Related papers: Strong normalisation for applied lambda calculi
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
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 lambda-calculus with de Bruijn indices assembles each alpha-class of lambda-terms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable…
In this paper, we prove the strong normalisation for Martin-L\"{o}f's Logical Framework, and suggest that {}``correct arity'', a condition weaker than well-typedness, will also guarantee the strong normalisation.
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
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 categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We present a quantitative basis-independent analysis of combinatory logic. Using a general argument regarding plane binary trees with labelled leaves, we generalise the results of David et al. and Bendkowski et al. to all Turing-complete…
This paper provides foundations for strong (that is, possibly under abstraction) call-by-value evaluation for the lambda-calculus. Recently, Accattoli et al. proposed a form of call-by-value strong evaluation for the lambda-calculus, the…
This paper extends the dual calculus with inductive types and coinductive types. The paper first introduces a non-deterministic dual calculus with inductive and coinductive types. Besides the same duality of the original dual calculus, it…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and has a strong forcing axiom of higher order than usual. Instead of "for every suitable forcing…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We investigate completeness and parametricity for a general class of realizability semantics for System F defined in terms of closure operators over sets of $\lambda$-terms. This class includes most semantics used for normalization…