The history here is that Common Lisp gets reduce from APL (https://aplwiki.com/wiki/Reduce). It's not an attempt an ML-style fold, but a different formalism from a different lineage.
While reading this, I was immediately reminded of the reduce operator, glad to see my intuition wasn't far off.
The nifty thing about this operator in the array-langs compared to the usual fold function is that they usually define identity elements for all primitive functions, which means that no initial value has to be provided: https://aplwiki.com/wiki/Identity_element
The downside of this approach though, is that using reduce with non-primitive functions can result in domain errors (at least in APL). I think BQN's version of the operator is a bit nicer, in that it allows you to specify an initial value in this situation: https://mlochbaum.github.io/BQN/doc/fold.html
> they usually define identity elements for all primitive functions
> using reduce with non-primitive functions can result in domain errors
ml-style folds in the presence of ad-hoc polymorphism solve this rather handily -- in haskell for instance monoid is the typeclass that only requires an associative operation and an identity element
typeclasses have some clunkiness in this regard; you have to wrap numeric types as "sum" or "product" etc to go "ah yes today i want to say numbers are a monoid under this operation" but at the very least it does enable formal, user-defined associations between identity elements and functions
luckily most things programmers deal with are plausibly just one kind of monoid. for instance the eleventy billion different string types haskell programmers love to use all tend to satisfy monoid under concatenation without any wrappers
> downside of this approach though, is that using reduce with non-primitive functions can result in domain errors
Yes, that's another problem. There is precedent for associating metadata with user-defined functions (eg inverses); identities seem to have fallen by the wayside, but I am planning to fix that for j.
I never heard of apl's allowing for an explicit choice of initial value, nor direction control ('from-end'), which mls typically also provide (foldl vs foldr). On the other hand, the ad-hoc choice of result for an empty input is a flaw common to cl and apl.
myco_logic|2 years ago
The nifty thing about this operator in the array-langs compared to the usual fold function is that they usually define identity elements for all primitive functions, which means that no initial value has to be provided: https://aplwiki.com/wiki/Identity_element
The downside of this approach though, is that using reduce with non-primitive functions can result in domain errors (at least in APL). I think BQN's version of the operator is a bit nicer, in that it allows you to specify an initial value in this situation: https://mlochbaum.github.io/BQN/doc/fold.html
0x69420|2 years ago
ml-style folds in the presence of ad-hoc polymorphism solve this rather handily -- in haskell for instance monoid is the typeclass that only requires an associative operation and an identity element
typeclasses have some clunkiness in this regard; you have to wrap numeric types as "sum" or "product" etc to go "ah yes today i want to say numbers are a monoid under this operation" but at the very least it does enable formal, user-defined associations between identity elements and functions
luckily most things programmers deal with are plausibly just one kind of monoid. for instance the eleventy billion different string types haskell programmers love to use all tend to satisfy monoid under concatenation without any wrappers
moonchild|2 years ago
Yes, that's another problem. There is precedent for associating metadata with user-defined functions (eg inverses); identities seem to have fallen by the wayside, but I am planning to fix that for j.
082349872349872|2 years ago
moonchild|2 years ago