He develops a constructive framework for proving equalities about programs, and shows how to derive the free theorems in a purely syntactic way.
The standard method of proving this fact is via lambda representability of all (partial) recursive functions.
We discuss a known method of proving correctness of definite programs and introduce a method for proving completeness.
But in the context of proving that learning has taken place, the value of a certificate proving attendance can be doubtful.
These programs rely on the user to annotate the loops, and provide assistance only in proving the correctness of the annotations.
We answer this question in the affirmative, by proving the following theorem.
Note, however, that proving lower bounds for graphs may be an even more difficult task than for boolean functions.
We will show that the image vectors of are independent, thus proving the - theorem.
