CSE 341 : 3 May 2001

Lexical scoping and nested functions

An environment defines a set of bindings between symbols and their values:

val a = 15; val b = "foo"; val c = fn (n, p) => p = (n * p); val d = [1,2];

When you evaluate a let expression, you create a new environment whose bindings temporarily shadow those in its parent environment. You can visualize this as sub-environment with a link to its parent environment; evaluation begins at the current environment, and proceeds upwards in the parent chain:

let val a = 20 in hd(d) + a end;

Nested functions can access environments in surrounding scopes; this is known as lexical scoping. To support lexical scoping, however, a function must remember the environment in existence when the function is defined. A function value therefore must be a pair of items: a pointer to the parent environment, and a pointer to a procedure (so, the above diagrams are inaccurate). This environment/procedure pair is known as a closure:

(* Declare f *) fun f(x, y) = let fun nested(z) = a + x + z in nested(y) end;