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We propose a model-based approach to the model checking problem for recursive schemes. Since simply typed lambda calculus with the fixpoint operator, lambda-Y-calculus, is equivalent to schemes, we propose the use of a model of…
We study the correspondence between a concurrent lambda-calculus in administrative, continuation passing style and a pi-calculus and we derive a termination result for the latter.
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
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…
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…
Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the insertion of double negations. Recently, Brown and Rizkallah extended this translation to higher-order logic. In this paper, we adapt it for…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
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…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
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,…
Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…
Lambda calculi with algebraic data types lie at the core of functional programming languages and proof assistants, but conceal at least two fundamental theoretical problems already in the presence of the simplest non-trivial data type, the…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…