https://github.com/tarao/lambda-scala

Type level lambda calculus in Scala
https://github.com/tarao/lambda-scala

lambda-calculus scala typelevel

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Type level lambda calculus in Scala

• Host: GitHub
• URL: https://github.com/tarao/lambda-scala
• Owner: tarao
• Created: 2015-05-05T04:53:57.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2015-05-05T04:54:21.000Z (over 9 years ago)
• Last Synced: 2023-03-12T22:43:13.513Z (over 1 year ago)
• Topics: lambda-calculus, scala, typelevel
• Language: Scala
• Size: 97.7 KB
• Stars: 33
• Watchers: 4
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
Type level lambda calculus in Scala

===================================

This repository demonstrates an implementation of lambda calculus in

Scala types.

Untyped lambda calculus

-----------------------

```scala

import lambda._

case class Equals[A >: B <: B, B]() // this checks type equality

type S = x ->: y ->: z ->: ( x @@ z @@ (y @@ z) )

type K = x ->: y ->: x

type result = ( S @@ K @@ K @@ a ) # ->*

Equals[result, a]

```

More examples are found in [TermSpec.scala][example].

### Syntax

|                         |Code              |

|:------------------------|:-----------------|

|Variables                |`a`, `b`, ..., `z`|

|Abstraction              |`v ->: M`         |

|Application              |`M @@ N`          |

|Terms                    |`M`, `N`          |

|1-step beta reduction    |`M # ->`          |

|Multi-step beta reduction|`M # ->*`         |

- You can define your own variables by calling `#next` of existing (last defined) variable

  ```scala

  type variableName1 = z #next

  type variableName2 = variableName1 #next

  ```

- You may need parenthesis to avoid ambiguity

### Capture-avoiding substitutions

Lambda terms are converted internally to

[De Bruijn indexed terms][debruijn] and indices are shifted during

substitution to ensure capture-avoiding semantics.

License

-------

- Copyright (C) INA Lintaro

- MIT License

References

----------

- [Scala type level encoding of the SKI calculus][ski]

- [Type-Level Programming in Scala][typelevel]

[example]: src/test/scala/lambda/TermSpec.scala

[debruijn]: http://en.wikipedia.org/wiki/De_Bruijn_index

[ski]: https://michid.wordpress.com/2010/01/29/scala-type-level-encoding-of-the-ski-calculus/

[typelevel]: https://apocalisp.wordpress.com/2010/06/08/type-level-programming-in-scala/