PHP RFC: Disjunctive Normal Form Types


Disjunctive Normal Form (DNF) is a standard way of organizing boolean expressions. Specifically, it means structuring a boolean expression into an ORed series of ANDs. When applied to type declarations, it allows for a standard way to write combined Union and Intersection types that the parser can handle.

This RFC proposes to support DNF types in order to allow mixing of union and intersection types.



For all examples that follow, assume the following definitions exist:

interface A {}
interface B {}
interface C extends A {}
interface D {}
class W implements A {}
class X implements B {}
class Y implements A, B {}
class Z extends Y implements C {}

DNF types would allow type declarations for properties, parameters, and return values in the following form:

// Accepts an object that implements both A and B,
// OR an object that implements D.

// Accepts an object that implements C, 
// OR a child of X that also implements D,
// OR null.

// Accepts an object that implements all three of A, B, and D, 
// OR an int, 
// OR null.

The following examples are not in DNF form, and thus will generate a parse error. However, they can be rewritten to DNF as shown.

// Can be rewritten as (A&B)|(A&D)

// Can be rewritten as A|(B&D)|(B&W)|null

The order of types within each AND/OR section is irrelevant, and thus the following type declarations are all equivalent:


Requiring DNF for all type declarations allows conceptually all potential combinations of intersection and union rules, but in a standard fashion that is easier for the engine and easier for humans and static analyzers to comprehend.

The parentheses around each intersection segment is required. Single-type segments do not require parentheses.

Return co-variance

When extending a class, a method return type may narrow only. That is, it must be the same or more restrictive as its parent. In practice, that means additional ANDs may be added, but not additional ORs.

interface ITest {
  public function stuff(): (A&B)|D;
// Acceptable.  A&B is more restrictive.
class TestOne implements ITest {
  public function stuff(): (A&B) {}
// Acceptable. D is is a subset of A&B|D
class TestTwo implements ITest {
  public function stuff(): D {}
// Acceptable, since C is a subset of A&B,
// even though it is not identical.
class TestThree implements ITest {
  public function stuff(): C|D {}
// Not acceptable. This would allow an object that
//  implements A but not B, which is wider than the interface.
class TestFour implements ITest {
  public function stuff(): A|D {}
interface ITestTwo {
  public function things(): C|D {}
// Not acceptable. Although C extends A and B, it's possible
// for an object to implement A and B without implementing C.
// Thus this definition is wider, and not allowed.
class TestFive implements ITestTwo {
  public function things(): (A&B)|D {}

Parameter contra-variance

When extending a class, a method parameter type may widen only. That is, it must be the same or less restrictive as its parent. In practice, that means additional ORs may be added, but not additional ANDs.

interface ITest {
  public function stuff((A&B)|D $arg): void {}
// Acceptable. Everything that ITest accepts is still valid
// and then some.
class TestOne implements ITest {
  public function stuff((A&B)|D|Z $arg): void {}
// Acceptable. This accepts objects that implement just
// A, which is a super-set of those that implement A&B.
class TestOne implements ITest {
  public function stuff(A|D $arg): void {}
// Not acceptable. The interface says D is acceptable,
// but this class does not.
class TestOne implements ITest {
  public function stuff((A&B) $arg): void {}
interface ITestTwo {
  public function things(C|D $arg): void;
// Acceptable. Anything that implements C implements A&B,
// but this rule also allows classes that implement A&B
// directly, and thus is wider.
class TestFive implements ITestTwo {
  public function things((A&B)|D $arg): void;

Property invariance

Object properties are already invariant in inheritance. This RFC does not change that. The type of a redeclared child property must logically match its parent. However, the order of segments remains irrelevant. The type declaration may be reordered provided that it is logically identical to its parent.

Duplicate and redundant types

To catch some simple bugs in type declarations, redundant types that can be detected without performing class loading will result in a compile-time error. This is similar to the logic applied to Intersection and Union types already, and is a super-set of it.

  • Each segment of a DNF type must be unique.

A type declaration of (A&B)|(B&A) is invalid. The two ORed segments are logically equivalent, and thus superficially redundant.

Note that a type declaration of (A&B)|C is not necessarily redundant, as C could include other methods beyond what it inherits, and an object could implement A, B, and D and still be accepted by the first segment and not the second.

  • Segments that are strict subsets of others are disallowed.

For example, the type definition (A&B)|A is redundant, because all instances of A are already allowed, whether they also implement B or not. That definition is redundant and thus invalid.

This does not guarantee that the type is “minimal”, because doing so would require loading all used class types.


This RFC does not introduce any new reflection classes. However, it does make one change to the Reflection API, in that ReflectionUnionType::getTypes() previously was guaranteed to always return an array of ReflectionNamedType instances. Now it will return some combination of ReflectionNamedType and ReflectionIntersectionType instances. The method is already typed to return ReflectionType so this is not an API change, but the previous de facto assumption is no longer valid.

ReflectionIntersectionType::getTypes() will still only return ReflectionNamedType in practice, although its return type is similarly ReflectionType.

Backward Incompatible Changes

The sub-values of a ReflectionUnionType may now be ReflectionIntersectionType instances, rather than always being ReflectionNamedType.

Proposed PHP Version(s)



As per the voting RFC a yes/no vote with a 2/3 majority is needed for this proposal to be accepted.

Voting started on 2022-06-17 and will end on 2022-07-01.

Accept Disjunctive Normal Form Types RFC?
Real name Yes No
aaronjunker (aaronjunker)  
asgrim (asgrim)  
beberlei (beberlei)  
brzuchal (brzuchal)  
bwoebi (bwoebi)  
colinodell (colinodell)  
crell (crell)  
derick (derick)  
dmitry (dmitry)  
girgias (girgias)  
kguest (kguest)  
kocsismate (kocsismate)  
lbarnaud (lbarnaud)  
marandall (marandall)  
mcmic (mcmic)  
nicolasgrekas (nicolasgrekas)  
ocramius (ocramius)  
petk (petk)  
pierrick (pierrick)  
reywob (reywob)  
sergey (sergey)  
svpernova09 (svpernova09)  
theodorejb (theodorejb)  
timwolla (timwolla)  
trowski (trowski)  
villfa (villfa)  
Final result: 25 1
This poll has been closed.

Future Scope

Non-DNF types

In theory, supporting conjunctive normal form type definitions (and ANDed list of ORs) or types which are not in a normalised form may be possible, either by supporting them directly or doing a compile time rewrite of the type expression.

However, as DNF is able to represent all reasonable boolean expressions and having a normalized form simplifies both the engine implementation and user-space reflection code, the authors have no intent to pursue this direction.

Type aliasing

DNF types have the potential to be rather verbose. That puts additional pressure on the language to develop a type aliasing mechanism to allow for more convenient type names. Such an RFC is best implemented as a separate follow up.

Proposed Voting Choices

This is a simple yes/no vote to include DNF types. 2/3 required to pass.

Patches and Tests

Patch is available here: https://github.com/php/php-src/pull/8725


After the project is implemented, this section should contain

  1. the version(s) it was merged into
  2. a link to the git commit(s)
  3. a link to the PHP manual entry for the feature
  4. a link to the language specification section (if any)


Links to external references, discussions or RFCs

Rejected Features

Keep this updated with features that were discussed on the mail lists.

rfc/dnf_types.txt · Last modified: 2022/07/03 02:17 by girgias