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+# The "Ory Permission Language" Specification
+
+Enforcing fine-grained permissions is a critical building block of mature
+technology solutions that protect privacy and identity in the information age.
+Several proprietary languages to represent permission already exist, namely the
+[Authzed Schema Language](https://docs.authzed.com/reference/schema-lang) and
+[Auth0 FGA](https://docs.fga.dev/). Most permissions are defined by normal
+developers who typically are most familiar with Web technologies like JavaScript
+or Typescript. We see the need for a developer-friendly configuration language
+for permissions that has such a small learning curve that most developers can
+understand and use it with close to no effort. We therefore chose to define our
+permissions configuration language as a subset of the most common
+general-purpose programming language: JavaScript/TypeScript.
+
+The Ory Permission Language is a syntactical subset of TypeScript. Along with
+type definitions for the syntax elements of the language (such as `Namespace` or
+`Context`), users can get context help from their IDE while writing the
+configuration.
+
+## Notation
+
+The syntax is specified using the Extended Backus-Naur Form (EBNF):
+
+```ebnf
+Production  = production_name "=" [ Expression ] "." .
+Expression  = Alternative { "|" Alternative } .
+Alternative = Term { Term } .
+Term        = production_name | token [ "…" token ] | Group | Option | Repetition .
+Group       = "(" Expression ")" .
+Option      = "[" Expression "]" .
+Repetition  = "{" Expression "}" .
+```
+
+Productions are expressions constructed from terms and the following operators,
+in increasing precedence:
+
+```ebnf
+|   alternation
+()  grouping
+[]  option (0 or 1 times)
+{}  repetition (0 to n times)
+```
+
+Lower-case production names are used to identify lexical tokens. Non-terminals
+are in CamelCase. Lexical tokens are enclosed in double quotes `""` or single
+quotes `''`.
+
+The form `a … b` represents the set of characters from a through b as
+alternatives. The horizontal ellipsis `…` is also used elsewhere in the spec to
+informally denote various enumerations or code snippets that are not further
+specified.
+
+## Configuraton text representation
+
+The configuration is encoded in UTF-8.
+
+## Lexical elements
+
+### Comments
+
+1. Line comments start with the character sequence `//` and stop at the end of
+   the line.
+2. General comments start with the character sequence `/*` and stop with the
+   first subsequent character sequence `*/`.
+3. Documentation comments start with the character sequence `/**` and stop with
+   the first subsequent character sequence `*/`.
+
+### Identifiers
+
+Identifiers name program entities such as variables and types. An identifier is
+a sequence of one or more letters and digits. The first character in an
+identifier must be a letter.
+
+```ebnf
+identifier = letter { letter | digit } .
+digit      = "0" … "9" .
+letter     = "A" … "Z" | "a" … "z" | "_" .
+```
+
+### String literals
+
+String literals represent string constants as sequences of characters.
+
+```ebnf
+string_lit    = single_quoted | double_quoted .
+single_quoted = "'" identifier "'" .
+double_quoted = '"' identifier '"' .
+```
+
+### Keywords
+
+The configuration language has the following keywords:
+
+- `class`
+- `implements`
+- `related`
+- `permits`
+- `this`
+- `ctx`
+- `id`
+- `imports`
+- `exports`
+- `as`
+
+### Builtin Types
+
+The following types are built in:
+
+- `Context`
+- `Namespace`
+- `Namespace[]`
+- `boolean`
+- `string`
+- `SubjectSet<T, R>`
+
+In TypeScript, they would be defined as follows:
+
+```typescript
+type Context = { subject: never }
+
+interface Namespace {
+  related?: { [relation: string]: Namespace[] }
+  permits?: { [method: string]: (ctx: Context) => boolean }
+}
+
+interface Array<Namespace> {
+  includes(element: Namespace): boolean
+  traverse(iteratorfn: (element: Namespace) => boolean): boolean
+}
+
+type SubjectSet<A extends Namespace, R extends keyof A["related"]> =
+  A["related"][R] extends Array<infer T> ? T : never
+```
+
+### Operators
+
+The following character sequences represent boolean operators:
+
+| Operator | Signature      | Semantic                             |
+| -------- | -------------- | ------------------------------------ |
+| `&&`     | _x_ `&&` _y_   | true iff. both _x_ and _y_ are true  |
+| `\|\|`   | _x_ `\|\|` _y_ | true iff. either _x_ or _y_ are true |
+| `!`      | `!` _x_        | true iff. _x_ is false               |
+
+The following character sequences represent miscellaneous operators:
+
+| Operator | Example                                  | Semantic                                                          |
+| -------- | ---------------------------------------- | ----------------------------------------------------------------- |
+| `(`, `)` | `x()`                                    | call function `x`                                                 |
+| `[]`     | `T[]`                                    | `T` is an array type                                              |
+| `<`, `>` | `SubjectSet<Group, "members">`           | Type reference to the "members" relation of the "Group" namespace |
+| `{`, `}` | `class x {}`                             | Scope delimiters                                                  |
+| `=>`     | `list.transitive(el => f(el))`           | Lambda definition token.                                          |
+| `.`      | `this.x`                                 | Property traversal token                                          |
+| `:`      | `relation: type`                         | Relation/type separator token                                     |
+| `=`      | `permits = {...}`                        | Assignment token                                                  |
+| `,`      | `{x: 1, y: 2}`                           | Property separator                                                |
+| `'`      | `'string'`                               | Single quoted string literal                                      |
+| `"`      | `"string"`                               | Double quoted string literal                                      |
+| `*`      | `import * from @ory/permission-language` | Import glob                                                       |
+| `\|`     | `(User \| Group)[]`                      | Type union                                                        |
+
+## Statements
+
+### Type declaration
+
+The top level of the configuration consists of a list of `class` declarations
+for each namespace. Each `class` consists of relation declarations and
+permission declarations.
+
+```ebnf
+Config          = [ ClassDecl ] .
+ClassDecl       = "class" identifier "implements" "Namespace" "{" ClassSpec "}" .
+ClassSpec       = [ RelationDecls ] | [ PermissionDefns] .
+```
+
+The following example declares the type _User_.
+
+```ts
+class User implements Namespace {}
+```
+
+### Relation declaration
+
+The `related` section of type declarations defines relations. Unlike regular
+TypeScript, `RelationName` must be a unique identifier used as the relation
+strings in the tuples. The `TypeName` must be the name of another `type` that is
+defined above or below (in TypeScript: a class that implements `Namespace`).
+
+Type unions (`|`) can be used to denote that a relation can have subjects of
+multiple types, e.g., `viewers: (User | SubjectSet<Group, "members">)[]`,
+meaning that the subject of the "viewer" relation can be either a "User", or a
+subject set "Group#members".
+
+```ebnf
+RelationDecls   = "related" "=" "{" { RelationName ":" ArrayType } "}" .
+RelationName    = identifier .
+ArrayType       = RelationType | ( "(" RelationType { "|" RelationType } ")" ) "[]" .
+RelationType    = SubjectType | SubjectSetType .
+SubjectType     = TypeName .
+SubjectSetType  = "SubjectSet" "<" TypeName, string_lit ">" .
+TypeName        = identifier .
+```
+
+Note that all relations are defined as array types `T[]` because there are
+naturally only many-to-many relations in Keto.
+
+The following declares a type _Document_ with three relations: _owners_ and
+_viewers_, both of which have _users_ as subjects. Additionally, the relation
+_parent_ has type _Document_.
+
+```ts
+class User {}
+
+class Document {
+  related = {
+    parents: Document[]
+    owners: User[]
+    viewers: User[]
+  }
+}
+```
+
+### Permission definition
+
+Permissions are defined as functions within class declarations that take a
+parameter `ctx` of type `Context` and evaluate to a boolean `true` or `false`.
+
+The type annotations for `ctx` and the return value are optional.
+
+```ebnf
+PermissionDefns = "permits" "=" "{" Permission [ "," Permission ] "}" .
+Permission      = PermissionSign "=>" PermissionBody .
+PermissionSign  = PermissionName ":" "(" "ctx" [ ":" "Context" ] ")" [ ":" "boolean" ] .
+PermissionName  = identifier .
+```
+
+The `ctx` object is a fixed parameter that contains the `subject` for which the
+permission check should be conducted:
+
+```ts
+ctx = { subject: "some_user_id" }
+```
+
+The context will contain more fields in the future, e.g., the IP range or
+geolocation, the time of day, or the security level of the device making the
+request.
+
+```ebnf
+PermissionBody  = ( "(" PermissionBody ")" ) | ( "!" PermissionBody ) | ( PermissionCheck | { Operator PermissionBody } ) .
+Operator        = "||" | "&&" .
+PermissionCheck = TransitiveCheck | IncludesCheck .
+```
+
+The body of a permission check is either one of:
+
+- a `IncludesCheck`, a check that something is in a set, e.g.,
+  `this.related.viewers.includes(ctx.subject)`:
+
+  ```ebnf
+  IncludesCheck = Var "." "related" "." RelationName "." "includes" "(" "ctx" "." "subject" ")" .
+  Var           = identifier .
+  ```
+
+- a `TranstitiveCheck`, a call to a permission on a relation, e.g.,
+  `this.related.parents.transitive(p => p.permits.view(ctx))`:
+
+  ```ebnf
+  TransitiveCheck = "this" "." "related" "." RelationName "." "transitive" "(" Var "=>" ( PermissionCall | IncludesCheck ) ")" .
+  PermissionCall  = Var "." "permits" "." PermissionName "(" "ctx" ")" .
+  ```
+
+## Implementation notes
+
+`IncludeCheck` and `TransitiveCheck` translate to Zanzibar concepts as follows:
+
+| Keto Config                                               | Zanzibar AST                                                                         |
+| --------------------------------------------------------- | ------------------------------------------------------------------------------------ |
+| `this.related.R.includes(ctx.subject)`                    | `computed_userset { relation: "R" } }`                                               |
+| `this.related.R.transitive(x = x.permits.P(ctx.subject))` | `tuple_to_userset { tupleset { relation: "R" } computed_userset { relation: "P" } }` |
+
+## Type checking
+
+The following type checks are performed once the config is fully parsed:
+
+- Given a `TypeName` as `X` (e.g., in `RelationDecls`), we check that there
+  exists a class declaration for `X`.
+- Given a `SubjectSetType` as `SubjectSet<T, R>`, we check that `R` is a
+  relation defined for `T`.
+- Given an `IncludesCheck` as `this.related.R.includes(ctx.subject)`, we check
+  that
+  - `R` is a relation defined for the current namespace.
+- Given a `TransitiveCheck` as
+  `this.related.R.transitive(x = x.permits.P(ctx.subject))`, we check that
+  - `R` is a relation defined for the current namespace and that
+  - `P` is a permission defined for all types referenced by `R`.
+- Given a `TransitiveCheck` as
+  `this.related.R.transitive(x = x.related.S.includes(ctx.subject))`, we check
+  that
+  - `R` is a relation defined for the current namespace and that
+  - `S` is a relation defined for all types referenced by `R`.
+
+## Examples
+
+The config can be type-checked in `strict` mode by TypeScript with the
+[noLib](https://www.typescriptlang.org/tsconfig#noLib) option (preventing the
+standard globals), and the
+[strictPropertyInitialization](https://www.typescriptlang.org/tsconfig#strictPropertyInitialization)
+option (allowing uninitialized properties).
+
+```ts
+class User implements Namespace {
+  related: {
+    manager: User[]
+  }
+}
+
+class Group implements Namespace {
+  related: {
+    members: (User | Group)[]
+  }
+}
+
+class Folder implements Namespace {
+  related: {
+    parents: File[]
+    viewers: (User | SubjectSet<Group, "members">)[]
+  }
+
+  permits = {
+    view: (ctx: Context): boolean => this.related.viewers.includes(ctx.subject),
+  }
+}
+
+class File implements Namespace {
+  related: {
+    parents: (File | Folder)[]
+    viewers: (User | SubjectSet<Group, "members">)[]
+    owners: (User | SubjectSet<Group, "members">)[]
+    siblings: File[]
+  }
+
+  permits = {
+    view: (ctx: Context): boolean =>
+      this.related.parents.traverse((p) =>
+        p.related.viewers.includes(ctx.subject),
+      ) ||
+      this.related.parents.traverse((p) => p.permits.view(ctx)) ||
+      this.related.viewers.includes(ctx.subject) ||
+      this.related.owners.includes(ctx.subject),
+
+    edit: (ctx: Context) => this.related.owners.includes(ctx.subject),
+
+    rename: (ctx: Context) =>
+      this.related.siblings.traverse((s) => s.permits.edit(ctx)),
+  }
+}
+```