Related papers: Explicit Substitutions for Contextual Type Theory
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
Intersection types are a standard tool in operational and semantical studies of the lambda calculus. De Carvalho showed how multi types, a quantitative variant of intersection types providing a handy presentation of the relational…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We develop a unified categorical theory of substructural abstract syntax with variable binding and single-variable (capture-avoiding) substitution. This is done for the gamut of context structural rules given by exchange (linear theory)…
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…
The elementary affine lambda-calculus was introduced as a polyvalent setting for implicit computational complexity, allowing for characterizations of polynomial time and hyperexponential time predicates. But these results rely on type…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
Measuring semantic change has thus far remained a task where methods using contextual embeddings have struggled to improve upon simpler techniques relying only on static word vectors. Moreover, many of the previously proposed approaches…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
We conduct a large scale empirical investigation of contextualized number prediction in running text. Specifically, we consider two tasks: (1)masked number prediction-predicting a missing numerical value within a sentence, and (2)numerical…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly…
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient inductive-inductive type. Algebraic definitions of type…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear…