On 2020-06-18 13:47, Nils Bruin wrote: > > To compare: magma has function-application-on-the right in the notation x@f > and map composition f*g (for right action). So with
Off-topic: For some programming-language design trivia, the explicit syntax for function application on the right has a lot going for it. Using parentheses has well-known problems, particularly to anyone who has taught the chain rule. They also make it awkward to curry functions of multiple arguments. If I want to write the function that adds three to its argument on a chalkboard, I have to make up some junk like plus(3,--) with a dash or dot in the hole where the argument goes. In python, I have to use e.g. lambda x: plus(3,x). Many functional languages solve that problem by using spaces for function application, and by treating all functions as functions of one argument (that return other functions). So you would write plus for the function that takes an argument and returns (a function that takes another argument and adds the first argument to it). Thus plus 3 is the function that adds three to its argument, and plus 3 4 = (plus 3) 4 is probably 7. Of course, that has problems too, not the least of which is having the most important operation in the language be invisible and generally unparseable. If I want to make a higher level function, how do I apply some other function to a space? Is your language going to parse " " as function application applied to function application? Nah. An explicit visible application syntax solves those problems and others. To keep the same example, 3@plus would be what we want, and 4@3@plus = 4@(3@plus) = 7 Finally, working left-to-right eliminates all of the annoying problems that arise when you do something to (f `compose` g) and everything flips. It's also just nicer to read, because when you see ((x@foo)@bar)@baz you can start reading, "I take x, and give it to foo; then I take the result and feed it to bar..." Whereas with baz(bar(foo(x))) you have to get all the way to the end before you can reverse engineer what's about to happen. There is also usually shortcut for function composition mentioned, so that the parentheses above can be avoided above, like x@foo;bar;baz The paper "A useful lambda-notation" by Fairouz Kamareddine and Rob Nederpelt was once recommended to me on this same topic. Curiously (after I spent 2 months figuring out how to read it), the "item notation" they devise for the lambda calculus is basically "@". But @ is matrix multiplication in python, so we're screwed there =) -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/976f2cac-5c96-40db-d159-30d2e192ed74%40orlitzky.com.
