## EECS 321 Programming Languages: Homework 2

Due: Friday, January 18th, 2013, noon

### Part 1 – Free Identifiers

Implement the function free-ids, which take a WAE (see PLAI §3 or the lecture slides) and produces a list of symbols. The list should contain a symbol for each free identifier in the given WAE, each symbol should appear at most once in the list, and the symbols should be ordered according to the following comparison procedure:

```  (define (symbol<? a b)
(string<? (symbol->string a) (symbol->string b)))```

Hint 1: First, write a function that generates an unordered list of symbols with duplicates, and then write separate functions to re-order the list and then remove duplicates.

Hint 2: The free variables of a with form include all of the free variable of the named expression, plus all of the free variables in the body expression except for the name bound by with.

Hint 3: The PLAI language includes several helpful list-processing functions:

• filter - takes a predicate and a list, and returns a list that contains only values for which the predicate returned true. This is useful for removing a value from a list.
• sort - takes a list and a less-than comparison function (i.e., a function of two arguments where the result is true when the first argument is less than the second) and produces a sorted list.
• member - takes a value and a list, and returns a boolean indicating whether the value is in the list.

### Part 2 – Binding Identifiers

Implement the function binding-ids, which is like free-ids, but the result list contains a symbol for each binding identifier in the given WAE (whether or not the binding identifier is ever referenced by a bound identifier). The result list of symbols must be sorted and have no duplicates.

### Part 3 – Bound Identifiers

Implement the function bound-ids, which is like free-ids, but the result list contains a symbol for each bound identifier in the given WAE. The result list of symbols must be sorted and have no duplicates.

### Part 4 – Shadowed Variables

Implement the function shadowed-variable?, which accepts a WAE and returns a boolean. The boolean should be #t when the WAE has an bound variable that refers to a shadowed binding and #f otherwise.

` `

Submit your code using the Handin button in DrRacket.

 Last update: Thursday, January 17th, 2013robby@eecs.northwestern.edu