Related papers: Handling Higher-Order Effectful Operations with Ju…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…
Parameterization extends higher-order processes with the capability of abstraction and application (like those in lambda-calculus). This extension is strict, i.e., higher-order processes equipped with parameterization is computationally…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
We analyse the problem of combining linearity, effects, and exceptions, in abstract models of programming languages, as the issue of providing some kind of strength for a monad $T(- \oplus E)$ in a linear setting. We consider in particular…
We show that the techniques for resource control that have been developed in the so-called "light logics" can be fruitfully applied also to process algebras. In particular, we present a restriction of Higher-Order pi-calculus inspired by…
We present a new modular proof method of termination for second-order computation, and report its implementation SOL. The proof method is useful for proving termination of higher-order foundational calculi. To establish the method, we use a…
We notice that the type of catch :: c a -> (e -> c a) -> c a operator is a special case of monadic bind operator (>>=) :: m a -> (a -> m b) -> m b, the semantics (surprisingly) matches, and this observation has many interesting…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
In semantics and in programming practice, algebraic concepts such as monads or, essentially equivalently, (large) Lawvere theories are a well-established tool for modelling generic side-effects. An important issue in this context are…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…