Losh doesn't use Church numerals, though, he represents numbers as lists. The fact that lists are also represented as functions is a diversion; his number three doesn't represent a function f -> x -> x that returns the threefold composition of its first argument applied to its second.
I didn't get too much into the original article but my impression is that he is using Scot encoding (essentially a 1-to1 translation of pattern matching) instead of church encoding (somethign equivalent to folds).
Scott encoding doesn't get much publicity but its perfectly valid and much more intuitive, IMO.
There must be some confusion here. For "the threefold composition of its first argument applied to its second" the type should be "(x -> x) -> x -> x".
Comments
Losh doesn't use Church numerals, though, he represents numbers as lists. The fact that lists are also represented as functions is a diversion; his number three doesn't represent a function f -> x -> x that returns the threefold composition of its first argument applied to its second.
I didn't get too much into the original article but my impression is that he is using Scot encoding (essentially a 1-to1 translation of pattern matching) instead of church encoding (somethign equivalent to folds).
Scott encoding doesn't get much publicity but its perfectly valid and much more intuitive, IMO.
Also this encoding is cool:
http://okmij.org/ftp/tagless-final/course/Boehm-Berarducci.h...
There must be some confusion here. For "the threefold composition of its first argument applied to its second" the type should be "(x -> x) -> x -> x".
Right, I was (stupidly, it was early!) just using "f" as a shorthand for a function type like x -> x.