Computing sums

20 Feb 2010

      The other day, I found myself writing the following code:

data Property x y = forall s. Property s (x -> s -> s) (s -> y)

step :: x -> Property x y -> Property x y
step x (Property s f g) = Property (f x s) f g

read :: Property x y -> y
read (Property s _ g) = g s

pure :: (x -> y) -> Property x y
pure f = Property undefined const f

fold :: (x -> y -> y) -> y -> Property x y
fold f y = Property y f id

fold1 :: (x -> x -> x) -> Property x x
fold1 f = Property Nothing (\x mx -> maybe (Just x) (Just . f) mx) fromJust

(>==>) :: Property x y -> Property y z -> Property x z
p0 >==> p1 = Property (p0,p1) (\x (q0,q1) -> let w0 = step x q0 in (w0, 
step (read w0) q1)) (\(_,q1) -> (read q1))

(>==<) :: Property x y -> Property x y' -> Property x (y,y')
p0 >==< p1 = Property (p0,p1) (\x (q0,q1) -> (step x q0, step x q1)) 
(\(q0,q1) -> (read q0, read q1))

sum = fold (+) 0
count = pure (const 1) >==> sum
minimum = fold1 min
maximum = fold1 max

Have I just invented arrows?

(And if so, why is the above code nowhere to be seen in the libraries?)

Andrew Coppin

Luke Palmer

Andrew Coppin

Andrew Coppin

Stephen Tetley

Andrew Coppin

Max Rabkin

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