In the style of recursive programming compelled by the available
meta primitive, a function effectively requires a copy of its own
machine code as its left argument. Bringing about that state of
affairs is an interesting party trick.
If we had a definition of bu in the standard library implying
bu]] (f,k)) x = f(k,x)
which for the sake of concreteness can be done like this,
bu = (hired compose)(
left,
(hired couple)(compose(constant,right),constant identity))
then a definition of refer as
refer = (hired bu)(identity,identity)
would be consistent with the following property of the operator.
refer]] f) x = f (f,x)
The proof, as always, is a matter of routine calculation in the manner
of the section on how avram thinks.
However, this pattern would occur so frequently in recursively defined functions as to be a significant waste of space and time. Therefore, rather than requiring it to be defined in terms of other operations, the virtual machine specification recognizes a pattern of the form below with respect to property P15,
refer]] f = (((f,nil),nil),nil)
and takes the property to be true by definition of the operator. A
definition of refer consistent with T17 is therefore to
be found in the standard library, not the definition proposed above.