[Haskell-cafe] A functor for two Peano systems
Galaxy Being
borgauf at gmail.com
Mon Apr 5 05:17:23 UTC 2021
I'm just not understanding the concept of a functor in this context: I have
this
plus :: Int -> Int -> Int
plus n m = if (n == 0)
then m
else sCessor (plus (pCessor n) m)
where sCessor x = x + 1
pCessor x = if (x == 0)
then error "too small"
else (x - 1)
and this
data MyNum = MNZero | OneMoreThan MyNum deriving (Show,Eq,Ord)
plus2 :: MyNum -> MyNum -> MyNum
plus2 n m = if (n == MNZero)
then m
else sCessor (plus2 (pCessor n) m)
where sCessor x = (OneMoreThan x)
pCessor x = if (x == MNZero)
then (error "too small")
else (oneLess x)
oneLess MNZero = MNZero
oneLess (OneMoreThan myn) = myn
It seems there should be just one plus, function that would handle both an
Int-based Peano and the MyNum-based Peano, not two. But in this definition
fmap :: (a -> b) -> f a -> f b
The (a -> b) should be "lifted" over the f a -> f b But I can't conceive of
how this should all fit together, i.e., to create just one generic plus
that would handle both the plus :: Int -> Int -> Int and the plus2 :: MyNum
-> MyNum -> MyNum. Trying to get started, I would assume I need some sort
of instance Functor MyNum describing, yeah, what? Or am I barking up the
completely wrong tree here, i.e., this isn't a functor issue?
LB
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