From: Jim Date: Mon, 2 Feb 2015 23:04:24 +0000 (-0500) Subject: refine note on sections X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=1c0cc2347294f30ca830e4a3eb7597c70f52b669 refine note on sections --- diff --git a/topics/week1_advanced_notes.mdwn b/topics/week1_advanced_notes.mdwn index 8f0fb851..613cd451 100644 --- a/topics/week1_advanced_notes.mdwn +++ b/topics/week1_advanced_notes.mdwn @@ -190,9 +190,14 @@ or like this: lambda (x, y). x + y -They permit you to appreviate the first λ-expression as simply `(10 - )`. We know there's an argument missing, because the infix operator `-` demands two arguments, but we've only supplied one. So `(10 - )` expresses a function that takes an argument `x` and evaluates to `10 - x`. In other words, it expresses λ`x. 10 - x`.Similarly, `( & ys)` expresses a function that takes an argument `x` and evaluates to `x & ys`. And --- can you guess what the last one will be? --- `( + )` expresses a function that takes two arguments `(x, y)` and evaluates to `x + y`. +They permit you to appreviate the first λ-expression as simply `(10 - )`. We know there's an argument missing, because the infix operator `-` demands two arguments, but we've only supplied one. So `(10 - )` expresses a function that takes an argument `x` and evaluates to `10 - x`. In other words, it expresses λ`x. 10 - x`.Similarly, `( & ys)` expresses a function that takes an argument `x` and evaluates to `x & ys`. -Wait a second, you might say. Isn't that last operation exactly 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: +All of this only works with infix operators like `-`, `&` and `+`. You can't write `1 swap` or `swap 1` to mean λ`x. (1, x)`. + +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: x + y