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EPISODE · Feb 4, 2023 · 11 MIN

Extensional Martin-Loef Type Theory

from Iowa Type Theory Commute · host Aaron Stump

In this episode, I discuss the basic distinguishing rule of Extensional Martin-Loef Type Theory, namely equality reflection.  This rule says that propositional equality implies definitional equality.  Algorithmically, it would imply that the type checker should do arbitrary proof search during type checking, to see if two expressions are definitionally equal.  This immediately gives us undecidability of type checking for the theory, at least as usually realized.

Episode metadata supplied by the publisher feed · Published Feb 4, 2023

What this episode covers

In this episode, I discuss the basic distinguishing rule of Extensional Martin-Loef Type Theory, namely equality reflection. This rule says that propositional equality implies definitional equality. Algorithmically, it would imply that the type checker should do arbitrary proof search during type checking, to see if two expressions are definitionally equal. This immediately gives us undecidability of type checking for the theory, at least as usually realized.

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Extensional Martin-Loef Type Theory

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How long is this episode of Iowa Type Theory Commute?

This episode is 11 minutes long.

When was this Iowa Type Theory Commute episode published?

This episode was published on February 4, 2023.

What is this episode about?

In this episode, I discuss the basic distinguishing rule of Extensional Martin-Loef Type Theory, namely equality reflection.  This rule says that propositional equality implies definitional equality.  Algorithmically, it would imply that the type...

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