Related papers: A static higher-order dependency pair framework
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual…
This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The…
Pairwise model comparisons drawn from foundation-model benchmarks ("A is safer than B") are read as quantitative verdicts but hinge on harness choices benchmark papers under-specify. We close one theory-benchmark loop on this primitive: a…
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…
This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…
String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is…
In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite…
We present new proofs of termination of evaluation in reduction semantics (i.e., a small-step operational semantics with explicit representation of evaluation contexts) for System F with control operators. We introduce a modified version of…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
This paper describes an algorithm for the compilation of a two (or more) level orthographic or phonological rule notation into finite state transducers. The notation is an alternative to the standard one deriving from Koskenniemi's work: it…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…