Lab 3🔗

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1. Develop a representation for bicycles; A bicycle can be either a Trek, a Bianchi, or a Gunnar. Each one has a single field that is a number. I don’t care what the single field of each kind bicycle is called. Actually, I don’t care whether they have fields or not, but experience shows that constructors with no arguments along with higher-order procedures confuse the heck out of students just getting used to Racket. If this doesn’t make sense to you, just take my advice and make up a field for each one. How about num-wheels? Define these using a define-type and a set of structs.

   Note that every structure you define in this course should have the #:transparent tag. There’s a note about this in the Hints linked to in the syllabus.

2. Note! After defining a structure named s1 with fields f1 and f2, you will be able to use the function s1? to determine whether a given value is a structure created with s1, as well as being able to use s1-f1 to get the contents of field f1 and s1-f2 to get the contents of field f2. This will be useful later....

3. Develop the function only-treks, that consumes a list of bicycles and returns a list containing only the Treks. Hint: it’s fine to use a match as part of the list template, but don’t use a match to determine what kind of bicycle you have; this will impair the abstraction that’s supposed to happen two problems in the future. (Also, don’t use the built-in filter function; the idea of this lab is to give you practice in writing recursive functions on lists. Unless you re-implement filter. Then it’s fine.)

4. Develop the function only-bianchis, that consumes a list of bicycles and returns a list containing only the Bianchis. Hint: same hint as last time.

5. Abstract over the two of these to obtain the function onlyThese, that consumes a list of bicycles and a particular bicycle predicatePredicate: a function that accepts any value and returns a boolean, used to represent a set or property. For instance, an even? function or Java’s isOrdered. f (e.g., Gunnar?, or maybe a function that always returns false) and returns a list of bicycles containing only those elements of the list that satisfy f. (Note: you’re passing the function Gunnar? here. If this doesn’t make sense, ask for help!

   Hint: use (Listof Bicycle) as the return type of onlyThese.

6. Develop the my-append function that consumes two lists and returns the result of appending the second one to the first. So, if called with the list '(a b c) and the list '(d e f), it would return '(a b c d e f). (Don’t use the built-in append function, please.)

7. Develop the my-take function that consumes a list and a number n and returns the first n elements of the list. If the list contains fewer than n elements, it returns the entire list. (Again, don’t use take, or reverse, or drop, etc. etc.)