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In redtt, we have dealt with restrictions by parameterizing typechecking over an equivalence relation on dimensions; but in the evaluator, it is more complicated, since we have seemed to need to actua…
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Turns out an inductive definition of terms without their type annotations is not super useful.
In particular we already lose the ability to check local closure, since bound variables may appear in …
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RedPRL's syntactic framework is two-level: there is a theory of parameters, and then second-order operator signatures are indexed over this theory. Then, the second-order theory is generated from such…
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Considering there has been an actual type system with conversion rules for a while:
http://www.cse.chalmers.se/~coquand/face.pdf
It would be interesting to have a proper proof assistant which imple…
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See https://github.com/jonsterling/JonPRL/blob/master/src/refiner/rules/ceq.fun#L169
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We can probably just try and use the linear pattern unification machinery from `sml-typed-abts` here; I suppose it might be nice to have a bit more general unification, but this would at least be a go…
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In JonPRL, we constructed explicit derivations as the syntheses of the sequent judgment, rather than merely extracting programs. This was perhaps useful for a couple reasons:
1. It was helpful for deb…
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In the _Definition_, we should cite and briefly summarize both _Syntax and Semantics of Abstract Binding Trees_ and _Type Refinements for the Working Class_.
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No need to add custom infix notation just yet; but we do need to set up the `parcom` machinery for parsing built-in infix operators properly, as well as `ap(M;N)` by adjacency (`M N`).
We had this in…
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I think that cubical type theory is sufficiently technical and not-yet-figured-out that it might be a bit too advanced a topic. cubical type theories as published today do not have the canonicity prop…