Clausal Language (ver. 5.81.16, by P.J. Voda, J. Komara, J. Kluka)
Chapter. Primitive Recursive Functions.
|
|
Part. Arithmetization of finite sequences of numbers.
|
|
Exercise. Show that the predicate
holding of prime numbers is primitive recursive.
|
|
[CL] Characteristic function of the prime predicate.
|
|
|
|
Exercise. Show that the function
counting the number of primes
is primitive recursive.
|
|
Exercise. Show that the function
yielding the (i+1)-st prime number, i.e.
is primitive recursive.
|
|
Exercise. Show that the function
yielding the exponent of
in the prime factorization of the number
is primitive recursive. We set
.
|
|
Coding of finite sequences of numbers. Examples:
-
the empty sequence is coded by the number
,
-
the non-empty sequence
is coded by the number
|
|
Exercise. [Premiova uloha (1 bod)] Show that the predicate
holding of the codes of finite sequences of numbers is primitive recursive.
|
|
Exercise. [Premiova uloha (1 bod)] Show that the function
yielding the length of a finite sequence coded by
is primitive recursive.
|
|
Exercise. Show that the function
yielding the (i+1)-st element of a finite sequence coded by
is primitive recursive.
|
|
Heap used: 372564 free: 133843716
Time used: 0:0:0:12