Related papers: Minimal lambda-theories by ultraproducts
We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The…
We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of…
In this paper we provide an abstract model theory for the untyped differential lambda-calculus and the resource calculus. In particular we propose a general definition of model of these calculi, namely the notion of linear reflexive object…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
We give a characterization, with respect to a large class of models of untyped $\lambda$-calculus, of those models that are fully abstract for head-normalization, i.e., whose equational theory is $\mathcal{H}^*$. An extensional K-model $D$…
We show that in a locally lambda-presentable category, every lambda(m)-injectivity class (i.e., the class of all the objects injective with respect to some class of lambda-presentable morphisms) is a weakly reflective subcategory determined…
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 study approximability of regular constraint satisfaction problems, i.e., CSPs where each variable in an instance has the same number of occurrences. In particular, we show that for any CSP $\Lambda$, existence of an $\alpha$…
We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial…
The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the…
Fix a language L extending the language of real closed fields by at least one new predicate or function symbol. Call an L-structure R pseudo-o-minimal if it is (elementarily equivalent to) an ultraproduct of o-minimal structures. We show…
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
Suppose that $\lambda=\lambda^{<\lambda} \ge\aleph_0$, and we are considering a theory $T$. We give a criterion on $T$ which is sufficient for the consistent existence of $\lambda^{++}$ universal models of $T$ of size $\lambda^+$ for models…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…