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# Lambda Calculus Examples
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A series of Lambda Calculus implementations starting from Simply Typed
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evaluation, then work up through bidirectional typechecking,
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normalization by evaluation, elaboration and then various type system
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extensions.
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evaluation, then work up through bidirectional typechecking, normalization by
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evaluation, elaboration and various type system extensions.
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These examples build up sequentially, but each module is a standalone program
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that can be read independently. we skip parsing for brevity but include pretty
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printers from the concrete syntax to a human readable notation to make the
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examples easier to read.
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The goal is to provide best practices examples of all the features you
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might want to include in your custom language in one place.
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The goal is to provide best practices examples of all the features you might
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want to include in your custom language in one place.
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- [X] SimplyTypedEvaluation
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- [X] BidirectionalTypechecking
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- [X] Martin-Lof Type Theory (Pi and Sigma Types)
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- [X] Type Universes
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- [X] Universe Polymorphism
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- [ ] Indexed Inductive Types (with eliminators)
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- [ ] Dependent Patern Matching
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- [ ] Case-Trees
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- [ ] Termination / Coverage Checking
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- [ ] Implicit Universe Levels with Constraint Solving
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- [ ] Tarski Universes
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- [ ] Implicits
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- [ ] Indexed Inductive Types
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- [ ] Equality
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- [ ] Case-Trees
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- [ ] Row Polymorphism
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- [ ] Linear Types
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- [ ] View Patterns
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- [ ] Cubical
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- [ ] Modules
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Additionally we plan to provide complete examples of STLC, SystemF, and MLTT

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