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11 votes
5 answers
2k views

How do real-world proof assistants bind variables and check equality?

There are many possible ways to represent syntax with variable binding, such as named variables, De Bruijn indices, De Bruijn levels, locally nameless terms, nominal type theories, etc. There are also ...
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 ...
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