Sometimes it's useful to bind variables against overlapping parts of a structure. For instance, suppose I'm writing a pattern that is to be matched against multivalues like `([10, 20], 'true)`. And suppose I want to end up with `ys` bound to `[10, 20]`, `x` bound to `10`, and `xs` bound to `[20]`. Using the techniques introduced so far, I have two options. First, I could bind `ys` against `[10, 20]`, and then initiate a second pattern-match to break that up into `10` and `[20]`. Like this:
case ([10, 20], 'true) of
- [ys, _] then case ys of
+ (ys, _) then case ys of
x & xs then ...;
...
end;
Alternatively, I could directly bind `x` against `10` and `xs` against `[20]`. But then I would have to re-cons them together again to get `ys`. Like this:
case ([10, 20], 'true) of
- [x & xs, _] then let
+ (x & xs, _) then let
ys match x & xs
in ...;
...
Both of these strategies work. But they are a bit inefficient. I said you didn't really need to worry about efficiency in this seminar. But these are also a bit cumbersome to write. There's a special syntax that enables us to bind all three of `ys`, `x`, and `xs` in the desired way, despite the fact that they will be matching against overlapping, rather than discrete, parts of the value `[10, 20]`. The special syntax looks like this:
case ([10, 20], 'true) of
- [(x & xs) as ys, _] then ...
+ ((x & xs) as ys, _) then ...
...
end
Can you guess what our shortcut for the last function will be? It's `( + )`. That
expresses a function that takes two arguments `(x, y)` and evaluates to `x + y`.
-Wait a second, you say. Isn't that just what `+` does *already*? Why am I making a distinction between `+` and `(+)`? The difference is that bare `+` without any parentheses is an *infix* operator that comes between its arguments. Whereas when we wrap it with parentheses, it loses its special infix syntax and then just behaves like a plain variable denoting a function, like `swap`. Thus whereas we write:
+Wait a second, you say. Isn't that just what `+` does *already*? Why am I making a distinction between `+` and `( + )`? The difference is that bare `+` without any parentheses is an *infix* operator that comes between its arguments. Whereas when we wrap it with parentheses, it loses its special infix syntax and then just behaves like a plain variable denoting a function, like `swap`. Thus whereas we write:
x + y
if we want to use `( + )`, we have to instead write:
- (+) (x, y)
+ ( + ) (x, y)
It may not be obvious now why this would ever be useful, but sometimes it will be.
-Confession: actually, what I described here diverges a *tiny* bit from what OCaml and Haskell do. They wouldn't really write `(+) (x, y)` like I just did. Instead they'd write `(+) x y`. We will look at the difference between these next week.
+All of these shorthands `(10 - )`, `( & ys)` and `( + )` are called "sections". I don't know exactly why.
+
+Confession: actually, what I described here diverges *a bit* from how OCaml and Haskell treat `( + )`. They wouldn't really write `( + ) (x, y)` like I did. Instead they'd write `( + ) x y`. We will look at the difference between these next week.