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https://github.com/brendanzab/rust-nbe-for-mltt

Normalization by evaluation for Martin-Löf Type Theory with dependent records
https://github.com/brendanzab/rust-nbe-for-mltt

bidirectional-typechecking debruijn-indices dependent-record-types dependent-records dependent-types normalization-by-evaluation rust semantic-typechecking type-checker type-inference type-system type-theory unification

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Normalization by evaluation for Martin-Löf Type Theory with dependent records

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# rust-nbe-for-mltt



This originally started as a Rust port of Danny Gratzer's implementation of

[Normalization by Evaluation for Martin-Löf Type Theory][nbe-for-mltt], but it

has a slightly different architecture and some additional language features.

The algorithm for the insertion and unification of metavariables was partly

taken from Andras Korvacs' [Minimal TT Exampls][minimal-tt-examples] and

[smalltt][smalltt] (although gluing is not yet implemented here).

It will probably become the basis for a new front-end for

[Pikelet](https://github.com/pikelet-lang/pikelet).



In traditional type checking and normalization that uses [DeBruijn indices][de-bruijn-indices],

you are required to shift variable indices whenever you open up binders. This

is extremely expensive, and rules out future optimizations, like [using

visitors][visitors] to reduce the number of intermediate allocations as the AST

is traversed. This implementation avoids these problems by using a "semantic

type checking"  algorithm that uses DeBruijn indices for the core syntax, and

DeBruijn levels in the syntax of the semantic domain.



| Syntax        | Binding method              | Example                         |

|---------------|-----------------------------|---------------------------------|

| Concrete      | Nominal                     | `λz. (λy. y (λx. x)) (λx. z x)` |

| Core          | Nameless (DeBruijn Indices) | `λ . (λ . 0 (λ . 0)) (λ . 1 0)` |

| Domain        | Nameless (DeBruijn Levels)  | `λ . (λ . 1 (λ . 2)) (λ . 0 1)` |



[nbe-for-mltt]: https://github.com/jozefg/nbe-for-mltt

[minimal-tt-examples]: https://github.com/AndrasKovacs/minimal-tt-examples

[smalltt]: https://github.com/AndrasKovacs/smalltt

[de-bruijn-indices]: https://en.wikipedia.org/wiki/De_Bruijn_index

[visitors]: https://github.com/pikelet-lang/pikelet/issues/75



## TODO



- [x] Convert data types to Rust

- [x] Port NbE and bidirectional type checking

- [x] Add a parser for the concrete syntax

- [x] Desugaring of concrete syntax to core syntax

- [x] Resugaring of core syntax to concrete syntax

- [ ] Pretty printing

    - [x] Basic pretty printing

    - [x] Preserve pretty names through type checking and normalization

    - [ ] Unfold metavariables when pretty printing values

    - [ ] Attempt to avoid unfolding variables when pretty printing values

- [x] Add a REPL

- [x] Add span information to ASTs to improve diagnostics

- [ ] Pattern matching elaboration

    - [x] Simple cases

    - [ ] Nested cases

    - [ ] Multiple scrutinees

    - [ ] Lambda case

- [x] Dependent record types

- [x] Primitive operations

- [ ] Unification

    - [x] Basic unification

    - [x] Function eta rules

    - [x] Record eta rules

    - [ ] [Pruning](https://gitter.im/pikelet-lang/Lobby?at=5cd519e60f381d0a768e7811)

    - [ ] [Skolemization](https://gitter.im/pikelet-lang/Lobby?at=5cd129ca6a84d76ed85bbefd)

- [x] Metavariable insertion

- [ ] Integration tests

  - [ ] Parse (pass)

  - [ ] Parse (fail)

  - [x] Elaboration (pass)

  - [ ] Elaboration (fail)

  - [ ] Normalization tests

  - [x] Sample modules

- [ ] Error recovery in:

  - [x] Lexer

  - [ ] Parser

  - [ ] Elaborator

  - [ ] Validator