55 lines
1022 B
Markdown
55 lines
1022 B
Markdown
# pi
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A dependently typed system
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# Implemented
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* A Basic dependent lambda calculus
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* lambda abstractions
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* variables
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* pi types
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* type of types
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* let ... in ...
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* Unit type
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* Empty type
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* Natural numbers
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* Σ Types
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* Martin-Löf Identity types
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# TODO
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* Universes (a la tarksi)
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* Elaboration
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* Implicit arguments
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* Universe family application
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* Syntax level russel universes
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* Universe of all other universes? (universe polymorphism)
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* Inductives
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* Indexed inductives
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## Things that could be fun to do sometime eventually
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* Pattern matching in elaborator
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* Write down the rules
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* Performence optimisation?
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* Compile to scheme
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# References
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Some of the material I found helpful in groking dependent type checking:
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* Coquand, Thierry. “An Algorithm for Type-Checking Dependent Types.” Science of Computer Programming 26, no. 1–3 (May 1996): 167–77. https://doi.org/10.1016/0167-6423(95)00021-6.
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* Brady, Edwin. "SPLV20 course notes". GitHub. https://github.com/edwinb/SPLV20
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