Re: [isabelle] argument order of List.foldr
as far as I know, the folds in the List theory, as well as
Library.foldl/foldr in ML are memories from a distant past... they are
just what they happen to be, but there is no "why".
The "one and only true fold" is the "fold" of ML, with variant fold_rev.
But it is not so much folding a binary operation like "+" but more an
iteration of a transformation of a state. But it is the only version
that composes (fold o fold).
Brian Huffman wrote:
Here is the type of List.foldr from the Standard ML basis library:
val foldr : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b
and the type of foldr from Haskell's List library:
foldr :: (a -> b -> b) -> b -> [a] -> b
But List.foldr in Isabelle has this type:
foldr :: "('a => 'b => 'b) => 'a list => 'b => 'b"
Why are the arguments in that order?
The standard argument order would be much more useful for partial application.
Maybe it is based on Isabelle's Library.foldr, which has this type:
Library.foldr : ('a * 'b -> 'b) -> 'a list * 'b -> 'b
Since it has an uncurried type, the argument order doesn't make any
difference here as far as partial application is concerned, and I
recognize that there is a mnemonic benefit to this argument order:
Library.foldr (op +) ([1,2,3], 4) = 1 + (2 + (3 + 4))
But I think that being amenable to partial application is more important.
Does anyone else have an opinion on this?
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