Week 13 Set a

Due Date Mon at 9:00pm (Week 13)

Purpose to get a first impression of syntax transformations

Finger Exercises

Exercise 1 Design the function if-transformer, which transforms the S-expression representation of an if expression into a cond expression.

Exercise 2 Design the function local-transformer, which transforms the S-expression representation of an additive local expressions into the S-expression representations of an immediate application of a lambda expression.

An additive local expressions has the following shape:

(local ((define name1 (+ Expression1-1 Expression1-2))

...

(define nameN (+ ExpressionN-1 ExpressionN-2)))

Expression)

As usual the expressions in line i + 1 may refer to the names defined in lines 1 through i (and of course any names defined outside of the local expression).

An immediate application of a lambda expression refers to the idea that the latter can appear in function position. For example,

((lambda (x) x) 10)

is the immediate application of (lambda (x) x).

Hint Experiment with check-expect on real local and lambda expressions first to make sure you understand how these two kinds of expressions are equivalent.

Graded Exercises

Exercise 3 Design the function cond-transformer, which transforms an S-expression representation of a cond expression into an S-expression representation of nested if expressions.

Exercise 4 Design the function curry, which transforms the S-expression representation of a multi-argument lambda expression of many arguments into a nest of one-argument (representations of) lambda expressions.

History The name of the function honors Haskell Curry, the logician who realized that working with n nested one-argument lambda expressions with distinct parameters is equivalent to an n-argument lambda (with the same n parameters).