Computable functions

Question 1

program output

Answer 1

computed as a function of program inputs and state of the machine before the program starts

Question 2

effectively computable

Answer 2

computable with finite resources in a finite time

Question 3

Undefined operation

Answer 3

e. g. division by zero

- may halt with error condition

Question 4

non termination -

Answer 4

never delivers a result
- this is a partial function : not defined on all arguments
cannot be detected at compile time

Question 5

functions as graphs

Answer 5

f: x -> y

f is a set of pair X x Y

Question 6

extensional equality

Answer 6

two functions are equal if given the same input they yield the same output (even if they have different algorithms)

Question 7

Total functions definition

Answer 7

the total function F:A->B os a subset B x A where for every x E A there is some y EB with E F
Also if E F and E F then y = z (single valued)

Question 8

Partial function definition

Answer 8

the partial function F:A->B os a subset B x A where for every x E A there is some y EB with E F
Also if E F and E F then y = z (single valued)

this means that a partial function is single valued but need not be deifnied on all elements of its domain