Inferring static non-monotonically sized types through testing

We propose a size analysis algorithm that combines testing and type checking to automatically obtain static output-on-input size dependencies for first-order functions. Attention is restricted to functions for which the size of the result is strictly polynomial, not necessarily monotonic, in the sizes of the arguments. To infer a size dependency, the algorithm generates hypotheses for increasing degrees of polynomials. For each degree, a polynomial is defined by a finite number of points. The function is evaluated with a large enough set of appropriate measurement data to get these points and determine the coefficients of the polynomial. The resulting hypothesis is then checked using an existing type checking procedure. The algorithm is not tied to the current sized type checker. The sized type of a function will be inferred if it exists and if it is accepted by the sized type checker. For terminating functions, our sized type inference algorithm is complete with respect to type checking. Hence, using a more complete sized type checker yields a more complete sized type inference algorithm.