type from Data.Dependent.Sum in both examples)


GEq k ((:=) k a) 

defaultEq :: GEq f => f a -> f b -> Bool Source

If f has a GEq instance, this function makes a suitable default implementation of '(==)'.

defaultNeq :: GEq f => f a -> f b -> Bool Source

If f has a GEq instance, this function makes a suitable default implementation of '(/=)'.

data GOrdering a b where Source

A type for the result of comparing GADT constructors; the type parameters of the GADT values being compared are included so that in the case where they are equal their parameter types can be unified.


GLT :: GOrdering a b 
GEQ :: GOrdering t t 
GGT :: GOrdering a b 


GRead k (GOrdering k a) 
GShow k (GOrdering k a) 
Show (f a) => ShowTag k (GOrdering k a) f 
Typeable (k -> k -> *) (GOrdering k) 
Eq (GOrdering k a b) 
Ord (GOrdering k a b) 
Show (GOrdering k a b) 

weakenOrdering :: GOrdering a b -> Ordering Source

TODO: Think of a better name

This operation forgets the phantom types of a GOrdering value.

class GEq f => GCompare f where Source

Type class for comparable GADT-like structures. When 2 things are equal, must return a witness that their parameter types are equal as well (GEQ).


gcompare :: f a -> f b -> GOrdering a b Source


GCompare k ((:=) k a) 

defaultCompare :: GCompare f => f a -> f b -> Ordering Source

data a :~: b :: k -> k -> * where infix 4

Propositional equality. If a :~: b is inhabited by some terminating value, then the type a is the same as the type b. To use this equality in practice, pattern-match on the a :~: b to get out the Refl constructor; in the body of the pattern-match, the compiler knows that a ~ b.



Refl :: (:~:) k a1 a1 


TestEquality k ((:~:) k a) 
GRead k ((:=) k a) 
GShow k ((:=) k a) 
GCompare k ((:=) k a) 
GEq k ((:=) k a) 
Ord (f a) => OrdTag k ((:=) k a) f 
Eq (f a) => EqTag k ((:=) k a) f 
Read (f a) => ReadTag k ((:=) k a) f

In order to make a Read instance for DSum tag, tag must be able to parse itself as well as any value of the tagged type. GRead together with this class provides the interface by which it can do so.

ReadTag tag => t is conceptually equivalent to something like this imaginary syntax: (forall a. Inhabited (tag a) => Read a) => t, where Inhabited is an imaginary predicate that characterizes non-empty types, and a does not occur free in t.

The Tag example type introduced in the DSum section could be given the following instances:

instance GRead Tag where
    greadsPrec _p str = case tag of
       "AString"   -> [(\k -> k AString, rest)]
       "AnInt"     -> [(\k -> k AnInt,   rest)]
       _           -> []
       where (tag, rest) = break isSpace str
instance ReadTag Tag where
    readTaggedPrec AString = readsPrec
    readTaggedPrec AnInt   = readsPrec
Show (f a) => ShowTag k ((:=) k a) f 
Typeable (k -> k -> *) ((:~:) k) 
(~) k a b => Bounded ((:~:) k a b) 
(~) k a b => Enum ((:~:) k a b) 
Eq ((:~:) k a b) 
Ord ((:~:) k a b) 
(~) k a b => Read ((:~:) k a b) 
Show ((:~:) k a b)