Related papers: A Complete Proof Synthesis Method for the Cube of …
By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs.…
We define a sound and complete proof system for affine beta-eta-retractions in simple types built over many atoms, and we state simple necessary conditions for arbitrary beta-eta-retractions in simple and polymorphic types.
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
Systems of dyadic cubes are the basic tools of harmonic analysis and geometry, and this notion had been extended to general metric spaces. In this paper, we construct systems of dyadic cubes of complete, doubling, uniformly perfect metric…
Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
We present a new type system combining refinement types and the expressiveness of intersection type discipline. The use of such features makes it possible to derive more precise types than in the original refinement system. We have been…
General purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this work we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably…
We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases of the Bayesian posterior of a synthesis problem. This new…
We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can…
We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge…
In this paper we explore a family of type isomorphisms in System F whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalence stronger than…
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is…
A system $\boldsymbol\lambda_{\theta}$ is developed that combines modal logic and simply-typed lambda calculus, and that generalizes the system studied by Montague and Gallin. Whereas Montague and Gallin worked with Church's simple theory…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…