Questions tagged [coinductive-type]

Use with coinductive types.

Filter by
Sorted by
Tagged with
11 votes
0 answers
76 views

Rules for mutual inductive/coinductive types

Some proof assistants, like Agda and maybe Coq, allow families of mutually defined types, or nested definitions of types, in which some are inductive and others are coinductive. I have no idea what ...
user avatar
  • 2,079
10 votes
1 answer
212 views

Is induction over mutually inductive coinductive types possible?

You can encode ordinals in Coq as Inductive ord := O | S (n: ord) | Lim (s: nat -> ord). Suppose you use the following encoding instead ...
user avatar
9 votes
2 answers
187 views

Comparison between proof assistants for coinductive structures and proofs

I have a quite vague and naïve question: what are the differences between the different proof assistants regarding coinduction? My motivation is that I'd like to formalize some proofs, basically about ...
user avatar
16 votes
1 answer
229 views

What is the state of coinductive types and reasoning in Coq?

Ever since the work by Gimenez for his PhD thesis, Coq has supported positive coinductive types. For example, the type of always-infinite streams containing elements of type ...
user avatar
  • 165
7 votes
1 answer
97 views

Is it possible to define `fib` coinductive stream w/o sized types?

In Agda with --guardedness, we can define productive definitions using copatterns like the following ...
user avatar
  • 4,136
18 votes
1 answer
135 views

When to use coinductive types?

One could define streams in the following manner ...
user avatar