6. Updating variants

6.1. Mapping a single type: mapVariant

We can easily apply a function f :: A -> B to a variant so that its value type A is replaced with B. If the value in the variant has type A, then f is applied to it to get the new value. Example:

x,y :: V '[String,Int]
x = V "test"
y = V @Int 10

> mapVariant ((+5) :: Int -> Int) x
V @String "test"

> mapVariant ((+5) :: Int -> Int) y
V @Int 15

Note that the resulting variant may contain the same type more than once. To avoid this, we can either use nubVariant or directly use mapNubVariant:

> :t mapVariant (length :: String -> Int) x
mapVariant (length :: String -> Int) x :: V '[Int, Int]

> :t mapNubVariant (length :: String -> Int) x
mapNubVariant (length :: String -> Int) x :: V '[Int]

> mapNubVariant (length :: String -> Int) x
V @Int 4

Generic code can be written with the MapVariant a b cs constraint and the ReplaceAll type family so that: mapVariant :: MapVariant a b cs => (a -> b) -> V cs -> V (ReplaceAll a b cs)

6.2. Mapping by index: mapVariantAt

If we know the index of the value type we want to map, we can use mapVariantAt. Example:

x,y :: V '[String,Int]
x = V "test"
y = V @Int 10

> mapVariantAt @0 length x
V @Int 4

> mapVariantAt @0 length y
V @Int 10

> mapVariantAt @1 (+5) x
V @[Char] "test"

> mapVariantAt @1 (+5) y
V @Int 15

Note that the compiler uses the type of the element whose index is given as first argument to infer the type of the functions length and +5, hence we don’t need type ascriptions.

We can use mapVariantAtM to perform an applicative (or monadic) update. For example:

add :: Int -> Int -> IO Integer
add a b = do
   putStrLn "Converting the result into Integer!"
   return (fromIntegral a + fromIntegral b)

> mapVariantAtM @1 (add 5) x
V @[Char] "test"

> mapVariantAtM @1 (add 5) y
Converting the result into Integer!
V @Integer 15

6.3. Mapping only the first matching type: mapVariantFirst

A variant can have the same type more than once in its value type list. mapVariant updates all the matching types in the list but sometimes that’s not what we want. We can use mapVariantAt if we know the index of the type we want to update. We can also use mapVariantFirst as follows if we want to update only the first matching type:

vv :: V '[Int,Int,Int]
vv = toVariantAt @1 5

> r0 = mapVariant (show :: Int -> String) vv
> r1 = mapVariantFirst (show :: Int -> String) vv

> :t r0
r0 :: V '[String,String,String]

> :t r1
r1 :: V '[String, Int, Int]

> r0
V @[Char] "5"

> r1
V @Int 5

We can also apply an applicative (or monadic) function with mapVariantFirstM:

printRetShow :: Show a => a -> IO String
printRetShow a = do
   print a
   return (show a)

> r2 = mapVariantFirstM (printRetShow @Int) vv
> r2
V @Int 5

> :t r2
r2 :: IO (V '[String, Int, Int])

6.4. TODO

• foldMapVariantFirst[M]

• foldMapVariant

• alterVariant

• traverseVariant