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Superdevelopments for Weak Reduction [PDF]

Electronic Proceedings in Theoretical Computer Science, 2010
We study superdevelopments in the weak lambda calculus of Cagman and Hindley, a confluent variant of the standard weak lambda calculus in which reduction below lambdas is forbidden. In contrast to developments, a superdevelopment from a term M allows not
Eduardo Bonelli, Pablo Barenbaum
doaj   +5 more sources

Completeness of algebraic CPS simulations [PDF]

Electronic Proceedings in Theoretical Computer Science, 2012
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms.
Ali Assaf, Simon Perdrix
doaj   +6 more sources

Encoding many-valued logic in $\lambda$-calculus [PDF]

Logical Methods in Computer Science, 2021
We will extend the well-known Church encoding of Boolean logic into $\lambda$-calculus to an encoding of McCarthy's $3$-valued logic into a suitable infinitary extension of $\lambda$-calculus that identifies all unsolvables by $\bot$, where $\bot$ is a ...
Fer-Jan de Vries
doaj   +3 more sources

Modules over monads and operational semantics (expanded version) [PDF]

Logical Methods in Computer Science, 2022
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi.
André Hirschowitz, Tom Hirschowitz, Ambroise Lafont   +2 more
doaj   +1 more source

Relational Parametricity and Control [PDF]

Logical Methods in Computer Science, 2006
We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus.
Masahito Hasegawa
doaj   +1 more source

The untyped stack calculus and Bohm's theorem [PDF]

Electronic Proceedings in Theoretical Computer Science, 2013
The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus.
Alberto Carraro
doaj   +1 more source

Finitary Simulation of Infinitary $\beta$-Reduction via Taylor Expansion, and Applications [PDF]

Logical Methods in Computer Science, 2023
Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation theorem relating
Rémy Cerda, Lionel Vaux Auclair
doaj   +1 more source

Rewriting Modulo β in the λΠ-Calculus Modulo [PDF]

Electronic Proceedings in Theoretical Computer Science, 2015
The lambda-Pi-calculus Modulo is a variant of the lambda-calculus with dependent types where beta-conversion is extended with user-defined rewrite rules.
Ronan Saillard
doaj   +1 more source

Non-idempotent types for classical calculi in natural deduction style [PDF]

Logical Methods in Computer Science, 2020
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.
Delia Kesner, Pierre Vial
doaj   +1 more source

Superdeduction in Lambda-Bar-Mu-Mu-Tilde [PDF]

Electronic Proceedings in Theoretical Computer Science, 2011
Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way.
Clément Houtmann
doaj   +1 more source