transduce - adds numbers

Question

I have a calculation someting like the following:

;; for sake of simplicity we use round numbers
(def data [{:a 1} {:a 10} {:a 100}])

(reduce - 0.0 (map :a data))

And it evaluates to -111.0. I want to do the transformation with a transducer to speed it up a bit by preventing unnecessary allocations:

(transduce (map :a) - 0.0 data)

However, the signum of the result changed to positive! Apparently it does not matter if I use + or - as the reducer in the expression, as the form will evaluate to +111.0 in both cases.

This is surprising to me, why did the introduction of transduce change the semantics, what am I missing here?

(the strange behaviour happens with * and / too!)

Answer 1

So apparently transduce calls the reducer function on the result of the reduction, so - just flips the sign when the reduction is done. We need to wrap the reducer function with completing to hide this call:

(transduce (completing -) 0.0 (map :a data))

Although, at this point it is shorter to just write:

(- (transduce + 0.0 (map :a data)))

Answer 2

The problem has nothing to do with transduce itself, and everything to do with the fact that reduce and transduce use different default identities for the given reducing function.

The default identity for reduce is the first element in the input collection ({:a 1}).
This means that the expression (reduce - 0.0 (map :a data)) is equivalent to:

(- (- (- 0.0 1) 10) 100)

which evaluates to -111.0 as observed.

On the other hand, the default identity for transduce is the identity function for the given reducing function, which in this case is -.
This means that the expression (transduce (map :a) - 0.0 data) is equivalent to:

(- (- (- (- 0.0 1) 10) 100))

which evaluates to +111.0.

To get the same result using transduce as you did using reduce, use the completing transducer and provide the first element of the input collection as the initial value:

(transduce (completing -) 0.0 (map :a data))

This will give the same result as the original reduce expression.