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\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \)
Math and science::Theory of Computation::Lambda calculus

Confluence

Confluence

Let \( M \) be a lambda term. If \( M \multiBetaReduction N_1 \) and \( M \multiBetaReduction N_2 \) for some lambda terms \( N_1 \) and \( N_2 \), then there exists [...] such that [...].

Confluence is also called the Church-Rosser theorem.

There are three corollaries of the confluence theorem listed on the back side. Can you remember them?