A natural semantics for lazy evaluation
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An operational semantics for parallel lazy evaluation
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Deriving a lazy abstract machine
Journal of Functional Programming
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
Barendregt's Variable Convention in Rule Inductions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
General bindings and alpha-equivalence in nominal Isabelle
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
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We propose a locally nameless representation for Launchbury's natural semantics for lazy evaluation. Names are reserved for free variables, while bound variable names are replaced by indices. This avoids the use of α-conversion and Barendregt's variable convention, and facilitates proof formalization. Our definition includes the management of multi-binders to represent simultaneous recursive local declarations. We use cofinite quantification to express the semantic rules that require the introduction of fresh names, but we show that existential rules are admissible too. Moreover, we prove that the choice of names during the evaluation of a term is irrelevant as long as they are fresh enough.