Survey of Programming Language Concepts, cosc-3308 Lab/Assignment 4 Exercise 1. (Efficient Recurrence Relations Calculation) At slide 54 of Lecture 10, we have seen a concurrent implementation of classical Fibonacci recurrence. This is: fun (Fib X} if X==0 then 0 elseif X==1 then 1 else end end thread (Fib X-1} end + {Fib X-2} By calling Fib for actual parameter value 6, we get the following execution containing several calls of the same actual parameters. Execution of {Fib 6} F5 F4 10/27/2006 F4 F3 F2 F3: F2 F2 F1 F2 F1 F2 F1 CS2104, Lecture 7 (Fib 6) is denoted as F6,... Fork a thread Synchronize on result Running thread 56 For example, F3, that stands for {Fib 3}, is calculated independently three times (although it provides the same value every time). Write an efficient Oz implementation that is doing a function call for a given actual parameter only once. Consider a more general recurrence relation, e.g.: Fo, F1, ..., Fm-1 are known as initial values. Fn = g(Fn-1, ..., Fn-m), for any n ≥ m. For example, Fibonacci recurrence has m=2, g(x, y) = x+y, Fo=F₁=1.

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.