BYU CS classes

Learn more about higher-order functions:

• Simple type checker (composing type guards?)
• Introducing named parameters, or parameter defaults
• Chaining decorators (and make sure the default parameters are of the correct type!)

• Dump arguments
• Decoration
• Memoization
• Counting calls
• Profiling (?)
• Finite-difference gradient approximation
• Y-combinator (?)
• Trace functions - print args, indent proportional to depth, add function tags

You will again use DrRacket, which you should have downloaded and installed for the previous labs.

For this lab, you will need to implement the following decorator functions in Racket:

• check-parms - decorates a function to enforce parameter type checking
• default-parms - decorates a function to add default parameter values

You will also chain these together to add both parameter type checking and default parameters to a function.

(define (default-parms f values) ...)

where f is a function of arbitrary arity, values is a list of default parameter values of the same length as the arity of f, and the result is a function that behaves exactly like f but fills in corresponding default parameter values from the values list if given fewer parameters than expected.

For example, if f takes two parameters,

(define g (default-parms f (list 42 99))

would result in a function g such that (g) behaves the same as (f 42 99), (g 8) behaves the same as (f 8 99), and (g 8 9) behaves the same as (f 8 9).

Hint: You might find it useful to use the Racket function list-tail, which returns the rest of a list after some number of elements. For example, (list-tail (list 1 2 3 4 5) 2) returns the list (3 4 5).

(define (type-parms f types) ...)

where f is a function of arbitrary arity, types is a list of type predicates (e.g., number?, string?, etc.) of the same length as the arity of f, and the result is a function that behaves exactly like f but first checks each parameter passed in to make sure it is the correct type.

For example, if f takes two parameters,

(define g (type-parms f (list number? string?))

would result in a function g such that (g 0 “hello”) behaves just like (f 0 “hello”), but passing anything but a number for the first parameter or anything other than a string for the second parameter results in an error message.

If default-parms and type-parms are working correctly, you should be able to chain them together like this:

(define g (default-parms (type-parms f (list number? string?)) 0 ""))

would result in a function g that fills in any missing parameters with 0 and “” respectively, and then verifies that the passed parameters are a number and a string.

You again do not need to bulletproof the code to enforce proper inputs. Your code only needs to return correct values given correct inputs.