Related papers: Formal Semantics of a Classical-Quantum Language
We present a new approach to automated reasoning about higher-order programs by extending symbolic execution to use behavioral contracts as symbolic values, enabling symbolic approximation of higher-order behavior. Our approach is based on…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…
In this paper we provide two new semantics for proofs in the constructive modal logics CK and CD. The first semantics is given by extending the syntax of combinatorial proofs for propositional intuitionistic logic, in which proofs are…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
The field of proof-theoretic semantics (P-tS) offers an alternative approach to meaning in logic that is based on inference and argument (rather than truth in a model). It has been successfully developed for various logics; in particular,…
Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is…