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Better formulation of the commutativity theorem in overview
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0xd34df00d committed Oct 13, 2020
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Expand Up @@ -144,8 +144,8 @@ After formulating our surface and core languages, we define a translation from t
We also formulate two key theorems proving that the translation makes sense.
First, we prove that any well-typed surface language term has a translation to the core language.
Then, we prove that the small-step operational semantics of the languages match and commute with the translation:
if a surface language term evaluates to some other term in one step,
then its translation to the core language evaluates into an equivalent (core language) value, although, perhaps, in several steps.
if a surface language term $[[ es ]]$ evaluates to some other term $[[ es' ]]$ in one step,
then the translation of $[[ es ]]$ to the core language evaluates into the translationof $[[ es' ]]$, although, perhaps, in several steps.

\section{Calculi definitions}

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