Related papers: A Curry-Howard Correspondence for Linear, Reversib…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking…
Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
LogicWeb has traditionally lacked devices for dealing with intractable queries. We address this limitation by adopting length-bounded inference, a form of approximate reasoning. A length-bounded inference is of the form $prov(P,G,n)$ which…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
We wish to present a mirrored language structure (MLS) and four logic rules determined by this structure for the model of a computable Oracle Turing machine. MLS has novel features that are of considerable biological and computational…
We derive multiple program logics, including correctness, incorrectness, and relational Hoare logic, from the axioms of imperative categories: uniformly traced distributive copy-discard categories. We introduce an internal language for…
We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…
The starting point of this work is the observation that the Curry-Howard isomorphism, relating types and propositions, programs and proofs, composition and cut, extends to the correspondence of program fusion and cut elimination. This…
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features including record subtyping and combination of case branches. Our goal is…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
Motivated by a need for a model of reversible computation appropriate for a Brownian molecular architecture, the $\aleph$ calculus is introduced. This novel model is declarative, concurrent, and term-based--encapsulating all information…
Causal-consistent reversible debugging allows one to explore concurrent computations back and forth in order to locate the source of an error. In this setting, backward steps can be chosen freely as long as they are "causal consistent",…
We give a 'recursive' formula (in terms of reducible limits) for counting rational curves on a variety moving in any sufficiently large and well-behaved family. Our approach is completely elementary and makes no use of moduli spaces for…