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Questions tagged [coinduction]

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Definition of M-type in type theory

According to nLab, M-types are the dual of W-types. What are the introduction and elimination rules for M-types? Edit: For example, the formation/introduction/elimination rules for W-types are: $$\...
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How can one flip a stream using corecursion

Following is the definition of codata stream: codata Stream where hd : Stream −> A tl : Stream −> Stream For simplicity I assume I have just a ...
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Does co-inductive and co-recursive types also have their recursors?

I'm new to type theory, and recently read introductory materials where dependent type are discussed. One of my friend asked me, "Those dependent types are having recursors & 'inductors'(dependent ...
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Bisimulations: Proof that the following LTS are not bisimilar

I have the two LTS (labeled transition system) as seen in the following picture: And the book is telling me that between those two LTS, their $1$ and $1'$ are non-bisimilar. So I tried to get a ...
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Is the set finite words over an alphabet a final coalgebra*?

I am studying what coinduction is. In particular, I am reading that coinductive datatypes can be defined as elements of a final coalgebra for a given polynomial endofunctor on $\tt Set$. I've seen ...
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Typing rules of coinductive types?

Are there typing rules for specific coinductive types such as conat or stream, or even in general the M-types?
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Is extensionality for coinductive datatypes consistent with Coq's logic?

Given a coinductive datatype, one can usually (always?) define a bisimulation as the smallest equivalence relation over it. I would like to add an axiom stating that if two members of the type are ...
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What is coinduction?

I've heard of (structural) induction. It allows you to build up finite structures from smaller ones and gives you proof principles for reasoning about such structures. The idea is clear enough. But ...