Lab 4

1 Notes on Testing and Language Choice

First: unless you’re feeling really gung-ho, do this lab in #lang racket, not in #lang typed/racket.

Second: you can’t check equality of functions directly, which makes test cases difficult. When an exercise asks you to produce a function, the test case should go ahead and supply inputs to the function, so that you can test equality of numbers rather than functions.

2 Applying Lambdas

What should this expression produce?

((lambda (x) (+ x 2)) 3)

Try running it. Did it produce what you expected?

Next: what should this expression produce?

((lambda (f g) (f (g 3)))

(lambda (x) (+ x 3))

(lambda (x) (* x 2)))

Try to figure it out first! Then evaluate it.

3 curried-add

Develop the curried-add function. It takes a number ’a’ and returns a function that takes a number ’b’ and returns a+b. In other words, it has the type

(number -> (number -> number))

... where (t1 -> t2) is the type of a function that takes a t1 and produces a t2.

4 curry2

Develop the curry2 function; it takes a function of two arguments f, and produces a function that we’ll call M. The function M takes one argument and produces a function that we’ll call N. N takes one argument and produces the result of calling the input function f on the two given arguments. In other words, it has the type

(All (a b c) ((a b -> c) -> (a -> (b -> c))))

... for types a,b, and c. You will need lambda for this.

5 curry3

Develop the curry3 function; it takes a function of three arguments, and produces a function that takes one argument and produces a function that takes one argument and produces a function that takes one argument and produces the result of calling the input function on the three given arguments. In other words, it has the type

(All (a b c d) ((a b c -> d) -> (a -> (b -> (c -> d)))))

... for types a,b,c, and d. You will need lambda for this.

6 contains?

Develop the contains? function, that consumes a list and a symbol and returns true exactly when the symbol occurs in the list.

Use curry2 and contains? to develop in-list-many?, that consumes a source list of symbols and a list of query symbols, and returns a list of booleans indicating for the corresponding element of the query list whether it occurs in the source list. Use the built-in function map. This function should be a one-liner.