Assignment 3: Pseudorandom number generating function

Assignment 3 of 4

1. Develop a pseudorandom number generating function that is a given a seed value as an argument and will produce a value
between 0 and 10. You will need to investigate how this can be done, but as a clarifying example consider the pseudorandom
sequence 5, 13, 17, 19, 20, 10 ..., where the first element of the sequence is 5 and the i+1th element of the sequence is the result
of the expression mod (i*11) 21. (n.b., your pseudorandom number generating function is expected to be superior than the one
detailed above.)
Just like arithmetic expressions, expressions in propositions logic can be represented using trees. The Expression and Operator types
defined below are sufficient for representing logical expression using only the conjunction (AND) and disjunction (OR) operations.
data Expression = Literal Bool | Operation Operator Expression Expression
data Operator = AND | OR
2. Write a height function height that will count the number of edges (in the tree representation) on the longest path from the
root to any leaf node (i.e., Literals). Please note that the height of a tree that is just a single Literal should be reported as 0.
3. Write an evaluation function eval that takes an Expression as an argument and produces a Bool return value corresponding to
the result if the Expression were to be evaluated. As a clarifying example, the function call:
eval (Operation OR (Literal True) (Operation AND (Literal True) (Literal False)))
would be expected to result in the return value True.
4. Alter the type definitions so that you can also represent and evaluate negation operations (i.e., logical not) and exclusive
disjunction operations (i.e., logical xor).
5. Write a function to show the expression, using the characters T and F instead of True and False, respectively, and using the caret
symbol ^ for conjunction, the lowercase v for inclusive disjunction, the plus sign + for exclusive disjunction, and the tilde ~ for
negation. Your expression should be constructed with bracketing around each operation, but bonus marks will be rewarded if
you can avoid wrapping unnecessary brackets around literals. To clarify, a function call to show this expression:
(Operation OR (Literal True) (Operation AND (Literal True) (Literal False)))
would be accepted with full marks if it returned the string "(T) v ((T) ^ (F))"
and it would be accepted with a small bonus if it returned the string "T v (T ^ F)"