https://github.com/plt-amy/dep

A very small implementation of the Calculus of Constructions for experimentation purposes
https://github.com/plt-amy/dep

type-theory

Last synced: 3 months ago
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A very small implementation of the Calculus of Constructions for experimentation purposes

• Host: GitHub
• URL: https://github.com/plt-amy/dep
• Owner: plt-amy
• License: bsd-3-clause
• Created: 2018-06-17T23:08:35.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2018-06-17T23:16:53.000Z (over 6 years ago)
• Last Synced: 2024-05-01T16:34:57.365Z (7 months ago)
• Topics: type-theory
• Language: Haskell
• Size: 8.79 KB
• Stars: 12
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Changelog: ChangeLog.md
  • License: LICENSE

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dep

===

A small implementation of the Calculus of Constructions, a pure type

system (PTS) corresponding to the λΠ corner of Barendgret's

lambda cube. That is, it has:

  - terms depending on terms  (functions)

  - types depending on types  (type operators)

  - types depending on terms  (dependent functions)

  - values depending on types (polymorphism)

While simply-typed languages have distinct "type level" and "value

level" grammars, the CoC does away with the stratification by merging

these levels into a single language, expressed by the following Haskell

data type.

```haskell

data Term

  = Var String -- x

  | Lam String Term Term -- \(x : t). e

  | Pi String Term Term -- forall (x : k). t

  | Term :$ Term -- f x

  | Term ::: Term -- e : t

  | Type Int -- type i

  deriving (Eq, Ord)

```