All Questions
Tagged with agda type-theory
6
questions
1
vote
1
answer
376
views
Why does Agda use Set instead of Type?
In the 'Hello world' example in Agda — Agda 2.6.5 documentation, it straightforwardly uses Set as follows:
‘Hello world’ in Agda — Agda 2.6.5 documentation
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- 161
23
votes
0
answers
571
views
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 ...
- 3,200
1
vote
1
answer
300
views
Does Agda's --injective-type-constructors flag have canonicity?
Since 2010/01/07, when the Anti-classicality of Agda was proved by Chung-Kil Hur, Agda's --injective-type-constructors is separated from the main branch of Agda (...
- 279
22
votes
2
answers
409
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In what intensional type theories can absurdity be made definitionally proof irrelevant?
Various type theories have, over the years, explored extending the definitional equality with a variety of eta-laws and various forms of proof irrelevance.
Quite a lot of systems manage eta for ...
- 771
16
votes
2
answers
406
views
What are the upsides and downsides of typed vs untyped conversion?
What are the tradeoffs between untyped and type-directed conversion in dependent type theory, and is there any consensus on what's "better"?
Background
Generally speaking, in dependent type ...
- 394
26
votes
4
answers
2k
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What are the differences between MLTT and CIC?
In the theory and design of proof assistants based upon dependent types, I feel like there’s a somewhat cultural divide between the "MLTT" world (with Agda as the main representative proof ...
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