Related papers: Strong normalization results by translation
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…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
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…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
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…
It is well-known that intersection type assignment systems can be used to characterize strong normalization (SN). Typical proofs that typable lambda-terms are SN in these systems rely on semantical techniques. In this work, we study…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
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…
Asynchronous effects of Ahman and Pretnar complement the conventional synchronous treatment of algebraic effects with asynchrony based on decoupling the execution of algebraic operation calls into signalling that an operation's…
In the first part of this paper, we define two resource aware typing systems for the {\lambda}{\mu}-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
We present a framework for the formal meta-theory of lambda calculi in first-order syntax, with two sorts of names, one to represent both free and bound variables, and the other for constants, and by using Stoughton's multiple…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
We present a call-by-need $\lambda$-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…
This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…
We present a novel linear $\lambda$-calculus for Classical Multiplicative Exponential Linear Logic (\MELL) along the lines of the propositions-as-types paradigm. Starting from the standard term assignment for Intuitionistic Multiplicative…