https://github.com/susisu/system-f-js-impl

An implementation of System F in JS
https://github.com/susisu/system-f-js-impl

javascript system-f

Last synced: 2 days ago
JSON representation

An implementation of System F in JS

• Host: GitHub
• URL: https://github.com/susisu/system-f-js-impl
• Owner: susisu
• Created: 2017-05-28T01:29:54.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2017-05-28T05:21:41.000Z (over 7 years ago)
• Last Synced: 2024-11-06T04:41:30.650Z (about 2 months ago)
• Topics: javascript, system-f
• Language: JavaScript
• Homepage:
• Size: 11.7 KB
• Stars: 4
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
An implementation of [System F](https://en.wikipedia.org/wiki/System_F) in JavaScript, for my practicing and learning it and its treatment.

``` shell

git clone https://github.com/susisu/system-f-js-impl.git

cd system-f-js-impl

npm install

npm start

```

## Syntax

```

t ::=              -- term

      x            -- variable

      fun x: T. t  -- abstraction

      t t          -- application

      fun2 X. t    -- type abstraction

      t [T]        -- type application

T ::=

      X            -- type variable

      T -> T       -- arrow type (for abstractions)

      forall X. T  -- universal type (for type abstractions)

```

## Instructions

```

Variable X;       -- assumes type variable X

Axiom x: T;       -- assumes variable x: T (synonym: Hypothesis)

Define x = t;     -- defines x = t

Theorem x: T = t; -- checks t has a type T and defines x = t (synonyms: Lemma, Corollary)

Reduce t;         -- performs full beta-reduction on t

Print x;          -- prints term bound to x

Clear;            -- clears the context

```

## Example

```

> Variable False;

False is assumed.

> Axiom ex: forall X. False -> X;

ex: forall X. False -> X is assumed.

> Axiom dne: forall X. ((X -> False) -> False) -> X;

dne: forall X. ((X -> False) -> False) -> X is assumed.

> Theorem peirce: forall A, B. ((A -> B) -> A) -> A

| = fun2 A.

|   fun2 B.

|   dne [((A -> B) -> A) -> A] (

|     fun H: (((A -> B) -> A) -> A) -> False.

|     H (

|       fun H0: (A -> B) -> A.

|       H0 (

|         fun H1: A.

|         ex [B] (

|           H (

|             fun H2: (A -> B) -> A.

|             H1

|           )

|         )

|       )

|     )

|   );

peirce: forall A. forall B. ((A -> B) -> A) -> A is defined.

> Print peirce;

peirce: forall A. forall B. ((A -> B) -> A) -> A

= fun2 A. fun2 B. dne [((A -> B) -> A) -> A] (fun H: (((A -> B) -> A) -> A) -> False. H (fun H0: (A -> B) -> A. H0 (fun H1: A. ex [B] (H (fun H2: (A -> B) -> A. H1)))))

> Clear;

> Print peirce;

Reference Error at (line 1, column 1):

  unbound variable: peirce

> Define s = fun2 A, B, C. fun x: A -> B -> C, y : A -> B, z : A. x z (y z);

s: forall A. forall B. forall C. (A -> B -> C) -> (A -> B) -> A -> C is defined.

> Define k = fun2 A, B. fun x: A, y : B. x;

k: forall A. forall B. A -> B -> A is defined.

> Define i = fun2 A. fun x: A. x;

i: forall A. A -> A is defined.

> Reduce fun2 X. fun x: X. s [X] [X] [X] (k [X] [X]) (i [X]) x;

fun2 A. fun a: A. a

```