package example
import future.keywords

OPA is purpose built for reasoning about information represented in structured documents. The data that your service and its users publish can be inspected and transformed using OPA’s native query language Rego.

What is Rego?

Rego was inspired by Datalog, which is a well understood, decades old query language. Rego extends Datalog to support structured document models such as JSON.

Rego queries are assertions on data stored in OPA. These queries can be used to define policies that enumerate instances of data that violate the expected state of the system.

Why use Rego?

Use Rego for defining policy that is easy to read and write.

Rego focuses on providing powerful support for referencing nested documents and ensuring that queries are correct and unambiguous.

Rego is declarative so policy authors can focus on what queries should return rather than how queries should be executed. These queries are simpler and more concise than the equivalent in an imperative language.

Like other applications which support declarative query languages, OPA is able to optimize queries to improve performance.

The Basics

This section introduces the main aspects of Rego.

The simplest rule is a single expression and is defined in terms of a Scalar Value:

pi := 3.14159

Rules define the content of documents. We can query for the content of the pi document generated by the rule above:

pi

3.14159

Rules can also be defined in terms of Composite Values:

rect := {"width": 2, "height": 4}

The result:

rect

{
  "height": 4,
  "width": 2
}

You can compare two scalar or composite values, and when you do so you are checking if the two values are the same JSON value.

rect == {"height": 4, "width": 2}

true

You can define a new concept using a rule. For example, v below is true if the equality expression is true.

v if "hello" == "world"

If we evaluate v, the result is undefined because the body of the rule never evaluates to true. As a result, the document generated by the rule is not defined.

v

undefined decision

Expressions that refer to undefined values are also undefined. This includes comparisons such as !=.

v == true

undefined decision

v != true

undefined decision

We can define rules in terms of Variables as well:

t if { x := 42; y := 41; x > y }

The formal syntax uses the semicolon character ; to separate expressions. Rule bodies can separate expressions with newlines and omit the semicolon:

t2 if {
    x := 42
    y := 41
    x > y
}

Note that the future keyword if is optional. We could have written v and t2 like this:

v { "hello" == "world" }

t2 {
    x := 42
    y := 41
    x > y
}

When evaluating rule bodies, OPA searches for variable bindings that make all of the expressions true. There may be multiple sets of bindings that make the rule body true. The rule body can be understood intuitively as:

expression-1 AND expression-2 AND ... AND expression-N

The rule itself can be understood intuitively as:

rule-name IS value IF body

If the value is omitted, it defaults to true.

When we query for the value of t we see the obvious result:

t

true

Rego References help you refer to nested documents. For example, with:

sites := [{"name": "prod"}, {"name": "smoke1"}, {"name": "dev"}]

And

r if {
    some site in sites
    site.name == "prod"
}

The rule r above asserts that there exists (at least) one document within sites where the name attribute equals "prod".

The result:

r

true

We can generalize the example above with a rule that defines a set document instead of a boolean document:

q contains name if {
    some site in sites
    name := site.name
}

The value of q is a set of names

q

[
  "dev",
  "prod",
  "smoke1"
]

We can re-write the rule r from above to make use of q. We will call the new rule p:

p if q["prod"]

Querying p will have the same result:

p

true

As you can see, rules which have arguments can be queried with input values:

q["smoke2"]

undefined decision

If you made it this far, congratulations!

This section introduced the main aspects of Rego. The rest of this document walks through each part of the language in more detail.

For a concise reference, see the Policy Reference document.

Scalar Values

Scalar values are the simplest type of term in Rego. Scalar values can be Strings, numbers, booleans, or null.

Documents can be defined solely in terms of scalar values. This is useful for defining constants that are referenced in multiple places. For example:

greeting   := "Hello"
max_height := 42
pi         := 3.14159
allowed    := true
location   := null

These documents can be queried like any other:

[greeting, max_height, pi, allowed, location]

[
  "Hello",
  42,
  3.14159,
  true,
  null
]

Strings

Rego supports two different types of syntax for declaring strings. The first is likely to be the most familiar: characters surrounded by double quotes. In such strings, certain characters must be escaped to appear in the string, such as double quotes themselves, backslashes, etc. See the Policy Reference for a formal definition.

The other type of string declaration is a raw string declaration. These are made of characters surrounded by backticks (`), with the exception that raw strings may not contain backticks themselves. Raw strings are what they sound like: escape sequences are not interpreted, but instead taken as the literal text inside the backticks. For example, the raw string `hello\there` will be the text “hello\there”, not “hello” and “here” separated by a tab. Raw strings are particularly useful when constructing regular expressions for matching, as it eliminates the need to double escape special characters.

A simple example is a regex to match a valid Rego variable. With a regular string, the regex is "[a-zA-Z_]\\w*", but with raw strings, it becomes `[a-zA-Z_]\w*`.

Composite Values

Composite values define collections. In simple cases, composite values can be treated as constants like Scalar Values:

cube := {"width": 3, "height": 4, "depth": 5}

The result:

cube.width

3

Composite values can also be defined in terms of Variables or References. For example:

a := 42
b := false
c := null
d := {"a": a, "x": [b, c]}

+----+-------+------+---------------------------+
| a  |   b   |  c   |             d             |
+----+-------+------+---------------------------+
| 42 | false | null | {"a":42,"x":[false,null]} |
+----+-------+------+---------------------------+

By defining composite values in terms of variables and references, rules can define abstractions over raw data and other rules.

Objects

Objects are unordered key-value collections. In Rego, any value type can be used as an object key. For example, the following assignment maps port numbers to a list of IP addresses (represented as strings).

ips_by_port := {
    80: ["1.1.1.1", "1.1.1.2"],
    443: ["2.2.2.1"],
}

ips_by_port[80]

[
  "1.1.1.1",
  "1.1.1.2"
]

some port; ips_by_port[port][_] == "2.2.2.1"

+------+
| port |
+------+
| 443  |
+------+

When Rego values are converted to JSON non-string object keys are marshalled as strings (because JSON does not support non-string object keys).

ips_by_port

{
  "443": [
    "2.2.2.1"
  ],
  "80": [
    "1.1.1.1",
    "1.1.1.2"
  ]
}

Sets

In addition to arrays and objects, Rego supports set values. Sets are unordered collections of unique values. Just like other composite values, sets can be defined in terms of scalars, variables, references, and other composite values. For example:

s := {cube.width, cube.height, cube.depth}

+---------+
|    s    |
+---------+
| [3,4,5] |
+---------+

Set documents are collections of values without keys. OPA represents set documents as arrays when serializing to JSON or other formats that do not support a set data type. The important distinction between sets and arrays or objects is that sets are unkeyed while arrays and objects are keyed, i.e., you cannot refer to the index of an element within a set.

When comparing sets, the order of elements does not matter:

{1,2,3} == {3,1,2}

true

Because sets are unordered, variables inside sets must be unified with a ground value outside of the set. If the variable is not unified with a ground value outside the set, OPA will complain:

{1,2,3} == {3,x,2}

1 error occurred: 1:1: rego_unsafe_var_error: var x is unsafe

Because sets share curly-brace syntax with objects, and an empty object is defined with {}, an empty set has to be constructed with a different syntax:

count(set())

0

Variables

Variables are another kind of term in Rego. They appear in both the head and body of rules.

Variables appearing in the head of a rule can be thought of as input and output of the rule. Unlike many programming languages, where a variable is either an input or an output, in Rego a variable is simultaneously an input and an output. If a query supplies a value for a variable, that variable is an input, and if the query does not supply a value for a variable, that variable is an output.

For example:

sites := [
    {"name": "prod"},
    {"name": "smoke1"},
    {"name": "dev"}
]

q contains name if {
    some site in sites
    name := site.name
}

In this case, we evaluate q with a variable x (which is not bound to a value). As a result, the query returns all of the values for x and all of the values for q[x], which are always the same because q is a set.

q[x]

+----------+----------+
|    x     |   q[x]   |
+----------+----------+
| "dev"    | "dev"    |
| "prod"   | "prod"   |
| "smoke1" | "smoke1" |
+----------+----------+

On the other hand, if we evaluate q with an input value for name we can determine whether name exists in the document defined by q:

q["dev"]

"dev"

Variables appearing in the head of a rule must also appear in a non-negated equality expression within the same rule. This property ensures that if the rule is evaluated and all of the expressions evaluate to true for some set of variable bindings, the variable in the head of the rule will be defined.

References

References are used to access nested documents.

The examples in this section use the data defined in the Examples section.

The simplest reference contains no variables. For example, the following reference returns the hostname of the second server in the first site document from our example data:

sites[0].servers[1].hostname

"helium"

References are typically written using the “dot-access” style. The canonical form does away with . and closely resembles dictionary lookup in a language such as Python:

sites[0]["servers"][1]["hostname"]

"helium"

Both forms are valid, however, the dot-access style is typically more readable. Note that there are four cases where brackets must be used:

1. String keys containing characters other than [a-z], [A-Z], [0-9], or _ (underscore).
2. Non-string keys such as numbers, booleans, and null.
3. Variable keys which are described later.
4. Composite keys which are described later.

The prefix of a reference identifies the root document for that reference. In the example above this is sites. The root document may be:

• a local variable inside a rule.
• a rule inside the same package.
• a document stored in OPA.
• a documented temporarily provided to OPA as part of a transaction.
• an array, object or set, e.g. [1, 2, 3][0].
• a function call, e.g. split("a.b.c", ".")[1].
• a comprehension.

Variable Keys

References can include variables as keys. References written this way are used to select a value from every element in a collection.

The following reference will select the hostnames of all the servers in our example data:

sites[i].servers[j].hostname

+---+---+------------------------------+
| i | j | sites[i].servers[j].hostname |
+---+---+------------------------------+
| 0 | 0 | "hydrogen"                   |
| 0 | 1 | "helium"                     |
| 0 | 2 | "lithium"                    |
| 1 | 0 | "beryllium"                  |
| 1 | 1 | "boron"                      |
| 1 | 2 | "carbon"                     |
| 2 | 0 | "nitrogen"                   |
| 2 | 1 | "oxygen"                     |
+---+---+------------------------------+

Conceptually, this is the same as the following imperative (Python) code:

def hostnames(sites):
    result = []
    for site in sites:
        for server in site.servers:
            result.append(server.hostname)
    return result

In the reference above, we effectively used variables named i and j to iterate the collections. If the variables are unused outside the reference, we prefer to replace them with an underscore (_) character. The reference above can be rewritten as:

sites[_].servers[_].hostname

+------------------------------+
| sites[_].servers[_].hostname |
+------------------------------+
| "hydrogen"                   |
| "helium"                     |
| "lithium"                    |
| "beryllium"                  |
| "boron"                      |
| "carbon"                     |
| "nitrogen"                   |
| "oxygen"                     |
+------------------------------+

The underscore is special because it cannot be referred to by other parts of the rule, e.g., the other side of the expression, another expression, etc. The underscore can be thought of as a special iterator. Each time an underscore is specified, a new iterator is instantiated.

Under the hood, OPA translates the _ character to a unique variable name that does not conflict with variables and rules that are in scope.

Composite Keys

References can include Composite Values as keys if the key is being used to refer into a set. Composite keys may not be used in refs for base data documents, they are only valid for references into virtual documents.

This is useful for checking for the presence of composite values within a set, or extracting all values within a set matching some pattern. For example:

s := {[1, 2], [1, 4], [2, 6]}

s[[1, 2]]

[
  1,
  2
]

s[[1, x]]

+---+-----------+
| x | s[[1, x]] |
+---+-----------+
| 2 | [1,2]     |
| 4 | [1,4]     |
+---+-----------+

Multiple Expressions

Rules are often written in terms of multiple expressions that contain references to documents. In the following example, the rule defines a set of arrays where each array contains an application name and a hostname of a server where the application is deployed.

apps_and_hostnames[[name, hostname]] {
    some i, j, k
    name := apps[i].name
    server := apps[i].servers[_]
    sites[j].servers[k].name == server
    hostname := sites[j].servers[k].hostname
}

The result:

apps_and_hostnames[x]

+----------------------+-----------------------+
|          x           | apps_and_hostnames[x] |
+----------------------+-----------------------+
| ["mongodb","oxygen"] | ["mongodb","oxygen"]  |
| ["mysql","carbon"]   | ["mysql","carbon"]    |
| ["mysql","lithium"]  | ["mysql","lithium"]   |
| ["web","beryllium"]  | ["web","beryllium"]   |
| ["web","boron"]      | ["web","boron"]       |
| ["web","helium"]     | ["web","helium"]      |
| ["web","hydrogen"]   | ["web","hydrogen"]    |
| ["web","nitrogen"]   | ["web","nitrogen"]    |
+----------------------+-----------------------+

Don’t worry about understanding everything in this example right now. There are just two important points:

1. Several variables appear more than once in the body. When a variable is used in multiple locations, OPA will only produce documents for the rule with the variable bound to the same value in all expressions.
2. The rule is joining the apps and sites documents implicitly. In Rego (and other languages based on Datalog), joins are implicit.

Self-Joins

Using a different key on the same array or object provides the equivalent of self-join in SQL. For example, the following rule defines a document containing apps deployed on the same site as "mysql":

same_site[apps[k].name] {
    some i, j, k
    apps[i].name == "mysql"
    server := apps[i].servers[_]
    server == sites[j].servers[_].name
    other_server := sites[j].servers[_].name
    server != other_server
    other_server == apps[k].servers[_]
}

The result:

same_site[x]

+-------+--------------+
|   x   | same_site[x] |
+-------+--------------+
| "web" | "web"        |
+-------+--------------+

Comprehensions

Comprehensions provide a concise way of building Composite Values from sub-queries.

Like Rules, comprehensions consist of a head and a body. The body of a comprehension can be understood in exactly the same way as the body of a rule, that is, one or more expressions that must all be true in order for the overall body to be true. When the body evaluates to true, the head of the comprehension is evaluated to produce an element in the result.

The body of a comprehension is able to refer to variables defined in the outer body. For example:

region := "west"
names := [name | sites[i].region == region; name := sites[i].name]

+-----------------+--------+
|      names      | region |
+-----------------+--------+
| ["smoke","dev"] | "west" |
+-----------------+--------+

In the above query, the second expression contains an Array Comprehension that refers to the region variable. The region variable will be bound in the outer body.

When a comprehension refers to a variable in an outer body, OPA will reorder expressions in the outer body so that variables referred to in the comprehension are bound by the time the comprehension is evaluated.

Comprehensions are similar to the same constructs found in other languages like Python. For example, we could write the above comprehension in Python as follows:

# Python equivalent of Rego comprehension shown above.
names = [site.name for site in sites if site.region == "west"]

Comprehensions are often used to group elements by some key. A common use case for comprehensions is to assist in computing aggregate values (e.g., the number of containers running on a host).

Array Comprehensions

Array Comprehensions build array values out of sub-queries. Array Comprehensions have the form:

[ <term> | <body> ]

For example, the following rule defines an object where the keys are application names and the values are hostnames of servers where the application is deployed. The hostnames of servers are represented as an array.

app_to_hostnames[app_name] := hostnames if {
    app := apps[_]
    app_name := app.name
    hostnames := [hostname | name := app.servers[_]
                            s := sites[_].servers[_]
                            s.name == name
                            hostname := s.hostname]
}

The result:

app_to_hostnames[app]

+-----------+------------------------------------------------------+
|    app    |                app_to_hostnames[app]                 |
+-----------+------------------------------------------------------+
| "mongodb" | ["oxygen"]                                           |
| "mysql"   | ["lithium","carbon"]                                 |
| "web"     | ["hydrogen","helium","beryllium","boron","nitrogen"] |
+-----------+------------------------------------------------------+

Object Comprehensions

Object Comprehensions build object values out of sub-queries. Object Comprehensions have the form:

{ <key>: <term> | <body> }

We can use Object Comprehensions to write the rule from above as a comprehension instead:

app_to_hostnames := {app.name: hostnames |
    app := apps[_]
    hostnames := [hostname |
                    name := app.servers[_]
                    s := sites[_].servers[_]
                    s.name == name
                    hostname := s.hostname]
}

The result is the same:

app_to_hostnames[app]

+-----------+------------------------------------------------------+
|    app    |                app_to_hostnames[app]                 |
+-----------+------------------------------------------------------+
| "mongodb" | ["oxygen"]                                           |
| "mysql"   | ["lithium","carbon"]                                 |
| "web"     | ["hydrogen","helium","beryllium","boron","nitrogen"] |
+-----------+------------------------------------------------------+

Object comprehensions are not allowed to have conflicting entries, similar to rules:

{"foo": y | z := [1, 2, 3]; y := z[_] }

1 error occurred: "foo": eval_conflict_error: object keys must be unique

Set Comprehensions

Set Comprehensions build set values out of sub-queries. Set Comprehensions have the form:

{ <term> | <body> }

For example, to construct a set from an array:

a := [1, 2, 3, 4, 3, 4, 3, 4, 5]
b := {x | x = a[_]}

a
b

+---------------------+-------------+
|          a          |      b      |
+---------------------+-------------+
| [1,2,3,4,3,4,3,4,5] | [1,2,3,4,5] |
+---------------------+-------------+

Rules

Rules define the content of Virtual Documents in OPA. When OPA evaluates a rule, we say OPA generates the content of the document that is defined by the rule.

The sample code in this section make use of the data defined in Examples.

Generating Sets

The following rule defines a set containing the hostnames of all servers:

hostnames contains name if {
    name := sites[_].servers[_].hostname
}

Note that the (future) keyword if is optional here.

When we query for the content of hostnames we see the same data as we would if we queried using the sites[_].servers[_].hostname reference directly:

hostnames[name]

+-------------+-----------------+
|    name     | hostnames[name] |
+-------------+-----------------+
| "beryllium" | "beryllium"     |
| "boron"     | "boron"         |
| "carbon"    | "carbon"        |
| "helium"    | "helium"        |
| "hydrogen"  | "hydrogen"      |
| "lithium"   | "lithium"       |
| "nitrogen"  | "nitrogen"      |
| "oxygen"    | "oxygen"        |
+-------------+-----------------+

This example introduces a few important aspects of Rego.

First, the rule defines a set document where the contents are defined by the variable name. We know this rule defines a set document because the head only includes a key. All rules have the following form (where key, value, and body are all optional):

<name> <key>? <value>? <body>?

For a more formal definition of the rule syntax, see the Policy Reference document.

Second, the sites[_].servers[_].hostname fragment selects the hostname attribute from all of the objects in the servers collection. From reading the fragment in isolation we cannot tell whether the fragment refers to arrays or objects. We only know that it refers to a collections of values.

Third, the name := sites[_].servers[_].hostname expression binds the value of the hostname attribute to the variable name, which is also declared in the head of the rule.

Generating Objects

Rules that define objects are very similar to rules that define sets.

apps_by_hostname[hostname] := app if {
    some i
    server := sites[_].servers[_]
    hostname := server.hostname
    apps[i].servers[_] == server.name
    app := apps[i].name
}

The rule above defines an object that maps hostnames to app names. The main difference between this rule and one which defines a set is the rule head: in addition to declaring a key, the rule head also declares a value for the document.

The result:

apps_by_hostname["helium"]

"web"

Incremental Definitions

A rule may be defined multiple times with the same name. When a rule is defined this way, we refer to the rule definition as incremental because each definition is additive. The document produced by incrementally defined rules is the union of the documents produced by each individual rule.

For example, we can write a rule that abstracts over our servers and containers data as instances:

instances contains instance if {
    server := sites[_].servers[_]
    instance := {"address": server.hostname, "name": server.name}
}

instances contains instance if {
    container := containers[_]
    instance := {"address": container.ipaddress, "name": container.name}
}

If the head of the rule is same, we can chain multiple rule bodies together to obtain the same result. We don’t recommend using this form anymore.

instances contains instance if {
    server := sites[_].servers[_]
    instance := {"address": server.hostname, "name": server.name}
} {
    container := containers[_]
    instance := {"address": container.ipaddress, "name": container.name}
}

An incrementally defined rule can be intuitively understood as <rule-1> OR <rule-2> OR ... OR <rule-N>.

The result:

instances[x]

+-----------------------------------------------+-----------------------------------------------+
|                       x                       |                 instances[x]                  |
+-----------------------------------------------+-----------------------------------------------+
| {"address":"10.0.0.1","name":"big_stallman"}  | {"address":"10.0.0.1","name":"big_stallman"}  |
| {"address":"10.0.0.2","name":"cranky_euclid"} | {"address":"10.0.0.2","name":"cranky_euclid"} |
| {"address":"beryllium","name":"web-1000"}     | {"address":"beryllium","name":"web-1000"}     |
| {"address":"boron","name":"web-1001"}         | {"address":"boron","name":"web-1001"}         |
| {"address":"carbon","name":"db-1000"}         | {"address":"carbon","name":"db-1000"}         |
| {"address":"helium","name":"web-1"}           | {"address":"helium","name":"web-1"}           |
| {"address":"hydrogen","name":"web-0"}         | {"address":"hydrogen","name":"web-0"}         |
| {"address":"lithium","name":"db-0"}           | {"address":"lithium","name":"db-0"}           |
| {"address":"nitrogen","name":"web-dev"}       | {"address":"nitrogen","name":"web-dev"}       |
| {"address":"oxygen","name":"db-dev"}          | {"address":"oxygen","name":"db-dev"}          |
+-----------------------------------------------+-----------------------------------------------+

Complete Definitions

In addition to rules that partially define sets and objects, Rego also supports so-called complete definitions of any type of document. Rules provide a complete definition by omitting the key in the head. Complete definitions are commonly used for constants:

pi := 3.14159

Rego allows authors to omit the body of rules. If the body is omitted, it defaults to true.

Documents produced by rules with complete definitions can only have one value at a time. If evaluation produces multiple values for the same document, an error will be returned.

For example:

# Define user "bob" for test input.
user := "bob"

# Define two sets of users: power users and restricted users. Accidentally
# include "bob" in both.
power_users := {"alice", "bob", "fred"}
restricted_users := {"bob", "kim"}

# Power users get 32GB memory.
max_memory := 32 if power_users[user]

# Restricted users get 4GB memory.
max_memory := 4 if restricted_users[user]

Error:

1 error occurred: module.rego:16: eval_conflict_error: complete rules must not produce multiple outputs

OPA returns an error in this case because the rule definitions are in conflict. The value produced by max_memory cannot be 32 and 4 at the same time.

The documents produced by rules with complete definitions may still be undefined:

max_memory with user as "johnson"

undefined decision

In some cases, having an undefined result for a document is not desirable. In those cases, policies can use the Default Keyword to provide a fallback value.

Functions

Rego supports user-defined functions that can be called with the same semantics as Built-in Functions. They have access to both the the data Document and the input Document.

For example, the following function will return the result of trimming the spaces from a string and then splitting it by periods.

trim_and_split(s) := x if {
     t := trim(s, " ")
     x := split(t, ".")
}

trim_and_split("   foo.bar ")

[
  "foo",
  "bar"
]

Functions may have an arbitrary number of inputs, but exactly one output. Function arguments may be any kind of term. For example, suppose we have the following function:

foo([x, {"bar": y}]) := z if {
    z := {x: y}
}

The following calls would produce the logical mappings given:

If you need multiple outputs, write your functions so that the output is an array, object or set containing your results. If the output term is omitted, it is equivalent to having the output term be the literal true. Furthermore, if can be used to write shorter definitions. That is, the function declarations below are equivalent:

f(x) { x == "foo" }
f(x) if { x == "foo" }
f(x) if x == "foo"

f(x) := true { x == "foo" }
f(x) := true if { x == "foo" }
f(x) := true if x == "foo"

The outputs of user functions have some additional limitations, namely that they must resolve to a single value. If you write a function that has multiple possible bindings for an output variable, you will get a conflict error:

p(x) := y if {
    y := x[_]
}

p([1, 2, 3])

1 error occurred: module.rego:4: eval_conflict_error: functions must not produce multiple outputs for same inputs

It is possible in Rego to define a function more than once, to achieve a conditional selection of which function to execute:

Functions can be defined incrementally.

q(1, x) := y if {
    y := x
}
q(2, x) := y if {
    y := x*4
}

q(1, 2)

2

q(2, 2)

8

A given function call will execute all functions that match the signature given. If a call matches multiple functions, they must produce the same output, or else a conflict error will occur:

r(1, x) := y if {
    y := x
}

r(x, 2) := y if {
    y := x*4
}

r(1, 2)

1 error occurred: module.rego:4: eval_conflict_error: functions must not produce multiple outputs for same inputs

On the other hand, if a call matches no functions, then the result is undefined.

s(x, 2) := y if {
    y := x * 4
}

s(5, 2)

20

s(5, 3)

undefined decision

Negation

To generate the content of a Virtual Document, OPA attempts to bind variables in the body of the rule such that all expressions in the rule evaluate to True.

This generates the correct result when the expressions represent assertions about what states should exist in the data stored in OPA. In some cases, you want to express that certain states should not exist in the data stored in OPA. In these cases, negation must be used.

For safety, a variable appearing in a negated expression must also appear in another non-negated equality expression in the rule.

OPA will reorder expressions to ensure that negated expressions are evaluated after other non-negated expressions with the same variables. OPA will reject rules containing negated expressions that do not meet the safety criteria described above.

The simplest use of negation involves only scalar values or variables and is equivalent to complementing the operator:

t if {
    greeting := "hello"
    not greeting == "goodbye"
}

The result:

t

true

Negation is required to check whether some value does not exist in a collection. That is, complementing the operator in an expression such as p[_] == "foo" yields p[_] != "foo". However, this is not equivalent to not p["foo"].

For example, we can write a rule that defines a document containing names of apps not deployed on the "prod" site:

prod_servers contains name if {
    some site in sites
    site.name == "prod"
    some server in site.servers
    name := server.name
}

apps_in_prod contains name if {
    some site in sites
    some app in apps
    name := app.name
    some server in app.servers
    prod_servers[server]
}

apps_not_in_prod contains name if {
    some app in apps
    name := app.name
    not apps_in_prod[name]
}

The result:

apps_not_in_prod[name]

+-----------+------------------------+
|   name    | apps_not_in_prod[name] |
+-----------+------------------------+
| "mongodb" | "mongodb"              |
+-----------+------------------------+

Universal Quantification (FOR ALL)

Rego allows for several ways to express universal quantification.

For example, imagine you want to express a policy that says (in English):

There must be no apps named "bitcoin-miner".

The most expressive way to state this in Rego is using the every keyword:

import future.keywords.every

no_bitcoin_miners_using_every if {
    every app in apps {
        app.name != "bitcoin-miner"
    }
}

Variables in Rego are existentially quantified by default: when you write

array := ["one", "two", "three"]; array[i] == "three"

The query will be satisfied if there is an i such that the query’s expressions are simultaneously satisfied.

+-----------------------+---+
|         array         | i |
+-----------------------+---+
| ["one","two","three"] | 2 |
+-----------------------+---+

Therefore, there are other ways to express the desired policy.

For this policy, you can also define a rule that finds if there exists a bitcoin-mining app (which is easy using the some keyword). And then you use negation to check that there is NO bitcoin-mining app. Technically, you’re using 2 negations and an existential quantifier, which is logically the same as a universal quantifier.

For example:

no_bitcoin_miners_using_negation if not any_bitcoin_miners

any_bitcoin_miners if {
    some app in apps
    app.name == "bitcoin-miner"
}

no_bitcoin_miners_using_negation with apps as [{"name": "web"}]

true

no_bitcoin_miners_using_negation with apps as [{"name": "bitcoin-miner"}, {"name": "web"}]

undefined decision

A common mistake is to try encoding the policy with a rule named no_bitcoin_miners like so:

no_bitcoin_miners if {
    app := apps[_]
    app.name != "bitcoin-miner"  # THIS IS NOT CORRECT.
}

It becomes clear that this is incorrect when you use the some keyword, because the rule is true whenever there is SOME app that is not a bitcoin-miner:

no_bitcoin_miners if {
    some app in apps
    app.name != "bitcoin-miner"
}

You can confirm this by querying the rule:

no_bitcoin_miners with apps as [{"name": "bitcoin-miner"}, {"name": "web"}]

true

The reason the rule is incorrect is that variables in Rego are existentially quantified. This means that rule bodies and queries express FOR ANY and not FOR ALL. To express FOR ALL in Rego complement the logic in the rule body (e.g., != becomes ==) and then complement the check using negation (e.g., no_bitcoin_miners becomes not any_bitcoin_miners).

Alternatively, we can implement the same kind of logic inside a single rule using Comprehensions.

no_bitcoin_miners_using_comprehension if {
    bitcoin_miners := {app | some app in apps; app.name == "bitcoin-miner"}
    count(bitcoin_miners) == 0
}

Modules

In Rego, policies are defined inside modules. Modules consist of:

• Exactly one Package declaration.
• Zero or more Import statements.
• Zero or more Rule definitions.

Modules are typically represented in Unicode text and encoded in UTF-8.

Comments

Comments begin with the # character and continue until the end of the line.

Packages

Packages group the rules defined in one or more modules into a particular namespace. Because rules are namespaced they can be safely shared across projects.

Modules contributing to the same package do not have to be located in the same directory.

The rules defined in a module are automatically exported. That is, they can be queried under OPA’s Data API provided the appropriate package is given. For example, given the following module:

package opa.examples

pi := 3.14159

The pi document can be queried via the Data API:

GET https://example.com/v1/data/opa/examples/pi HTTP/1.1

Valid package names are variables or references that only contain string operands. For example, these are all valid package names:

package foo
package foo.bar
package foo.bar.baz
package foo["bar.baz"].qux

These are invalid package names:

package 1foo        # not a variable
package foo[1].bar  # contains non-string operand

For more details see the language Grammar.

Imports

Import statements declare dependencies that modules have on documents defined outside the package. By importing a document, the identifiers exported by that document can be referenced within the current module.

All modules contain implicit statements which import the data and input documents.

Modules use the same syntax to declare dependencies on Base and Virtual Documents.

package opa.examples
import future.keywords # uses 'in' and 'contains' and 'if'

import data.servers

http_servers contains server if {
    some server in servers
    "http" in server.protocols
}

Similarly, modules can declare dependencies on query arguments by specifying an import path that starts with input.

package opa.examples
import future.keywords

import input.user
import input.method

# allow alice to perform any operation.
allow if user == "alice"

# allow bob to perform read-only operations.
allow if {
    user == "bob"
    method == "GET"
}

# allows users assigned a "dev" role to perform read-only operations.
allow if {
    method == "GET"
    input.user in data.roles["dev"]
}

# allows user catherine access on Saturday and Sunday
allow if {
    user == "catherine"
    day := time.weekday(time.now_ns())
    day in ["Saturday", "Sunday"]
}

Imports can include an optional as keyword to handle namespacing issues:

package opa.examples
import future.keywords

import data.servers as my_servers

http_servers contains server if {
    some server in my_servers
    "http" in server.protocols
}

Future Keywords

To ensure backwards-compatibility, new keywords (like every) are introduced slowly. In the first stage, users can opt-in to using the new keywords via a special import:

• import future.keywords introduces all future keywords, and
• import future.keyword.x only introduces the x keyword – see below for all known future keywords.

At some point in the future, the keyword will become standard, and the import will become a no-op that can safely be removed. This should give all users ample time to update their policies, so that the new keyword will not cause clashes with existing variable names.

Note that some future keyword imports have consequences on pretty-printing: If contains or if are imported, the pretty-printer will use them as applicable when formatting the modules.

This is the list of all future keywords known to OPA:

future.keywords.in

More expressive membership and existential quantification keyword:

deny {
    some x in input.roles # iteration
    x == "denylisted-role"
}
deny {
    "denylisted-role" in input.roles # membership check
}

in was introduced in v0.34.0. See the keywords docs for details.

future.keywords.every

Expressive universal quantification keyword:

allowed := {"customer", "admin"}

allow {
    every role in input.roles {
        role.name in allowed
    }
}

There is no need to also import future.keywords.in, that is implied by importing future.keywords.every.

every was introduced in v0.38.0. See Every Keyword for details.

future.keywords.if

This keyword allows more expressive rule heads:

deny if input.token != "secret"

if was introduced in v0.42.0.

future.keywords.contains

This keyword allows more expressive rule heads for partial set rules:

deny contains msg { msg := "forbdiden" }

contains was introduced in v0.42.0.

Some Keyword

The some keyword allows queries to explicitly declare local variables. Use the some keyword in rules that contain unification statements or references with variable operands if variables contained in those statements are not declared using := .

For example, the following rule generates tuples of array indices for servers in the “west” region that contain “db” in their name. The first element in the tuple is the site index and the second element is the server index.

tuples contains [i, j] if {
    some i, j
    sites[i].region == "west"
    server := sites[i].servers[j] # note: 'server' is local because it's declared with :=
    contains(server.name, "db")
}

If we query for the tuples we get two results:

tuples

[
  [
    1,
    2
  ],
  [
    2,
    1
  ]
]

Since we have declared i, j, and server to be local, we can introduce rules in the same package without affecting the result above:

# Define a rule called 'i'
i := 1

If we had not declared i with the some keyword, introducing the i rule above would have changed the result of tuples because the i symbol in the body would capture the global value. Try removing some i, j and see what happens!

The some keyword is not required but it’s recommended to avoid situations like the one above where introduction of a rule inside a package could change behaviour of other rules.

For using the some keyword with iteration, see the documentation of the in operator.

Every Keyword

import future.keywords.every

names_with_dev if {
    some site in sites
    site.name == "dev"

    every server in site.servers {
        endswith(server.name, "-dev")
    }
}

names_with_dev

true

The every keyword takes an (optional) key argument, a value argument, a domain, and a block of further queries, its “body”.

The keyword is used to explicity assert that its body is true for any element in the domain. It will iterate over the domain, bind its variables, and check that the body holds for those bindings. If one of the bindings does not yield a successful evaluation of the body, the overall statement is undefined.

If the domain is empty, the overall statement is true.

Evaluating every does not introduce new bindings into the rule evaluation.

Used with a key argument, the index, or property name (for objects), comes into the scope of the body evaluation:

import future.keywords.every

array_domain if {
    every i, x in [1, 2, 3] { x-i == 1 } # array domain
}

object_domain if {
    every k, v in {"foo": "bar", "fox": "baz" } { # object domain
        startswith(k, "f")
        startswith(v, "b")
    }
}

set_domain if {
    every x in {1, 2, 3} { x != 4 } # set domain
}

{
  "array_domain": true,
  "object_domain": true,
  "set_domain": true
}

Semantically, every x in xs { p(x) } is equivalent to, but shorter than, a “not-some-not” construct using a helper rule:

import future.keywords.every

xs := [2, 2, 4, 8]
larger_than_one(x) := x > 1

rule_every if {
    every x in xs { larger_than_one(x) }
}

not_less_or_equal_one if not lte_one

lte_one if {
    some x in xs
    not larger_than_one(x)
}

{
  "not_less_or_equal_one": true,
  "rule_every": true,
  "xs": [
    2,
    2,
    4,
    8
  ]
}

Negating every is forbidden. If you desire to express not every x in xs { p(x) } please use some x in xs; not p(x) instead.

With Keyword

The with keyword allows queries to programmatically specify values nested under the input Document or the data Document, or built-in functions.

For example, given the simple authorization policy in the Imports section, we can write a query that checks whether a particular request would be allowed:

allow with input as {"user": "alice", "method": "POST"}

true

allow with input as {"user": "bob", "method": "GET"}

true

not allow with input as {"user": "bob", "method": "DELETE"}

true

allow with input as {"user": "charlie", "method": "GET"} with data.roles as {"dev": ["charlie"]}

true

not allow with input as {"user": "charlie", "method": "GET"} with data.roles as {"dev": ["bob"]}

true

allow with input as {"user": "catherine", "method": "GET"}
      with data.roles as {"dev": ["bob"]}
      with time.weekday as "Sunday"

true

The with keyword acts as a modifier on expressions. A single expression is allowed to have zero or more with modifiers. The with keyword has the following syntax:

<expr> with <target-1> as <value-1> [with <target-2> as <value-2> [...]]

The <target>s must be references to values in the input document (or the input document itself) or data document, or references to functions (built-in or not).

The with keyword only affects the attached expression. Subsequent expressions will see the unmodified value. The exception to this rule is when multiple with keywords are in-scope like below:

inner := [x, y] if {
    x := input.foo
    y := input.bar
}

middle := [a, b] if {
    a := inner with input.foo as 100
    b := input
}

outer := result if {
    result := middle with input as {"foo": 200, "bar": 300}
}

When <target> is a reference to a function, like http.send, then its <value> can be any of the following:

1. a value: with http.send as {"body": {"success": true }}
2. a reference to another function: with http.send as mock_http_send
3. a reference to another (possibly custom) built-in function: with custom_builtin as less_strict_custom_builtin.

When the replacement value is a function, its arity needs to match the replaced function’s arity; and the types must be compatible.

Replacement functions can call the function they’re replacing without causing recursion. See the following example:

f(x) := count(x)

mock_count(x) := 0 if "x" in x
mock_count(x) := count(x) if not "x" in x

f([1, 2, 3]) with count as mock_count

3

f(["x", "y", "z"]) with count as mock_count

0

Each replacement function evaluation will start a new scope: it’s valid to use with <builtin1> as ... in the body of the replacement function – for example:

f(x) := count(x) if {
    rule_using_concat with concat as "foo,bar"
}

mock_count(x) := 0 if "x" in x
mock_count(x) := count(x) if not "x" in x

rule_using_concat if {
    concat(",", input.x) == "foo,bar"
}

f(["x", "y", "z"]) with count as mock_count with input.x as ["baz"]

0

Note that function replacement via with does not affect the evaluation of the function arguments: if input.x is undefined, the replacement of concat does not change the result of the evaluation:

count(input.x) with count as 3 with input.x as ["x"]

3

count(input.x) with count as 3 with input as {}

undefined decision

Default Keyword

The default keyword allows policies to define a default value for documents produced by rules with Complete Definitions. The default value is used when all of the rules sharing the same name are undefined.

For example:

default allow := false

allow if {
    input.user == "bob"
    input.method == "GET"
}

allow if input.user == "alice"

When the allow document is queried, the return value will be either true or false.

allow

{
    "user": "bob",
    "method": "POST"
}

false

Without the default definition, the allow document would simply be undefined for the same input.

When the default keyword is used, the rule syntax is restricted to:

default <name> := <term>

The term may be any scalar, composite, or comprehension value but it may not be a variable or reference. If the value is a composite then it may not contain variables or references.

Else Keyword

The else keyword is a basic control flow construct that gives you control over rule evaluation order.

Rules grouped together with the else keyword are evaluated until a match is found. Once a match is found, rule evaluation does not proceed to rules further in the chain.

The else keyword is useful if you are porting policies into Rego from an order-sensitive system like IPTables.

authorize := "allow" if {
    input.user == "superuser"           # allow 'superuser' to perform any operation.
} else := "deny" {
    input.path[0] == "admin"            # disallow 'admin' operations...
    input.source_network == "external"  # from external networks.
} # ... more rules

authorize

In the example below, evaluation stops immediately after the first rule even though the input matches the second rule as well.

{
  "path": [
    "admin",
    "exec_shell"
  ],
  "source_network": "external",
  "user": "superuser"
}

"allow"

In the next example, the input matches the second rule (but not the first) so evaluation continues to the second rule before stopping.

{
  "path": [
    "admin",
    "exec_shell"
  ],
  "source_network": "external",
  "user": "alice"
}

"deny"

The else keyword may be used repeatedly on the same rule and there is no limit imposed on the number of else clauses on a rule.

Operators

Membership and iteration: in

The membership operator in lets you check if an element is part of a collection (array, set, or object). It always evaluates to true or false:

import future.keywords.in

p := [x, y, z] if {
    x := 3 in [1, 2, 3]            # array
    y := 3 in {1, 2, 3}            # set
    z := 3 in {"foo": 1, "bar": 3} # object
}

{
  "p": [
    true,
    true,
    true
  ]
}

When providing two arguments on the left-hand side of the in operator, and an object or an array on the right-hand side, the first argument is taken to be the key (object) or index (array), respectively:

import future.keywords.in

p := [x, y] if {
    x := "foo", "bar" in {"foo": "bar"}    # key, val with object
    y := 2, "baz" in ["foo", "bar", "baz"] # key, val with array
}

{
  "p": [
    true,
    true
  ]
}

Note that in list contexts, like set or array definitions and function arguments, parentheses are required to use the form with two left-hand side arguments – compare:

import future.keywords.in

p := x if {
    x := { 0, 2 in [2] }
}
q := x if {
    x := { (0, 2 in [2]) }
}
w := x if {
    x := g((0, 2 in [2]))
}
z := x if {
    x := f(0, 2 in [2])
}

f(x, y) := sprintf("two function arguments: %v, %v", [x, y])
g(x) := sprintf("one function argument: %v", [x])

{
  "p": [
    true,
    0
  ],
  "q": [
    true
  ],
  "w": "one function argument: true",
  "z": "two function arguments: 0, true"
}

Combined with not, the operator can be handy when asserting that an element is not member of an array:

import future.keywords.in

deny if not "admin" in input.user.roles

test_deny {
    deny with input.user.roles as ["operator", "user"]
}

{
  "test_deny": true
}

Note that expressions using the in operator always return true or false, even when called in non-collection arguments:

import future.keywords.in

q := x if {
    x := 3 in "three"
}

{
  "q": false
}

Using the some variant, it can be used to introduce new variables based on a collections’ items:

import future.keywords.in

p[x] {
    some x in ["a", "r", "r", "a", "y"]
}

q[x] {
    some x in {"s", "e", "t"}
}

r[x] {
    some x in {"foo": "bar", "baz": "quz"}
}

{
  "p": [
    "a",
    "r",
    "y"
  ],
  "q": [
    "e",
    "s",
    "t"
  ],
  "r": [
    "bar",
    "quz"
  ]
}

Furthermore, passing a second argument allows you to work with object keys and array indices:

import future.keywords.in

p[x] {
    some x, "r" in ["a", "r", "r", "a", "y"] # key variable, value constant
}

q[x] = y if {
     some x, y in ["a", "r", "r", "a", "y"] # both variables
}

r[y] = x if {
    some x, y in {"foo": "bar", "baz": "quz"}
}

{
  "p": [
    1,
    2
  ],
  "q": {
    "0": "a",
    "1": "r",
    "2": "r",
    "3": "a",
    "4": "y"
  },
  "r": {
    "bar": "foo",
    "quz": "baz"
  }
}

Any argument to the some variant can be a composite, non-ground value:

import future.keywords.in

p[x] = y if {
    some x, {"foo": y} in [{"foo": 100}, {"bar": 200}]
}
p[x] = y if {
    some {"bar": x}, {"foo": y} in {{"bar": "b"}: {"foo": "f"}}
}

{
  "p": {
    "0": 100,
    "b": "f"
  }
}

Equality: Assignment, Comparison, and Unification

Rego supports three kinds of equality: assignment (:=), comparison (==), and unification =. We recommend using assignment (:=) and comparison (==) whenever possible for policies that are easier to read and write.

Assignment :=

The assignment operator (:=) is used to assign values to variables. Variables assigned inside a rule are locally scoped to that rule and shadow global variables.

x := 100

p if {
    x := 1     # declare local variable 'x' and assign value 1
    x != 100   # true because 'x' refers to local variable
}

Assigned variables are not allowed to appear before the assignment in the query. For example, the following policy will not compile:

p if {
    x != 100
    x := 1     # error because x appears earlier in the query.
}

q if {
    x := 1
    x := 2     # error because x is assigned twice.
}

2 errors occurred:
module.rego:6: rego_compile_error: var x referenced above
module.rego:11: rego_compile_error: var x assigned above

A simple form of destructuring can be used to unpack values from arrays and assign them to variables:

address := ["3 Abbey Road", "NW8 9AY", "London", "England"]

in_london if {
    [_, _, city, country] := address
    city == "London"
    country == "England"
}

{
  "address": [
    "3 Abbey Road",
    "NW8 9AY",
    "London",
    "England"
  ],
  "in_london": true
}

Comparison ==

Comparison checks if two values are equal within a rule. If the left or right hand side contains a variable that has not been assigned a value, the compiler throws an error.

p if {
    x := 100
    x == 100   # true because x refers to the local variable
}

{
  "p": true
}

y := 100
q if {
    y == 100   # true because y refers to the global variable
}

{
  "q": true,
  "y": 100
}

r if {
    z == 100   # compiler error because z has not been assigned a value
}

1 error occurred: module.rego:5: rego_unsafe_var_error: var z is unsafe

Unification =

Unification (=) combines assignment and comparison. Rego will assign variables to values that make the comparison true. Unification lets you ask for values for variables that make an expression true.

# Find values for x and y that make the equality true
[x, "world"] = ["hello", y]

+---------+---------+
|    x    |    y    |
+---------+---------+
| "hello" | "world" |
+---------+---------+

sites[i].servers[j].name = apps[k].servers[m]

+---+---+---+---+
| i | j | k | m |
+---+---+---+---+
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 2 | 1 | 0 |
| 1 | 0 | 0 | 2 |
| 1 | 1 | 0 | 3 |
| 1 | 2 | 1 | 1 |
| 2 | 0 | 0 | 4 |
| 2 | 1 | 2 | 0 |
+---+---+---+---+

As opposed to when assignment (:=) is used, the order of expressions in a rule does not affect the document’s content.

s if {
    x > y
    y = 41
    x = 42
}

Best Practices for Equality

Here is a comparison of the three forms of equality.

Equality  Applicable    Compiler Errors            Use Case
--------  -----------   -------------------------  ----------------------
:=        Everywhere    Var already assigned       Assign variable
==        Everywhere    Var not assigned           Compare values
=         Everywhere    Values cannot be computed  Express query

Best practice is to use assignment := and comparison == wherever possible. The additional compiler checks help avoid errors when writing policy, and the additional syntax helps make the intent clearer when reading policy.

Under the hood := and == are syntactic sugar for =, local variable creation, and additional compiler checks.

Comparison Operators

The following comparison operators are supported:

a  ==  b  #  `a` is equal to `b`.
a  !=  b  #  `a` is not equal to `b`.
a  <   b  #  `a` is less than `b`.
a  <=  b  #  `a` is less than or equal to `b`.
a  >   b  #  `a` is greater than `b`.
a  >=  b  #  `a` is greater than or equal to `b`.

None of these operators bind variables contained in the expression. As a result, if either operand is a variable, the variable must appear in another expression in the same rule that would cause the variable to be bound, i.e., an equality expression or the target position of a built-in function.

Built-in Functions

In some cases, rules must perform simple arithmetic, aggregation, and so on. Rego provides a number of built-in functions (or “built-ins”) for performing these tasks.

Built-ins can be easily recognized by their syntax. All built-ins have the following form:

<name>(<arg-1>, <arg-2>, ..., <arg-n>)

Built-ins usually take one or more input values and produce one output value. Unless stated otherwise, all built-ins accept values or variables as output arguments.

If a built-in function is invoked with a variable as input, the variable must be safe, i.e., it must be assigned elsewhere in the query.

Built-ins can include “.” characters in the name. This allows them to be namespaced. If you are adding custom built-ins to OPA, consider namespacing them to avoid naming conflicts, e.g., org.example.special_func.

See the Policy Reference document for details on each built-in function.

Errors

By default, built-in function calls that encounter runtime errors evaluate to undefined (which can usually be treated as false) and do not halt policy evaluation. This ensures that built-in functions can be called with invalid inputs without causing the entire policy to stop evaluating.

In most cases, policies do not have to implement any kind of error handling logic. If error handling is required, the built-in function call can be negated to test for undefined. For example:

allow if {
    io.jwt.verify_hs256(input.token, "secret")
    [_, payload, _] := io.jwt.decode(input.token)
    payload.role == "admin"
}

reason contains "invalid JWT supplied as input" if {
    not io.jwt.decode(input.token)
}

{
    "token": "a poorly formatted token"
}

{
  "reason": [
    "invalid JWT supplied as input"
  ]
}

If you wish to disable this behaviour and instead have built-in function call errors treated as exceptions that halt policy evaluation enable “strict built-in errors” in the caller:

Example Data

The rules below define the content of documents describing a simplistic deployment environment. These documents are referenced in other sections above.

sites := [
    {
        "region": "east",
        "name": "prod",
        "servers": [
            {
                "name": "web-0",
                "hostname": "hydrogen"
            },
            {
                "name": "web-1",
                "hostname": "helium"
            },
            {
                "name": "db-0",
                "hostname": "lithium"
            }
        ]
    },
    {
        "region": "west",
        "name": "smoke",
        "servers": [
            {
                "name": "web-1000",
                "hostname": "beryllium"
            },
            {
                "name": "web-1001",
                "hostname": "boron"
            },
            {
                "name": "db-1000",
                "hostname": "carbon"
            }
        ]
    },
    {
        "region": "west",
        "name": "dev",
        "servers": [
            {
                "name": "web-dev",
                "hostname": "nitrogen"
            },
            {
                "name": "db-dev",
                "hostname": "oxygen"
            }
        ]
    }
]

apps := [
    {
        "name": "web",
        "servers": ["web-0", "web-1", "web-1000", "web-1001", "web-dev"]
    },
    {
        "name": "mysql",
        "servers": ["db-0", "db-1000"]
    },
    {
        "name": "mongodb",
        "servers": ["db-dev"]
    }
]

containers := [
    {
        "image": "redis",
        "ipaddress": "10.0.0.1",
        "name": "big_stallman"
    },
    {
        "image": "nginx",
        "ipaddress": "10.0.0.2",
        "name": "cranky_euclid"
    }
]