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We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Nominal unification calculates substitutions that make terms involving binders equal modulo alpha-equivalence. Although nominal unification can be seen as equivalent to Miller's higher-order pattern unification, it has properties, such as…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
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…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Functional logic languages can solve equations over user-defined data and functions. Thus, the definition of an appropriate meaning of equality has a long history in these languages, ranging from reflexive equality in early equational logic…
We propose a method to write and check a specification including quantifiers using behaviors, i.e., input-output pairs. Our method requires the following input from the user: (1) answers to a finite number of queries, each of which presents…
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which…
In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the…
We study the complexity of deciding the equality of infinite objects specified by systems of equations, and of infinite objects specified by lambda-terms. For equational specifications there are several natural notions of equality: equality…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying…
Weak $\infty$-categories are known to be more expressive than their strict counterparts, but are more difficult to work with, as constructions in such a category involve the manipulation of explicit coherence data. This motivates the search…
In this paper a constructive formalization of quantifier elimination is presented, based on a classical formalization by Tobias Nipkow. The formalization is implemented and verified in the programming language/proof assistant Agda. It is…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…