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# Questions tagged [coinduction]

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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 largest equivalence relation over it. I would like to add an axiom stating that if two members of the type are ...
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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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### How to prove by coinduction?

Previously, I've asked a question about coinduction. That gave me a lot of useful high-level insights on what coinduction provides, and what are the usefulness of coinductive proofs. This question is ...
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### "Practical coinduction" over $\mathbb N_\infty$?

I've just finished reading the paper Practical Coinduction by Kozen and Silva. What is the difference between induction over $\mathbb N$ and coinduction over $\mathbb N_\infty$? From the paper, it ...
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### Understanding Isabelle's implementation of coinduction

I'm studying how coinduction was encoded in Isabelle. At page 7 of the attached document, the author describes how some datatypes can be encoded as initial algebras. Here is one example: Finite lists ...
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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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1 vote
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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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