Assignment 1, CSC429, Spring 2009

These are some warm-up exercises, to help you get used to programming in OCAML.

1 Test Cases

You must have test cases for each function; each test case should be an expression that produces true if the test case passes, and false if it fails. Ideally, it will also print a message when a test case fails.

2 OCaml’s if

In order to complete some of the problems here, you’ll need to use OCaml’s if, which won’t be too surprising except that it requires an explicit then:

So, for instance, these two expressions:

#     - : int = 156

#       - : string = "abc"

3 Recursion:

In order to make an OCaml function recursive, you must declare it with "let rec", rather than "let".

So, for instance, here’s an infinite loop (with a call to it):

let rec loop x = loop x;;

(loop "dontcare");;

4 Problems:

• Develop the function f1 with type (float -> float) defined by this equation: f1 (x) = 3x^2 + 14.

• Develop the function f2 with type (float -> float) defined by this equation: f2 (x) = x^3 + 2x^2

• Develop the function differ, that consumes a function and a value for x and produces an approximation of the value of the function’s first derivative at that point, by using the value of f at x and at x + (sqrt epsilon_float).

• Develop the function oneStep, that consumes a float and either increases it by 1 percent or decreases it by 1 percent, depending on the result of (Random.random ()). Writing a test case for this is tricky. Do your best.

• Develop the function nSteps, that consumes a float and an int >= 0 and returns the result of applying the oneStep function n times. Again, give some thought to a reasonable test case.