What are curry and high order irregular functions in ML

Question

fun curry fxy = f (x, y); fun uncurry f (x, y) = fxy; fun compose (f, g) x = f (gx); 

I understand that I will compose a function, but I do not quite understand curry and indecision in ML. Can anyone explain this?

Also, what do the following two lines mean?

 (1) compose (compose, uncurry compose) (2) compose (uncurry compose, compose) 

Answer 1

If you look at types, you will clearly see what curry and uncurry .

Remember that you can define a function that either takes its arguments as one big tuple, or as several arguments (in reality, it becomes a “chain” of functions, each of which takes one argument, see this wiki ):

 fun foo (a,x) = a*x+10 fun bar ax = a*x+20 

The difference is clearly visible in their types:

 val foo = fn : int * int -> int val bar = fn : int -> int -> int 

The curry function "converts" a function that takes its arguments as a tuple into a "chain" of functions, each of which takes 1 of the arguments. This is especially convenient when we want to compose a series of functions in which some of them are partially used with arguments. See how the foo type changes:

 - curry foo; val it = fn : int -> int -> int 

Now we can try to make up two functions:

 - (curry foo 5 o bar 1) 4; val it = 130 : int 

The first 4 is applied to bar 1 as the argument x , then the result of this calculation ( bar 1 4 ) is given as the argument x for foo .

Obviously, uncurry used for the reverse process:

 - uncurry bar; val it = fn : int * int -> int