- Either a single expression of a recursive function;
- Or a small piece of code of the form

where ....... are expression of M-recursive functions and the function to be compiled is main.f = .......

g = .......

:

main = .......

- 0 is the null fonction. It takes as many arguments you want and returns 0.
- S is the successor fonction. It takes one argument n and returns n+1.
- pi(k) is the k-th projection fonction. It takes several arguments and returns the k-th argument.

Example: When we apply pi(2) on (3, 4, 10), it returns 4. - o(f, g1, ... gk) is the composition of f and g1, ... gk where f : N^k ---> N and gi : N^l ---> N.
- rec(b, r) is the recursive scheme build up from the basis case b and the recursive case f.

If b : N^l ---> N and r : N^{l+2} ---> N

rec(b, r) is defined as- rec(b, r)(vec n, 0) = b(vec n)
- rec(b, r)(vec n, k+1) = r(rec(b, r)(vec n, k), vec n, k)

1 2 3 ... l+1 l+2 rec(b, r) n1 n2 ... nl k

Example:

In rec( pi(1), o(S, pi(1)) ), the basis case function is pi(1). And o(S, pi(1)) is the recursive case function. We obtain the function +. - The mu-minimisation operator is not implemented!