Questions tagged [agda]
For questions regarding Agda: the programming language / proof assistant.
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Categorical semantics of Agda
I would like to know the state of the art regarding the categorical semantics of the type theory implemented by Agda — or at least some approximation of that type theory that is amenable to ...
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How to improve/understand typechecking performance in Agda?
I've recently been trying to do some basic formalization of category theory in Agda. As part of this I need to prove a bunch of basic properties around products/monoidal categories. A bunch of these ...
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What was the first proof assistant with eta equality for records?
The Agda language supports eta equality for (non-(co)inductive) record types:
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Can Agda proofs be trusted and do they conform to a specific, well-defined type theory?
When using Agda proofs, how can you know whether to trust it? Also, do they conform to a specific, well-defined type theory?
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What are the conditions for Agda to detect that induction-recursion has a least fixed point?
This is a 3rd in a series of questions, spurred by my attempts to encode an argument by Danielsson [1] [2] regarding existence of syntactically non-strictly positive datatype.
The idea (rephrased):
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Lower bounds in type theory proof assistant with ordinals and universes without axioms
I saw a PowerPoint that claimed to achieve $\psi_0(\Gamma_{\Omega+1})$ in Agda without any axioms. I was wondering if a better lower bound exists in 2024?
My ...
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Descriptions of heterogenous datatypes
When attempting to describe the datatype as appearing in my previous question, using indexed descriptions in style of The Gentle Art of Levitation to describe this datatype (using Agda for examples):
<...
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