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Confluence properties of Weak and Strong Calculi of Explicit Substitutions
 JOURNAL OF THE ACM
, 1996
"... Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence prope ..."
Abstract

Cited by 120 (7 self)
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Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. [12, 21, 1, 23] are the following: 1. We present a confluent weak calculus of substitutions, where no variable clashes can be feared. 2. We solve a conjecture raised in [1]: oecalculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of oecalculus, named the Envcalculus in [23], called here the confluent oecalculus.
Formalization of a λCalculus with Explicit Substitutions in Coq
"... We present a formalization of the λσ⇑calculus[9] in the Coq V5.8 system[6]. The principal axiomatized result is the confluence of this calculus. Furthermore we propose a uniform encoding for manysorted first order term rewriting systems, on which we study the local confluence by critical pairs ana ..."
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We present a formalization of the λσ⇑calculus[9] in the Coq V5.8 system[6]. The principal axiomatized result is the confluence of this calculus. Furthermore we propose a uniform encoding for manysorted first order term rewriting systems, on which we study the local confluence by critical pairs analysis. 1