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HOUDEGBE NORTH AMERICAN UNIVERSTY, BENIN
SCHOOL OF COMPUTER SCIENCE, MATHEMATHICS AND INFORMATION TECHNOLOGY

DEPARMENT: COMPUTER SCIENCE A1

GROUP 3
NAMES OF GROUP MEMBERS MATRIC NUMBER
OSO ABAYOMI OMOBOLANLE 0907 IT 00989

PRESENTATION TOPIC: MU RECURSIVE FUCNTION
LECTURER NAME: MR OSHIBOGUN

RECURSIVE FUNCTION
Recursive functions are built up from basic functions by some operations.
The successor function
Lets get very primitive. Suppose we have 0 defined and want to build the nonnegative integers and entire number system. We define the successor operation S(x) that takes a number x to its successor X+1. This gives one the nonnegative integers N0= {0,1,2….}
We formalize the above process primitive recursive functions are built up from three basic functions using two operations these basic functions are:
1. Zero. Z(x)=0
2. Successor. S(x)= x+1.
3. Projection. A projection function selects out one of the argument. Specially P1(x,y)=x and P2(x,y)=y
The composition operation
There are two operations that make new functions from old: composition and primitive recursion
Composition replaces the arguments of a function by another. For example, one can define a function f by F(x,y)=g(h1(x,y), h2(x,y))
Where one supplies the functions g1, g2 and h.

Primitive recursion
A typical use of primitive recursion has the following form

Where one supplies the function g1, g2 and h.
For example, in the case of addition, the h is the successor function of the projection of the 2nd argument.
A special case of primitive recursion is for some constant number K:

A function is said to be recursive if it can be from by:
Composition function
Primitive function
Application of unbounded minimization to regular functions

DEFINITION
The family of recursive function is defined as follows:
i. The successor, zero and projection function are urecursive. ii. If h is an n-variable u recursive function and g1,. . .