Related papers: Strong normalization through idempotent intersecti…

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…

Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…

In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…

We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…

We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…

In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed lambda-calculus enriched by pattern-matching…

The lambda Pi calculus can be extended with rewrite rules to embed any functional pure type system. In this paper, we show that the embedding is conservative by proving a relative form of normalization, thus justifying the use of the lambda…

A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…

We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…

This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…

Refining and extending previous work by Retor\'e, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz…

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…

System I is a recently introduced simply-typed lambda calculus with pairs where isomorphic types are considered equal. In this work we propose a variant of System I with the type Top, and present a complete formalization of this calculus in…

Lambek's non-associative syntactic calculus (NL) excels in its resource consciousness: the usual structural rules for weakening, contraction, exchange and even associativity are all dropped. Recently, there have been proposals for…

We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…

Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…

We study Milner's lambda-calculus with partial substitutions. Particularly, we show confluence on terms and metaterms, preservation of \b{eta}-strong normalisation and characterisation of strongly normalisable terms via an intersection…

This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as…

Static single assignment form, or SSA, has been the dominant compiler intermediate representation for decades. In this paper, we give a type theory for a variant of SSA, including its equational theory, which are strong enough to validate a…