相关论文: On Completeness of Logical Relations for Monadic T…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive,…
We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…
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…
Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…
According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type…
Many well-known logical identities are naturally written as equivalences between contextual formulas. A simple example is the Boole-Shannon expansion $c[p] \equiv (p \wedge c[\mathrm{true}] ) \vee (\neg\, p \wedge c[\mathrm{false}] )$,…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
The existing call-by-need lambda calculi describe lazy evaluation via equational logics. A programmer can use these logics to safely ascertain whether one term is behaviorally equivalent to another or to determine the value of a lazy…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Logical vulnerabilities in software stem from flaws in program logic rather than memory safety, which can lead to critical security failures. Although existing automated program repair techniques primarily focus on repairing memory…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…