Related papers: Explicit Substitutions for Contextual Type Theory
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…
Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders,…
We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In $\textrm{Lambek}^D$, linear types are used as a syntax for formal grammars,and parsers can be written as linear…
Visual counterfactual explanations are ideal hypothetical images that change the decision-making of the classifier with high confidence toward the desired class while remaining visually plausible and close to the initial image. In this…
We reformulate recent advances in directed type theory--a type theory where the types have the structure of synthetic (higher) categories--as a logical calculus with multiple context 'zones', following the example of Pfenning and Davies.…
Metaprogramming enables the generation of performant code, while gradual typing facilitates the smooth migration from untyped scripts to robust statically typed programs. However, combining these features with imperative state -…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
In this paper we investigate the $\lambda$ -calculus, a $\lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and…
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…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
To discover intrinsic inter-class transition probabilities underlying data, learning with noise transition has become an important approach for robust deep learning on corrupted labels. Prior methods attempt to achieve such transition…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
This paper introduces a uniform substitution calculus for $\mathsf{dL}_\text{CHP}$, the dynamic logic of communicating hybrid programs. Uniform substitution enables parsimonious prover kernels by using axioms instead of axiom schemata.…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…
In this paper we develop a very special substitution method for solving a general linear programming problem (LPP). Of course the substitution is a kind of elimination of variable but this method must not be confused with the so-called…
We present a new approach to evaluate computational models for the task of text understanding by the means of out-of-context error detection. Through the novel design of our automated modification process, existing large-scale data sources…
Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and…
We describe a Martin-L\"of style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…