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Questions tagged [coq]

Coq is an interactive theorem prover.

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1answer
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Class of functions computable by Coq

Since it does not allow nonterminating computation, Coq is necessarily not Turing-complete. What is the class of functions that Coq can compute? (is there an interesting characterization thereof?)
48
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3answers
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Shallow versus Deep Embeddings

When encoding a logic into a proof assistant such as Coq or Isabelle, a choice needs to be made between using a shallow and a deep embedding. In a shallow embedding logical formulas are written ...
36
votes
3answers
4k views

Why does Coq have Prop?

Coq has a type Prop of proof irrelevant propositions which are discarded during extraction. What are the reason for having this if we use Coq only for proofs. Prop is impredicative, so Prop : Prop, ...
41
votes
4answers
3k views

How would I go about learning the underlying theory of the Coq proof assistant?

I'm going over the course notes at CIS 500: Software Foundations and the exercises are a lot of fun. I'm only at the third exercise set but I would like to know more about what's happening when I use ...
21
votes
1answer
2k views

Where is the proof that Coq + Excluded Middle is consistent

I've seen (and heard) it claimed that it is safe to add the classical axiom of excluded middle to Coq, but I can not seem to find a paper supporting this claim. The papers I see listed on the Coq wiki ...
5
votes
1answer
601 views

What exactly is “large elimination”?

I'm studying type theory (mostly Coq) and often encounter the term "large elimination", usually when talking about type universes hierarchy consistency, for example: impredicative polymorphism + ...
1
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0answers
226 views

Is it possible to type Ackermann function with (stratified variant of) System F?

I was surprised to find no open-source implementation of Ackermann function in pure System F as an illustrative example. I finally managed to implement it myself in Haskell using Church encoding: <...