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Polar Syntax

Polar is a declarative logic programming language, specialized for making authorization decisions and tightly integrating with your application’s native language.

This guide is a brief description of the core syntax elements of Polar.

Each Polar file defines a set of rules. When a Polar file is loaded into the authorization engine, all rules are added to the engine’s knowledge base.

The knowledge base may be queried. The behavior of queries is described further here.

Primitive Types

Polar has only a few primitive data types.

Numbers

Polar parses unquoted integers or floating point numbers as numeric values. For example, all of the following are parsed as numbers:

22
43
-7
22.3
-22.31
2.0e9

You can also perform basic arithmetic on numbers with the operators +, -, *, /, mod, and rem.

Boolean

Polar parses the keywords true and false as boolean values.

Strings

Polar supports quoted strings, which can be used to represent any textual data. Polar strings are quoted with double quotes ("). Quotes within strings can be escaped with a single backslash. Two strings are considered equal if they have the same length and each of their corresponding characters are equal.

The string type can be referenced (for use in specializers, or with the matches operator) as String.

Compound Types

To support more complex data, Polar includes the following compound data types.

Lists

A list is a sequence of values defined using brackets: [v1, v2, ..., vn]. For example:

["polar", "lang", "oso"]
["oso", ["polar", "lang"]]

Lists may have any length. List membership can be determined using the in operator.

Dictionaries

While lists are useful for representing ordered data, dictionaries (sometimes known as hash tables or associative arrays) can express unordered relational data such as mappings: {key1: value1, key2: value2, ..., keyN: valueN}.

For example:

{first_name: "Yogi", last_name: "Bear"}

If you want to associate a variable with the value in a dictionary under the key of the same name, you can use a shorter syntax similar to JavaScript object literals:

{ first_name, last_name } # or 
{ first_name, last_name: "Bear" }

Class Instances

A similar syntax is used to represent instances of classes. The class name is specified before the dictionary:

Bear{first_name: "Yogi", last_name: "Bear"}

Classes can be registered with the Oso library to integrate with Polar. See Application Types for more information.

An instance literal can only be used with the new operator or as a pattern.

Rules

Rules allow you to express conditional statements ("if this then that").

A rule in Polar takes the form HEAD if BODY; where HEAD must be a fact and BODY any number of terms. The meaning of a rule is that HEAD is true if each of the BODY terms is true. If there are be multiple rules with the same head, each BODY will be tried in turn, and any or all may succeed. For more on how rules are defined and applied see Polar Background.

The following is an example of a rule:

person("yogi", "bear") if bear("yogi", "bear");

This example says that Yogi is a person if Yogi is a bear. Bears are people, too.

Terms

A term is either a data type or a combination of facts using operators.

Variables

The example rule above is static. More powerful rules can be formed using variables. In Polar, a variable does not need a separate declaration; it is created the first time it is referenced. Variables can be substituted for values in dictionaries or items in a list or rule call.

The following are all variables:

foo
bar
myvar

To make the above rule more useful, we could write:

person(first, last) if bear(first, last);

This rule says that if there is a bear with some name, then that bear is also a person.

Singletons

If a variable occurs only once, then its value can’t be used for anything. Such variables are called singletons, and Polar will warn you if they occur in a rule. For example, if you try to load the rule…

user(first, last) if person("George", last);

…you’ll see the following message:

Singleton variable first is unused or undefined
001: user(first, last) if person("George", last);
          ^

The reason these warnings are important is that, as in this case, they indicate potential logical errors. Here, the error is forgetting to use the first name, and instead using a literal string in the call to person.

There are cases, however, where it isn’t an error to have a singleton variable. For example:

  • As a parameter with a specializer: allow(_actor: Person{first_name: "George"}, …);
  • As a parameter that is explicitly ignored: always_true(_);

In such cases, you can suppress the singleton variable warning by starting your variable’s name with an _ (underscore), e.g., _actor in the first example above.

A variable named just _ (as in the second example above) is called an anonymous variable, and it is always a singleton (but will never generate a warning). Each occurrence is translated into a fresh variable, guaranteed not to match any other variable. You may therefore have as many anonymous variables in a rule as you like, and each will be unique. It’s up to you whether to use an anonymous variable or a singleton with a descriptive name.

Operators

Operators are used to combine terms in rule bodies into expressions.

Unification

Unification is the basic matching operation in Polar. Two values are said to unify if they are equal or if there is a consistent set of variable bindings that makes them equal. Unification is defined recursively over compound types (e.g., lists and dictionaries): two compound values unify if all of their corresponding elements unify.

Unification may be performed explicitly with the unification operator (=), which is true if its two operands unify; e.g., 1 = 1, "a" = "a", or x = 1 where the variable x is either bound to 1 or unbound.

Unification is also used to determine if queries match rule HEAD s, and if the BODY of rules match other facts in the knowledge base. We will cover unification further in The Search Procedure.

Assignment

Assigning a value to an unbound variable can be done using the unification operator. However, the assignment operator (:=) may also be used, and will only succeed if the left-hand side operand is an unbound variable. For example, foo := 1. This operator can be used to improve readability and predictability by indicating explicit assignment. Attempting to assign to a non-variable will result in a parse error, while attempting to assign to a bound variable will result in a runtime error.

Conjunction (and)

To say that two terms in a rule’s body must both be true, the and operator can be used. For example, the rule…

oso_user(first, last) if
    user(first, last) and
    employee("Oso", first, last);

…will be satisfied if the named person is a user and that person is an employee of Oso.

Disjunction (or)

The or operator will be true if either its left or its right operand is true. Disjunctions can always be replaced by multiple rules with identical heads but different bodies (the operands), but may help simplify writing rules with alternatives.

Negation (not)

The not operator will succeed when its argument fails.

For example, the following rule will succeed when x != 0 (and could be written as such).

non_zero(x) if not x == 0;

not is helpful when negating the results of another rule call. For example,

positive(x) if
    non_zero(x) and
    not negative(x);

negative(x) if x < 0;

Above, positive will succeed if negative(x) returns no results.

To negate multiple expressions, use parentheses to group them:

positive(x) if
    not (x == 0 or negative(x));

Dictionary Key Access

The dot . operator can be used to access the value associated with a key in a dictionary. For example:

dict = { hello: "world" } and
dict.hello = "world"

A string stored in a variable can be used as the key in a dot lookup using the following syntax:

dict = { hello: "world" } and
key = "hello" and
dict.(key) = "world"

Application Field or Method Access

The dot . operator can also be used to access methods or fields on application instances or constants. Arguments can be passed into methods as positional or keyword arguments, depending on the application language. Keyword arguments are only supported in languages that themselves support them (e.g., Python, Ruby).

Accessing a field on an application instance looks like:

person = new Person() and
first_name = person.first_name

Calling an application method from a policy looks like this:

person = new Person() and
person.check_address("12345 Broadway", city: "New York", state: "NY");

Calling a class method on a class that has been registered as a constant could look like:

person = new Person() and
Person.log("created new person")

Comparison

The comparison operators can be used to compare values (> >= < <= == !=). For example…

age < 10

…will check that the value of the variable age is less than 10. Performing a comparison on application data will use the host language’s native comparison operation. Not all Oso language libraries support this feature.

Print

print() is a built-in operator that prints its arguments to the console. It always succeeds and can therefore be added anywhere in the body of a Polar rule. For example:

hello(x) if print("hello", x) and x = "world";

query> hello("world");
"hello", "world"
True

Cut

By default, Polar runs all of the definitions for a given rule that are applicable to the given set of arguments (i.e., whose specializers are matched). The cut operator overrides this behavior by committing to the enclosing rule definition: the query engine will not run any others. Rule definitions that have already run are not “un-run”, though, or avoided by using cut; it just ensures that no others will run.

Because Polar runs rules in most-to-least-specific order, these “other” rule definitions are always less specific than the current one; i.e., they may have specializers that are superclasses (and therefore less specific) of those in the current rule. This allows cut to override a rule that is specialized on a less specific class. You can think of cut as a sort of dual to super() in other object-oriented languages (e.g., Python): in Polar, the behavior of “methods” (rules) is to implicitly call the next method, but cut overrides that behavior; it says not to call any more methods (rules).

cut can appear anywhere in a rule body, but terms before it must succeed for it to be reached, so it frequently appears at the end of the body: if so-and-so is true, then cut out all other alternatives.

cut should be used sparingly.

New

The new operator is used to construct a new instance of an application class. (See Application Types for more about how to define and register application classes.) The name of the class to instantiate comes next, followed by a set of initialization arguments that are passed to the class’s constructor:

new Bear("yogi", "bear")

In host languages that support keyword arguments (e.g., Python & Ruby, but not Java), you can pass initialization arguments as keywords with the following syntax:

new Bear(first_name: "yogi", last_name: "bear")

If using a constructor with mixed positional and keyword arguments, positional arguments must come before keyword arguments:

new Bear("yogi", last_name: "bear")

In (List Membership)

The in operator can be used to iterate over elements of built-in and application types. Iterable built-in types are List, String, and Dictionary.

The first operand will be unified with each element. If the second operand is not iterable, the operation will fail. For example…

x in [1, 2, 3] and x = 1

…will bind x to 1, 2, 3, in turn, and check that x = 1 for each. This expression will only succeed for the first item (1). The left-hand side does not need to be a variable. for example…

1 in [1, 2, 3, 1]

…will succeed twice: 1 is in the first and fourth position.

Iterating over a String returns each character (as another string):

hexstring(s) if
  forall(c in s, c in "0123456789abcdef");

Iterating over a dictionary returns a list with two elements, the key (as a string) and the value:

x in {a: 1, b: 2}
[key, _] in {a: 1, b: 2}
[_, value] in {a: 1, b: 2}

The above returns:

x => ["a", 1]
x => ["b", 2]

key => "a"
key => "b"

value => 1
value => 2

For All

The forall operator is often useful in conjunction with the in operator. forall(condition, action) checks that action succeeds for every alternative produced by condition. For example…

forall(x in [1, 2, 3], x = 1)

…would fail because x only unifies with 1 for the first element in the list (the first alternative of the condition). In contrast…

forall(x in [1, 1, 1], x = 1)

…succeeds because the action holds for all values in the list.

forall can also be used with application data to check all elements returned by an application method:

forall(role = user.roles(), role = "admin")

Any bindings made inside a forall (role or x in the example above) cannot be accessed outside the forall operation.

*rest Operator

The rest operator (*) can be used to destructure a list. For example:

x = [1, 2, 3] and
[first, *tail] = x

After evaluating the above, the variable first will have the value 1 and tail will have the value [2, 3].

The rest operator is only valid within a list literal and in front of a variable. It must be the last element of the list literal ([*rest, tail]) is invalid. Any number of elements can come before the rest operator.

The rest operator is only useful when combined with a unification operation that assigns a value to it.

Patterns and Matching

Polar has powerful pattern matching facilities that are useful to control which rules execute & in what order.

Specialization

Rule heads (the part of the rule before the if keyword) can contain specializers. For example, the rule…

has_first_name(person: Person, name) if person.name = name;

…would only execute if the person argument is of the type Person.

Multiple rules of the same structure can be written with different specializers:

has_first_name(user: User, name) if user.name = name;

Now, the first_name rule can be used with instances of the User or Person type.

For more on this feature, see Application Types.

Patterns

The expression after the : is called a pattern. The following are valid patterns:

  • any primitive type
  • a dictionary literal
  • an instance literal (without the new operator)
  • a type name (used above)

When a rule is evaluated, the value of the argument is matched against the pattern. For primitive types, a value matches a pattern if it is equal.

For dictionary types, a value matches a pattern if the pattern is a subset of the dictionary. For example:

{x: 1, y: 2} matches {x: 1}
{x: 1, y: 3} matches {y: 3}
{x: 1, y: 3} matches {x: 1, y: 3}

# Does not match because y value are not equal
not {x: 1, y: 3} matches {x: 1, y: 4}

A type name matches if the value has the same type:

new Person() matches Person

The fields are checked in the same manner as dictionaries, and the type is checked in the same manner as the previous example:

new Person(x: 1, y: 2) matches Person{x: 1}

For type matching, subclasses are also considered. So, a class that is a subclass of Person would match Person{x: 1}.

Matches Operator

The above example used the matches operator to describe the behavior of pattern matching. This operator can be used anywhere within a rule body to perform a match. The same operation is used by the engine to test whether a rule argument matches the specializer.

Actor and Resource Specializers

Oso provides built-in specializers that will match any application type that has been declared via an actor or resource block.

The Actor specializer will match any application type that has been declared via an actor block, and Resource will match types declared via resource blocks.

E.g., the following is a valid head for an allow rule:

allow(actor: Actor, action, resource: Resource) if ...

Because of this, attempts to register application types named Actor or Resource will result in an error.

Actor and Resource specializers are used by Oso’s built-in rule types to validate policies.

Inline Queries (?=)

Queries can also be added to Polar files and will run when the file is loaded. Inline queries can be useful for testing a policy and confirming it behaves as expected.

To add an inline query to a Polar file, use the ?= operator:

?= allow("foo", "read", "bar")

An inline query is only valid at the beginning of a line.

Rule Types

A rule type specifies the shape of a rule — its number of arguments and, optionally, the type of each argument. If a rule type exists for has_permission(), then all has_permission() rules must conform to the rule type. Rule types have the same syntax as rule heads and are preceded by the keyword type:

type has_permission(actor: Actor, action: String, resource: Resource);

The above rule type specifies that any rule with the name has_permission must have three arguments where the first argument matches Actor, the second argument matches String, and the third argument matches Resource.

Argument matching is determined in the same way that matching is determined for rule evaluation. See Patterns and Matching.

Rule types are optional. If a rule type exists with the same name as a rule, then the rule must match that type or else an error will be thrown when the policy is loaded. If multiple rule types are defined for the same rule name, then a rule need only match one type to be valid.

You can find a reference for built-in rule types here.

Actor and Resource Blocks

Actor and resource blocks provide a way to organize authorization logic by application type. These blocks are especially useful for expressing role-based access control logic.

The simplest form of a block looks like this:

# Actor block
actor User {}

# Resource block
resource Repository {}

In the above example, User and Repository must be registered application types.

Inside of a block, you can declare permissions, roles, and relations and write shorthand rules.

A more complete block looks like this:

main.polar 
resource Repository {
  permissions = ["read", "push"];
  roles = ["contributor", "maintainer"];
  relations = { parent: Organization };

  # An actor has the "read" permission if they have the "contributor" role.
  "read" if "contributor";
  # An actor has the "push" permission if they have the "maintainer" role.
  "push" if "maintainer";

  # An actor has the "contributor" role if they have the "maintainer" role.
  "contributor" if "maintainer";

  # An actor has the "maintainer" role if they have the "owner" role on the "parent" Organization.
  "maintainer" if "owner" on "parent";
}

Once you have declared a block, you can use the built-in Actor and Resource specializers to match all types declared as actors or resources, respectively.

Permission Declarations

You can specify the permissions that are available for an actor or resource type using the following syntax:

resource Repository {
  permissions = ["read", "push"];
}

Permissions are always strings. You must declare permissions in order to use them in shorthand rules.

Role Declarations

You can specify the roles that are available for an actor or resource type using the following syntax:

resource Repository {
  roles = ["contributor", "maintainer", "admin"];
}

Roles are always strings. You must declare roles in order to use them in shorthand rules.

In order to use roles, you must write at least one has_role rule that gets user-role assignments stored in your application. This rule takes the following form:

has_role(actor: Actor, name: String, resource: Resource) if ...

For example:

# User-role assignment hook - required when using roles
has_role(user: User, name: String, repo: Repository) if
  # Look up user-role assignments from application, e.g.
  role in user.roles and
  role.repo_id = repo.id;

The name argument corresponds to the role names in the declaration list. The has_role rule must handle every declared role name, otherwise you may encounter application errors or unexpected policy behavior.

Relation Declarations

You can specify relations between actor/resource types using the following syntax:

resource Repository {
  relations = { parent: Organization };
}

Relations are key: value pairs where the key is the relation name and the value is the type of the related object. Related object types must also be declared in resource or actor blocks.

In order to use relations, you must write a has_relation rule that gets relationship data from your application. This rule takes the following form:

has_relation(subject: Resource/Actor, name: String, object: Resource/Actor) if ...

The object argument is the resource or actor type on which the relation was declared. In the example above, the object type is Repository and the subject type is Organization.

For example:

# Relation hook - required when using relations
has_relation(parent_org: Organization, "parent", repo: Repository) if
  # Look up parent-child relation from application, e.g.
  parent_org = repo.organization;

has_relation rules must be defined for every declared relation.

Shorthand Rules

Shorthand rules are concise rules that you can define inside actor and resource blocks using declared permissions, roles, and relations.

For example,

main.polar 
resource Repository {
  permissions = ["read", "push"];
  roles = ["contributor", "maintainer"];
  relations = { parent: Organization };

  # An actor has the "read" permission if they have the "contributor" role.
  "read" if "contributor";
  # An actor has the "push" permission if they have the "maintainer" role.
  "push" if "maintainer";

  # An actor has the "contributor" role if they have the "maintainer" role.
  "contributor" if "maintainer";

  # An actor has the "maintainer" role if they have the "owner" role on the "parent" Organization.
  "maintainer" if "owner" on "parent";
}

For shorthand rules to be evaluated by the Oso library, you must add the following rule to your policy:

allow(actor, action, resource) if has_permission(actor, action, resource);

This rule tells Oso to look for permissions that were granted through shorthand rules.

Shorthand Rules Without Relations

A shorthand rule has the basic form:

[result] if [condition];

Where "result" and "condition" can be permissions or roles that were declared inside the same block.

For example:

resource Repository {
  permissions = ["read", "push"];
  roles = ["contributor", "maintainer"];

  "read" if "contributor";  # "contributor" role grants "read" permission
  "push" if "maintainer";  # "maintainer" role grants "push" permission
  "contributor" if "maintainer";  # "maintainer" role grants "contributor" role
}

Shorthand Rules With Relations

If you have declared relations inside a block, you can also write shorthand rules of this form:

[result] if [condition] on [relation];

where result and condition can be permissions or roles, and relation can be a relation.

This form is used to grant results based on conditions on a related resource or actor. This form is commonly used with "parent" relations.

For example,

resource Repository {
  roles = ["contributor", "maintainer"];
  relations = { parent: Organization };

  "admin" if "owner" on "parent"  # "owner" role on parent Organization grants the "admin" role
  "contributor" if "member" on "parent"  # "member" role on parent Organization grants "contributor" role
}

Shorthand Rule Expansion

Shorthand rules are expanded to full Polar rules when they are loaded. The semantics of this expansion are as follows.

Expansion without relation

$x if $y;
=> rule1(actor: Actor, $x, resource: $Type) if rule2(actor, $y, resource);

where rule1 and rule2 are the expansions of $x and $y respectively.

If $x is a permission, then rule1 will be has_permission. If $x is a role, then rule1 will be has_role. The same semantics apply for $y and $rule2.

The resource argument specializer $Type is determined by the enclosing block definition. E.g., if the rule is defined inside of resource Repository {}, then $Type will be Repository.

For example,

# Shorthand rule
resource Repository {
  permissions = ["read"];
  roles = ["contributor"];

  "read" if "contributor";
}

# Expanded rule
#                            "read"                        if                 "contributor"           ;
#                              \/                                                  \/
has_permission(actor: Actor, "read", resource: Repository) if has_role(actor, "contributor", resource);

Expansion with relation

$x if $y on $z;
=> rule1(actor: Actor, $x, resource: $Type) if rule2(actor, $y, related) and has_relation(related, $z, resource);

where rule1, rule2, and has_relation are the expansions of $x, $y, and $z respectively.

The expansion of $x to rule1 and $y to rule2 follow the same semantics as expansion without relation above. $z must always be a declared relation in the enclosing block. The has_relation rule is necessary in order to access the related object that rule2 references. This expansion shows why it is necessary to define has_relation rules for every declared relation.

For example:

resource Repository {
  roles = ["admin"];
  relations = {parent: Organization};

  "admin" if "owner" on "parent";
}

# Expanded rule
#                      "admin"                        if                 "owner"            on                        "parent"          ;
#                        \/                                                \/        /------|-----------------\         \/
has_role(actor: Actor, "admin", resource: Repository) if has_role(actor, "owner", related) and has_relation(related, "parent", resource);

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