An equivalence between lambda-terms
Theoretical Computer Science
Reasoning about programs in continuation-passing style
Lisp and Symbolic Computation - Special issue on continuations—part I
ACM Transactions on Programming Languages and Systems (TOPLAS)
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Control reduction theories: The benefit of structural substitution
Journal of Functional Programming
Classical call-by-need and duality
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Call-by-Value solvability, revisited
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
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We give a decomposition of the equational theory of call-by-value ¿ -calculus into a confluent rewrite system made of three independent subsystems that refines Moggi's computational calculus: the purely operational system essentially contains Plotkin's β v rule and is necessary and sufficient for the evaluation of closed terms; the structural system contains commutation rules that are necessary and sufficient for the reduction of all "computational" redexes of a term, in a sense that we define; the observational system contains rules that have no proper computational content but are necessary to characterize the valid observational equations on finite normal forms. We extend this analysis to the case of λ -calculus with control and provide with the first presentation as a confluent rewrite system of Sabry-Felleisen and Hofmann's equational theory of λ -calculus with control. Incidentally, we give an alternative definition of standardization in call-by-value λ -calculus that, unlike Plotkin's original definition, prolongs weak head reduction in an unambiguous way.