https://github.com/phenax/ts-theorem-provinator

Experiment to use typescript's type system for theorem proving
https://github.com/phenax/ts-theorem-provinator

theorem-prover typescript typescript-types

Last synced: about 2 months ago
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Experiment to use typescript's type system for theorem proving

• Host: GitHub
• URL: https://github.com/phenax/ts-theorem-provinator
• Owner: phenax
• License: mit
• Created: 2023-12-10T12:03:40.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-12-22T14:55:15.000Z (over 1 year ago)
• Last Synced: 2025-03-28T04:30:40.166Z (2 months ago)
• Topics: theorem-prover, typescript, typescript-types
• Language: TypeScript
• Homepage:
• Size: 30.3 KB
• Stars: 5
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Theorem prover in ts types

Experiment to use typescript's type system to make a shitty theorem prover.

### Commutativity of addition in ts types or something?

```typescript

export type Commutativity = Rewrite, Add>;


export interface Comm_Base_Proof {

  type: 'rewrite',

  left: Equation, Add>; // 0 + b = b + 0

  right: ChainRewrites<[

    IdentityR,         // b = b + 0

    Sym>,     // b + 0 = b + 0

    Refl>,     // true

  ], this['left']>;

};


export interface Comm_Inductive_Proof {

  type: 'rewrite',

  left: Equation, B>, Add>>;  // succ(a) + b = b + succ(a)

  right: ChainRewrites<[

    SumSucc,          // succ(a + b) = b + succ(a)

    Commutativity,    // succ(b + a) = b + succ(a)

    SumSuccR,         // succ(b + a) = succ(b + a)

    Refl>>,  // true

  ], this['left']>;

};


export namespace spec {

  export type commutativity = [

    assert>>,

    assert>>,

  ]

}

```