Marty Stumpf
7 Apr 2022
•
4 min read
This is the eighth of a series of articles that illustrates functional programming (FP) concepts. As you go through these articles with code examples in Haskell (a very popular FP language), you gain the grounding for picking up any FP language quickly. Why should you care about FP? See this post.
In the last post, we wrote an unfold
function that works for the Monoid
type class. In this post we'll look at some examples of applying our unfold
to other type instances of Monoid
.
unfoldr
Recall Haskell's default unfold
with this signature:
unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
Note that this unfold takes an initial input. We saw an example of its usage:
example :: (Ord a, Num a) => a -> [a]
example = unfoldr (\x -> if x > 9 then Nothing else Just (x, x+1))
example 7
returns:
[7,8,9]
unfoldm
Our unfold is more general which means we can unfold to a list using it, like Haskell's default unfold. Recall our unfold's type signature:
unfoldm :: Monoid m => (t -> Maybe (m, t)) -> t -> m
Note that the Maybe
returns a tuple with its first element of a type that belongs to the Monoid
type class. When we use our unfoldm
, we need to make sure of that. To apply unfoldm
in a manner similar to the above example, we have to return [x]
not just x
in the else
case:
example =
unfoldm (\x -> if x > 9 then Nothing else Just ([x], x+1))
Running example 7
returns the same result as above.
Now, let's unfold to other Monoid
types!
Map
Haskell has a Map
data type. As mentioned in its reference:
data Map k a
A Map from keys k to values a.
Instance
Ord k => Monoid (Map k v)
Map
is a data type that maps keys to their values, similar to a dictionary. When you look up a key (or a word in the case of a dictionary), you get its associated value (or in the case of a dictionary, the meaning of the word).
Map
belongs to the Monoid
type class if the key k
is orderable . This means that if the key is orderable, we can use our unfold function to unfold to a Map
!
Here is an example of a unfolding a Map
with keys
that are of a type such that k > 26
is valid:
import Data.Map as Map
-- our unfoldm from the last post
unfoldm :: Monoid m => (t -> Maybe (m, t)) -> t -> m
unfoldm f a =
case f a of
Just (first, second) ->
first `mappend` (unfoldm f second)
Nothing -> mempty
mapExample :: (Ord k, Num k, Enum v) => (k, v) -> Map.Map k v
mapExample =
unfoldm
(\(x,y) ->
if x > 26 then Nothing
else Just ((Map.insert x y empty),((x+1),(succ y))))
Because the type of the keys also belongs to the Ord
typeclass, this Map
belongs to the Monoid
typeclass. Therefore, we can use our unfoldm
function with it.
I have specified the value
is of a type that belongs to the Enum
typeclass. This allows me to use the succ
(successor) function.
The function we input to our unfoldm
takes a tuple
. The first element of the tuple
is the key
, while the second element is the value
.
The unfolding stops when the key
is greater than 26. We start with the input key
and value
, then we mappend
(or insert
in this case with Map
) with the key
goes up by 1 and the value
being the successor of the current value each time.
Running mapExample
with the integer 1 and the Char
K
, or (1,'K')
gives:
*Main> mapExample (1,'K')
fromList [(1,'K'),(2,'L'),(3,'M'),(4,'N'),(5,'O'),(6,'P'),(7,'Q'),(8,'R'),(9,'S'),(10,'T'),(11,'U'),(12,'V'),(13,'W'),(14,'X'),(15,'Y'),(16,'Z'),(17,'['),(18,'\\'),(19,']'),(20,'^'),(21,'_'),(22,'`'),(23,'a'),(24,'b'),(25,'c'),(26,'d')]
Running it with the value
of type Float
works too, because it belongs to the Enum
class:
*Main> mapExample (0,1.55)
fromList [(0,1.55),(1,2.55),(2,3.55),(3,4.55),(4,5.55),(5,6.55),(6,7.55),(7,8.55),(8,9.55),(9,10.55),(10,11.55),(11,12.55),(12,13.55),(13,14.55),(14,15.55),(15,16.55),(16,17.55),(17,18.55),(18,19.55),(19,20.55),(20,21.55),(21,22.55),(22,23.55),(23,24.55),(24,25.55),(25,26.55),(26,27.55)]
Because the output of mapExample
is a Map
, we can apply Map
's method on it, for example, we can look up the value of a specific key using lookup
:
*Main> Map.lookup 10 (mapExample (1,'K'))
Just 'T'
Set
The Set e
type represents a set of elements of type e
. If e
is an orderable type then the Set e
type belongs to the Monoid
typeclass.
I challenge you to write a function that unfolds to a Set
using unfoldm
. Have fun!
As you can see, once we master some functional programming concepts, we can apply them in any way we want to great effect! With the concept of unfold and the Monoid type class, we built a more powerful unfold function. This is what I love about functional programming: it's so powerful!
In a later post, I will explain the concept of list being a free Monoid
- it will shed light on why Map
can be generated by a fromList
function above.
Marty Stumpf
Software engineer. Loves FP Haskell Coq Agda PLT. Always learning. Prior: Economist. Vegan, WOC in solidarity with POC.
See other articles by Marty
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