A frequent pattern in my Haskell code is element-wise recursion for transformation of a list with some carried state generated using the data in the list. Usually, this looks something like this:
doSomething :: (SomeA a, SomeB b) => [a] -> [b]
doSomething xs = doSomethingWithState xs []
where
doSomethingWithState [] _ = []
doSomethingWithState (x:xs) state
| someTest x state = someChange x : (doSomethingWithState xs newState)
| otherwise = someOtherChange x : (doSomethingWithState xs newState)
For example, say I wanted to count how many of each element appears in a list, turning something like [1, 3, 3, 3, 4, 7, 7, 8, 8, 9]
into [(9,1),(8,2),(7,2),(4,1),(3,3),(1,1)]
.
I'd probably do something like the following:
import Data.List
import Data.Maybe
counts :: (Eq a) => [a] -> [(a, Int)]
counts xs = countsWithState xs []
where
countsWithState [] state = state -- End of list, stop here
countsWithState (x:xs) state = countsWithState xs $ transformState state x
transformState state x -- To get the state...
| isNothing $ lookup x state = (x, 1) : state -- Add new elem if new
| otherwise = incrElem x state -- Increment elem if not
incrElem x [] = [] -- Should never be reached
incrElem x ((index, value):elems) -- Searching through list...
| index == x = (index, (value+1)) : elems -- Increment if found
| otherwise = (index, value) : incrElem x elems -- Try next if not
In a much simpler but very similar example, if I were trying to keep the running average of all elements in a list, transforming something like [1, 7, 4, 18, 7, 1, 8, 2, 8, 6, 18, 12]
into [1.0, 4.0, 4.0, 7.5, 7.4, 6.33..., 5.57..., 6.0, 6.22..., 6.2, 7.27..., 7.66...]
where every element in the output list is the average of that element and all previous elements in the input list, I might do something like this:
runningAvg :: (Fractional a) => [a] -> [a]
runningAvg xs = runningAvgWithState xs 0 1
where
runningAvgWithState [] _ _ = []
runningAvgWithState (x:xs) currentSum currentElems
= (currentSum + x) / currentElems
: runningAvgWithState xs (currentSum + x) (currentElems + 1)
Notice the pattern is the same. Take a recursive function of a list, define it in terms of a hidden modified version with added state, and with each round transform the state and output computed results as necessary. This pattern emerges all the time in my Haskell code.
Is there a more natural way of implementing this sort of behavior, without a more complicated xWithState
function running the show and adding unnecessary verbosity and complexity?
Best Answer
Your
doSomething
is more or lessmapAccumL
fromData.List
, except you've thrown away the accumulator (i.e., state) at the end. That is, you could write it as:In particular, the running average might look like:
Your counting example is somewhat different, since it doesn't produce a list of the same "shape" as the input. Instead, the "state" is the set of counts, and you return the final "state" (final set of counts) at the end. This is just a
foldl
, as others have noted.which would be straightforward if it wasn't for the fact that maintaining a set of counts as an association list makes
bumpCount
kind of gross. @amon's version ofbumpCount
(i.e.,count'
) seems fine, or you could write it as the following fold:By the way, this
bumpCount
fold is actually pretty incredible. Despite being a "fold", it stops searching the list once it finds and bumps a matching count.