# 5. Safe pattern matching¶

Suppose we have the following List EADT:

data ConsF a l = ConsF a l deriving (Functor)
data NilF    l = NilF      deriving (Functor)

type List a = EADT '[ConsF a, NilF]

-- pattern for a specific EADT: List a
pattern ConsList :: a -> List a -> List a
pattern ConsList a l = Cons a l

We can use pattern matching on List constructors:

showEADTList :: Show a => List a -> String
ConsList a l -> show a ++ " : " ++ showEADTList l
Nil          -> "Nil"
_            -> undefined

10 : 20 : 30 : Nil

However the compiler cannot detect that the pattern matching is complete, hence we have the choice between a warning or adding a wildcard match as we have done above.

Another solution is to rely on multi-continuations. Then we can provide a function per constructor as in a pattern-matching. For instance, with multi-continuations we can transform an EADT '[A,B,C] into a function whose type is (A -> r, B -> r, C -> r) -> r. Hence the compiler will ensure that we provide the correct number of alternatives in the continuation tuple (the first parameter).

## 5.1. Explicitly recursive example¶

Transforming an EADT into a multi-continuation is done with eadtToCont. Mapping the continuation tuple is done with >::>.

showCont' l = eadtToCont l >::>
( \(ConsF a r) -> show a ++ " : " ++ showCont' r -- explicit recursion
, \NilF        -> "Nil"
)

> showCont' intList
"10 : 20 : 30 : Nil"

## 5.2. Catamorphism example¶

Transforming a VariantF into a multi-continuation is done with toCont. It can be useful with recursion schemes.

showCont l = toCont l >::>
( \(ConsF a r) -> show a ++ " : " ++ r -- no explicit recursion
, \NilF        -> "Nil"
)

> cata showCont intList
"10 : 20 : 30 : Nil"

## 5.3. Transformation example¶

We can use this approach to transform EADT. For instance list mapping:

mapList f l = toCont l >::>
( \(ConsF a r) -> Cons (f a) r
, \NilF        -> Nil
)

> eadtShow (cata (mapList (+5)) intList :: List Int)
"15 : 25 : 35 : Nil"

-- Some new Even and Odd constructors
data EvenF a l = EvenF a l deriving (Functor)
data OddF a l  = OddF a l deriving (Functor)

instance (Show a) => MyShow' (EvenF a) where
myShow' (EvenF a l) = show a ++ " {even} : " ++ l

instance (Show a) => MyShow' (OddF a) where
myShow' (OddF a l) = show a ++ " {odd} : " ++ l

-- convert Cons constructor into Odd or Even constructor, depending on the
-- cell value
evenOdd l = toCont l >::>
( \(ConsF a r) -> if even a then Even a r
else Odd  a r
, \NilF        -> Nil
)

intList' :: List Int
intList' = Cons (3 :: Int) $Cons (4 :: Int)$ Cons (5 :: Int) Nil

> eadtShow (cata evenOdd intList' :: EADT '[EvenF Int, OddF Int, NilF])
"3 {odd} : 4 {even} : 5 {odd} : Nil"

## 5.4. Splitting constructors¶

We can chose to handle only a subset of the constructors of an EADT by using splitVariantF.

For instance in the following example we only handle EvenF Int and OddF Int constructors. The other ones are considered as left-overs:

alg x = case splitVariantF @'[EvenF Int, OddF Int] x of
Right v        -> toCont v >::>
( \(EvenF a l) -> "Even : " ++ l
, \(OddF a l)  -> "Odd : " ++ l
)
Left leftovers -> "something else"

We can test this code with:

eo :: EADT '[EvenF Int, OddF Int, NilF]
eo = cata evenOdd intList'

eo2 :: EADT '[ConsF Int, EvenF Int, OddF Int, NilF]
eo2 = Even (10 :: Int) $Odd (5 :: Int)$ Cons (7 :: Int) \$ Odd (7 :: Int) Nil

> cata alg eo
"Odd : Even : Odd : something else"

> cata alg eo2
"Even : Odd : something else"

Note that the traversal ends when it encounters an unhandled constructor.

## 5.5. Unordered continuations (>:%:>)¶

By using the >:%:> operator instead of >::>, we can provide continuations in any order as long as an alternative for each constructor is provided.

The types must be unambiguous as the EADT type can’t be used to infer the continuation types (as is done with >::>). Hence the type ascriptions in the following example:

showCont'' l = eadtToCont l >:%:>
( \(NilF :: NilF (List Int)) -> "Nil"
, \(ConsF a r)               -> show (a :: Int) ++ " : " ++ showCont'' r
)

> showCont'' intList
"10 : 20 : 30 : Nil"