It is a common knowledge that the integer functions definable in the simply typed λ-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p → p) → p → p where p is a base type and/or equality is taken as β-conversion. It is commonly believed that the same holds for βη-equality and for integers represented over any fixed type of the fo...

Analysis of exclusively-kinetic two-link underactuated mechanical systems is undertaken in this paper. It is first shown that such systems are not full-state feedback linearizable around any equilibirium point. Also, the equilibrium points for which the system is small-time locally controllable (STLC) is at most a one dimensional submanifold. A concept less restrictive than STLC, termed the sma...

This work considers small-time local controllability (STLC) of single and multiple-input systems, ẋ = f◦(x) + ∑m i=1 fiu i where f◦(x) contains homogeneous polynomials and f1, . . . , fm are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree h...

We report our experience with exploring a new point in the design space for formal reasoning systems: the development of the programming language Ωmega. Ωmega is intended as both a practical programming language and a logic. The main goal of Ωmega is to allow programmers to describe and reason about semantic properties of programs from within the programming language itself, mainly by using a p...