SI 413 Fall 2023 / Homeworks

This is the archived website of SI 413 from the Fall 2023 semester. Feel free to browse around; you may also find more recent offerings at my teaching page.

Homework 7: Scope Tree, Frames and Closures

1 Scope Tree

Consider the following program in a C-like syntax:

int x = 10;
int i = 5;

int foo(x) {
  if (x == i) {
    return 3;
  else {
    int i = x - 1;
    int j = foo(i);
    return 3 * j;

print foo(3);

Draw the scope tree for the program above. Then indicate what the final printed value would be using lexical scoping.

2 Frames and closures

Consider the following SPL code, which we will imagine is lexically scoped:

new counter := lambda start {
  new increment := lambda by {
    start := start + by;
    ret := start;
  ret := increment;
new A := counter @ 0;
new B := counter @ 5;
write A@0;
write B@0;
write A@6;

Draw all the frames and links that result after executing this program. See the reading assigned from Unit 6 for exactly how these should be drawn, particularly Section 3.2.3 of SICP.

Specifically, every variable name that refers to a function should point to a closure, which is represented by a pair of circles, pointing to the referencing environment and the function definition, respectively. (You do NOT have to write out the complete body of every function.)