Commit ad91dd0a authored by Giuseppe Castagna's avatar Giuseppe Castagna
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......@@ -333,4 +333,14 @@ doi = "",
url = "",
author = "Masako Takahashi",
abstract = "The notion of parallel reduction is extracted from the Tait-Martin-Löf proof of the Church-Rosser theorem (for β-reduction). We define parallel β-, η- and βη-reduction by induction, and use them to give simple proofs of some fundamental theorems in λ-calculus; the normal reduction theorem for β-reduction, that for βη-reduction, the postponement theorem of η-reduction (in βη-reduction), and some others."
author = {H. P. Barendregt},
title = {The Lambda Calculus Its Syntax and Semantics},
publisher = {North Holland},
year = {1984},
volume = {103},
edition = {Revised},
note = { Webpage}
\ No newline at end of file
......@@ -253,7 +253,8 @@ and that, under certain restrictions it is also complete.
This is a known result for the $\lambda-$calculus (even
extended with conditional, and basic types), see for instance
extended with conditional, and basic types), obtained using
the Tait and Martin-Löf technique (\cite{Bar84}). See for instance
\cite{Taka89} and \cite{Levy2017}.
The additional substitutions made by the rule \Rule{TestCtx}
will be performed later with the standard semantics.
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