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Finally it's worth noting that the typed tagless approach was originally developed as a way to encode partial evaluation in typed languages: the first paper was "Finally Tagless, Partially Evaluated: Tagless Staged Interpreters for Simpler Typed Languages"
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Yeah, it's super interesting! I really want to see something like this explored more in the future, perhaps treating 'phase' as a partial order on types. Conor Mc Bride has mentioned this quite a few times. Seems like a nicer approach to C++, D, and Rust's const expressions.
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Davies and Pfenning "A modal analysis of staged computation" develops a modal type theory for partial evaluation (allowing multiple stages) that might be exactly what you want.
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Thanks! We have a graded generalisation of Davies and Pfenning's system sketched on paper. Just need the person power to work on the implementation and work out the details!
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