Schema Definition

Defining schema to communicate an API or standard.

A data definition language describes the structure of data. The structure defined by such a language can, in turn, be used to verify implementations, validate inputs, or generate code.

Most modern dedicated data definition languages or standards allow more than just describing whether a field is an integer or a string. Standards like OpenAPI and CDDL allow defining things like default values, ranges, and various other constraints. OpenAPI even allows for complex logical combinators.

A key difference, however, is that these standards do not unify schema and values—the thing that makes CUE so powerful. There is no value lattice. This limits these standards in various ways.

Core issues addressed by CUE

Validating backwards compatibility

CUE’s model makes it easy to verify that newer versions of schema are backwards-compatible with older versions.

Consider the following versions of the same API:

// Release notes:
// - You can now specify your age and your hobby!
#V1: {
    age:   >=0 & <=100
    hobby: string
// Release notes:
// - People get to be older than 100, so we relaxed it.
// - It seems not many people have a hobby, so we made it optional.
#V2: {
    age:    >=0 & <=150 // people get older now
    hobby?: string      // some people don't have a hobby
// Release notes:
// - Actually no one seems to have a hobby nowadays anymore, so we dropped the field.
#V3: {
    age: >=0 & <=150

Declarations with a name starting with # are definitions. Definitions are not emitted when converting to data, for instance when exporting to JSON, and thus do not need to be concrete in such cases. Definitions assume the definition of closed structs, which means a user may only use fields that are explicitly defined.

In CUE, an API is backwards compatible if it subsumes the older one, or if the old one is an instance of the new one.

This can be computed using the API:

inst, err := r.Compile("apis", /* text of the above API */)
if err != nil {
    // handle error
v1, err1 := inst.LookupField("V1")
v2, err2 := inst.LookupField("V2")
v3, err3 := inst.LookupField("V3")
if err1 != nil || err2 != nil || err3 != nil {
	 // handle errors

// Check if V2 is backwards compatible with V1
fmt.Println(v2.Value.Subsumes(v1.Value))) // true

// Check if V3 is backwards compatible with V2
fmt.Println(v3.Value.Subsumes(v2.Value))) // false

It is as simple as that. This is the kind of thing that is made possible by ordering all values in a lattice, like CUE does. For CUE, checking whether one API is an instance of another is like checking whether 3 is less than 4.

Note that V2 strictly relaxed the API relative to V1. It allowed specifying a wider age range and made the hobby field optional. In V3 the hobby field is explicitly disallowed. This is not backwards compatibly as it breaks previous field that did contain a hobby field.

The current API only reports a yea or nay. The plan is to give full actionable reports. Feedback welcome!

Combining constraints from different sources

Most data definition languages are often not explicitly defined for commutativity. For instance, CDDL, although much less expressive than CUE, introduces operators that break commutativity.

The additive property obtained by commutativity is of great value for data definition. Constraints often come from many sources. For instance, one can have constraints from a base template, from code, policies provided by different departments and policies provided by a client.

CUE’s additive nature of constraints allows piling up constraints, in any order, to obtain a new definition. Which leads us to the next topic.

Normalization of data definitions

Adding constraints from many sources can result in a lot of redundancy. Even worse, constraints can be specified in different logical forms, making their additive form verbose and unwieldy. This is fine if all a system does using these constraints is validate data. But this is problematic if the added constraints are to form the basis for, say, human consumption.

CUE’s logical inference engine automatically reduces constraints. Its API makes it possible to compute and select between various normal forms to optimize for a certain representation. This is used in CUE’s OpenAPI generator, for instance.


JSON Schema / OpenAPI

JSON Schema and OpenAPI are purely data-driven data definition standards. OpenAPI originates from Swagger. As of version 3, OpenAPI is more or less a subset of JSON Schema. OpenAPI is used to define Kubernetes Custom Resource Definitions. As of 1.15, this requires a variant of OpenAPI called Structural OpenAPI. We will collectively refer to these as OpenAPI henceforth.

OpenAPI does not have any expressions or references. They have powerful logical operators, though, that make them remarkably expressive.

An advantage of OpenAPI is that it is purely defined in terms of data (JSON). This allows sending it over the wire. It is defined such that implementing an interpreter is fairly straightforward.

One disadvantage is that it is very verbose. Compare the following two equivalent schema definitions:

// Definitions.

// Info describes...
Info: {
    // Name of the adapter.
    name: string

    // Templates.
    templates?: [...string]

    // Max is the limit.
    max?: uint & <100
  "openapi": "3.0.0",
  "info": {
    "title": "Definitions.",
    "version": "v1beta1"
  "components": {
    "schemas": {
      "Info": {
        "description": "Info describes...",
        "type": "object",
        "required": [
        "properties": {
          "name": {
            "description": "Name of the adapter.",
            "type": "string",
            "format": "string"
          "templates": {
            "description": "Templates.",
            "type": "array",
            "items": {
              "type": "string",
              "format": "string"
          "max": {
            "description": "Max is the limit",
            "type": "integer",
            "minimum": 0,
            "exclusiveMaximum": 100

The difference gets more extreme as more constraints and logical combinators are used.

OpenAPI and CUE both have theirs roles. The JSON format of OpenAPI makes it good interchange standard. CUE, on the other hand, can serve as an engine to generate and interpret OpenAPI constraints. Note that CUE is generally more expressive and many CUE constraints will not be encodeable in OpenAPI.

OPA / Rego

Although not designed as a data definition language, Rego, the language used for Open Policy Agent (OPA), also solves the issue of being able to add constraints from multiple sources.

Rego, like CUE, has its roots in logic programming. It is based on Datalog, a restricted form of Prolog, whereas CUE is based on typed-feature structure or graph unification. Typed-feature structures were designed to deal with the shortcomings of Prolog for applications in encoding human languages.

Using a Datalog variant for what is essentially a constraint validation task is somewhat curious. Datalog makes an excellent query language. But for constraint enforcement, it is a bit cumbersome as one effectively first needs to query values to which to apply the constraints. CUE collates the constraints with the location of the data to which they apply. As a result, CUE constraints look a lot like the data they constrain, unlike Rego which will be more reminiscent of a Datalog program.

But more importantly, CUE’s approach is more amenable to finding normalized and simplified representations of constraints, which makes it more suitable for creating OpenAPI from them.


The Concise Data Definition Language (CDDL) is used to define the structure of CBOR or JSON data. CDDL shares many of the same constructs from CUE, including disjunctions, embedding, optional fields, and definitions.

CDDL, however, has no value lattice and does not define mathematical properties of its data. There several other aspects in CDDL that contradict the use of a value lattice or make it harder to do so. Overall this restricts the expressiveness of CDDL compared to CUE while complicating the ability to combine constraints on types from multiple sources.

Unlike OpenAPI, CDDL is a domain-specific language (DSL). It needs a specific interpreter. It also has some non-trivial aspects to its evaluation, making it much harder than OpenAPI to implement.