Related papers: Uniform Proofs of Normalisation and Approximation …
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
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…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
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,…
We show canonicity and normalization for dependent type theory with a cumulative sequence of universes and a type of Boolean. The argument follows the usual notion of reducibility, going back to Godel's Dialectica interpretation and the…
In the framework of explicit substitutions there is two termination properties: preservation of strong normalization (PSN), and strong normalization (SN). Since there are not easily proved, only one of them is usually established (and…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…
We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…
Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
The calculus of constructions (CC) is a core theory for dependently typed programming and higher-order constructive logic. Originally introduced in Coquand's 1985 thesis, CC has inspired 25 years of research in programming languages and…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
We present a new strictification method for type-theoretic structures that are only weakly stable under substitution. Given weakly stable structures over some model of type theory, we construct equivalent strictly stable structures by…
We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the…
We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent…