Due: Friday, January 18th, 2013, noon
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:
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.
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.
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.
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