# MLIR

Multi-Level IR Compiler Framework

# PDLL - PDL Language

This document details the PDL Language (PDLL), a custom frontend language for writing pattern rewrites targeting MLIR.

Note: This document assumes a familiarity with MLIR concepts; more specifically the concepts detailed within the MLIR Pattern Rewriting and Operation Definition Specification (ODS) documentation.

## Introduction ¶

Pattern matching is an extremely important component within MLIR, as it encompasses many different facets of the compiler. From canonicalization, to optimization, to conversion; every MLIR based compiler will heavily rely on the pattern matching infrastructure in some capacity.

The PDL Language (PDLL) provides a declarative pattern language designed from the ground up for representing MLIR pattern rewrites. PDLL is designed to natively support writing matchers on all of MLIRs constructs via an intuitive interface that may be used for both ahead-of-time (AOT) and just-in-time (JIT) pattern compilation.

## Rationale ¶

This section provides details on various design decisions, their rationale, and alternatives considered when designing PDLL. Given the nature of software development, this section may include references to areas of the MLIR compiler that no longer exist.

### Why build a new language instead of improving TableGen DRR? ¶

Note: This section assumes familiarity with TDRR, please refer the relevant documentation before continuing.

Tablegen DRR (TDRR), i.e. Table-driven Declarative Rewrite Rules, is a declarative DSL for defining MLIR pattern rewrites within the TableGen language. This infrastructure is currently the main way in which patterns may be defined declaratively within MLIR. TDRR utilizes TableGen’s dag support to enable defining MLIR patterns that fit nicely within a DAG structure; in a similar way in which tablegen has been used to defined patterns for LLVM’s backend infrastructure (SelectionDAG/Global Isel/etc.). Unfortunately however, the TableGen language is not as amenable to the structure of MLIR patterns as it has been for LLVM.

The issues with TDRR largely stem from the use of TableGen as the host language for the DSL. These issues have risen from a mismatch in the structure of TableGen compared to the structure of MLIR, and from TableGen having different motivational goals than MLIR. A majority (or all depending on how stubborn you are) of the issues that we’ve come across with TDRR have been addressable in some form; the sticking point here is that the solutions to these problems have often been more “creative” than we’d like. This is a problem, and why we decided not to invest a larger effort into improving TDRR; users generally don’t want “creative” APIs, they want something that is intuitive to read/write.

To highlight some of these issues, below we will take a tour through some of the problems that have arisen, and how we “fixed” them.

#### Multi-result operations ¶

MLIR natively supports a variable number of operation results. For the DAG based structure of TDRR, any form of multiple results (operations in this instance) creates a problem. This is because the DAG wants a single root node, and does not have nice facilities for indexing or naming the multiple results. Let’s take a look at a quick example to see how this manifests:

// Suppose we have a three result operation, defined as seen below.
def ThreeResultOp : Op<"three_result_op"> {
let arguments = (ins ...);

let results = (outs
AnyTensor:$output1, AnyTensor:$output2,
AnyTensor:$output3 ); } // To bind the results of ThreeResultOp in a TDRR pattern, we bind all results // to a single name and use a special naming convention: __N, where N is the // N-th result. def : Pattern<(ThreeResultOp:$results ...),
[(... $results__0), ..., (...$results__2), ...]>;


In TDRR, we “solved” the problem of accessing multiple results, but this isn’t a very intuitive interface for users. Magical naming conventions obfuscate the code and can easily introduce bugs and other errors. There are various things that we could try to improve this situation, but there is a fundamental limit to what we can do given the limits of the TableGen dag structure. In PDLL, however, we have the freedom and flexibility to provide a proper interface into operations, regardless of their structure:

// Import our definition of ThreeResultOp.
#include "ops.td"

Pattern {
...

// In PDLL, we can directly reference the results of an operation variable.
// This provides a closer mental model to what the user expects.
let threeResultOp = op<my_dialect.three_result_op>;
let userOp = op<my_dialect.user_op>(threeResultOp.output1, ..., threeResultOp.output3);

...
}


#### Constraints ¶

In TDRR, the match dag defines the general structure of the input IR to match. Any non-structural/non-type constraints on the input are generally relegated to a list of constraints specified after the rewrite dag. For very simple patterns this may suffice, but with larger patterns it becomes quite problematic as it separates the constraint from the entity it constrains and negatively impacts the readability of the pattern. As an example, let’s look at a simple pattern that adds additional constraints to its inputs:

// Suppose we have a two result operation, defined as seen below.
def TwoResultOp : Op<"two_result_op"> {
let arguments = (ins ...);

let results = (outs
AnyTensor:$output1, AnyTensor:$output2
);
}

// A simple constraint to check if a value is use_empty.
def HasNoUseOf: Constraint<CPred<"$_self.use_empty()">, "has no use">; // Check if two values have a ShapedType with the same element type. def HasSameElementType : Constraint< CPred<"$0.getType().cast<ShapedType>().getElementType() == "
"$1.getType().cast<ShapedType>().getElementType()">, "values have same element type">; def : Pattern<(TwoResultOp:$results $input), [(...), (...)], [(HasNoUseOf:$results__1),
(HasSameElementType $results__0,$input)]>;


Above, when observing the constraints we need to search through the input dag for the inputs (also keeping in mind the magic naming convention for multiple results). For this simple pattern it may be just a few lines above, but complex patterns often grow to 10s of lines long. In PDLL, these constraints can be applied directly on or next to the entities they apply to:

// The same constraints that we defined above:
Constraint HasNoUseOf(value: Value) [{
return success(value.use_empty());
}];
Constraint HasSameElementType(value1: Value, value2: Value) [{
return success(value1.getType().cast<ShapedType>().getElementType() ==
value2.getType().cast<ShapedType>().getElementType());
}];

Pattern {
// In PDLL, we can apply the constraint as early (or as late) as we want. This
// enables better structuring of the matcher code, and improves the
let op = op<my_dialect.two_result_op>(input: Value);
HasNoUseOf(op.output2);
HasSameElementType(input, op.output2);

// ...
}


#### Replacing Multiple Operations ¶

Often times a pattern will transform N number of input operations into N number of result operations. In PDLL, replacing multiple operations is as simple as adding two replace statements. In TDRR, the situation is a bit more nuanced. Given the single root structure of the TableGen dag, replacing a non-root operation is not nicely supported. It currently isn’t natively possible, and instead requires using multiple patterns. We could potentially add another special rewrite directive, or extend replaceWithValue, but this simply highlights how even a basic IR transformation is muddled by the complexity of the host language.

### Why not build a DSL in “X”? ¶

Yes! Well yes and no. To understand why, we have to consider what types of users we are trying to serve and what constraints we enforce upon them. The goal of PDLL is to provide a default and effective pattern language for MLIR that all users of MLIR can interact with immediately, regardless of their host environment. This language is available with no extra dependencies and comes “free” along with MLIR. If we were to use an existing host language to build our new DSL, we would need to make compromises along with it depending on the language. For some, there are questions of how to enforce matching environments (python2 or python3?, which version?), performance considerations, integration, etc. As an LLVM project, this could also mean enforcing a new language dependency on the users of MLIR (many of which may not want/need such a dependency otherwise). Another issue that comes along with any DSL that is embeded in another language: mitigating the user impedance mismatch between what the user expects from the host language and what our “backend” supports. For example, the PDL IR abstraction only contains limited support for control flow. If we were to build a DSL in python, we would need to ensure that complex control flow is either handled completely or effectively errors out. Even with ideal error handling, not having the expected features available creates user frustration. In addition to the environment constraints, there is also the issue of language tooling. With PDLL we intend to build a very robust and modern toolset that is designed to cater the needs of pattern developers, including code completion, signature help, and many more features that are specific to the problem we are solving. Integrating custom language tooling into existing languages can be difficult, and in some cases impossible (as our DSL would merely be a small subset of the existing language).

These various points have led us to the initial conclusion that the most effective tool we can provide for our users is a custom tool designed for the problem at hand. With all of that being said, we understand that not all users have the same constraints that we have placed upon ourselves. We absolutely encourage and support the existence of various PDL frontends defined in different languages. This is one of the original motivating factors around building the PDL IR abstraction in the first place; to enable innovation and flexibility for our users (and in turn their users). For some, such as those in research and the Machine Learning space, they may already have a certain language (such as Python) heavily integrated into their workflow. For these users, a PDL DSL in their language may be ideal and we will remain committed to supporting and endorsing that from an infrastructure point-of-view.

## Language Specification ¶

Note: PDLL is still under active development, and the designs discussed below are not necessarily final and may be subject to change.

The design of PDLL is heavily influenced and centered around the PDL IR abstraction, which in turn is designed as an abstract model of the core MLIR structures. This leads to a design and structure that feels very similar to if you were directly writing the IR you want to match.

### Includes ¶

PDLL supports an include directive to import content defined within other source files. There are two types of files that may be included: .pdll and .td files.

#### .pdll includes ¶

When including a .pdll file, the contents of that file are copied directly into the current file being processed. This means that any patterns, constraints, rewrites, etc., defined within that file are processed along with those within the current file.

#### .td includes ¶

When including a .td file, PDLL will automatically import any pertinent ODS information within that file. This includes any defined operations, constraints, interfaces, and more, making them implicitly accessible within PDLL. This is important, as ODS information allows for certain PDLL constructs, such as the operation expression, to become much more powerful.

### Patterns ¶

In any pattern descriptor language, pattern definition is at the core. In PDLL, patterns start with Pattern optionally followed by a name and a set of pattern metadata, and finally terminated by a pattern body. A few simple examples are shown below:

// Here we have defined an anonymous pattern:
Pattern {
// Pattern bodies are separated into two components:
// * Match Section
//    - Describes the input IR.
let root = op<toy.reshape>(op<toy.reshape>(arg: Value));

// * Rewrite Section
//    - Describes how to transform the IR.
//    - Last statement starts the rewrite.
replace root with op<toy.reshape>(arg);
}

// Here we have defined a pattern named ReshapeReshapeOptPattern with a
// benefit of 10:
Pattern ReshapeReshapeOptPattern with benefit(10) {
replace op<toy.reshape>(op<toy.reshape>(arg: Value))
with op<toy.reshape>(arg);
}


After the definition of the pattern metadata, we specify the pattern body. The structure of a pattern body is comprised of two main sections, the match section and the rewrite section. The match section of a pattern describes the expected input IR, whereas the rewrite section describes how to transform that IR. This distinction is an important one to make, as PDLL handles certain variables and expressions differently within the different sections. When relevant in each of the sections below, we shall explicitly call out any behavioral differences.

The general layout of the match and rewrite section is as follows: the last statement of the pattern body is required to be a operation rewrite statement, and denotes the rewrite section; every statement before denotes the match section.

Rewrite patterns in MLIR have a set of metadata that allow for controlling certain behaviors, and providing information to the rewrite driver applying the pattern. In PDLL, a pattern can provide a non-default value for this metadata after the pattern name. Below, examples are shown for the different types of metadata supported:

##### Benefit ¶

The benefit of a Pattern is an integer value that represents the “benefit” of matching that pattern. It is used by pattern drivers to determine the relative priorities of patterns during application; a pattern with a higher benefit is generally applied before one with a lower benefit.

In PDLL, a pattern has a default benefit set to the number of input operations, i.e. the number of distinct Op expressions/variables, in the match section. This rule is driven by an observation that larger matches are more beneficial than smaller ones, and if a smaller one is applied first the larger one may not apply anymore. Patterns can override this behavior by specifying the benefit in the metadata section of the pattern:

// Here we specify that this pattern has a benefit of 10, overriding the
// default behavior.
Pattern with benefit(10) {
...
}

##### Bounded Rewrite Recursion ¶

During pattern application, there are situations in which a pattern may be applicable to the result of a previous application of that same pattern. If the pattern does not properly handle this recusive application, the pattern driver could become stuck in an infinite loop of application. To prevent this, patterns by-default are assumed to not have proper recursive bounding and will not be recursively applied. A pattern can signal that it does have proper handling for recursion by specifying the recusion flag in the pattern metadata section:

// Here we signal that this pattern properly bounds recursive application.
Pattern with recusion {
...
}


#### Single Line “Lambda” Body ¶

Patterns generally define their body using a compound block of statements, as shown below:

Pattern {
replace op<my_dialect.foo>(operands: ValueRange) with operands;
}


Patterns also support a lambda-like syntax for specifying simple single line bodies. The lambda body of a Pattern expects a single operation rewrite statement:

Pattern => replace op<my_dialect.foo>(operands: ValueRange) with operands;


### Variables ¶

Variables in PDLL represent specific instances of IR entities, such as Values, Operations, Types, etc. Consider the simple pattern below:

Pattern {
let value: Value;
let root = op<mydialect.foo>(value);

replace root with value;
}


In this pattern we define two variables, value and root, using the let statement. The let statement allows for defining variables and constraining them. Every variable in PDLL is of a certain type, which defines the type of IR entity the variable represents. The type of a variable may be determined via either a constraint, or an initializer expression.

#### Variable “Binding” ¶

In addition to having a type, variables must also be “bound”, either via an initializer expression or to a non-native constraint or rewrite use within the match section of the pattern. “Binding” a variable contextually identifies that variable within either the input (i.e. match section) or output (i.e. rewrite section) IR. In the match section, this allows for building the match tree from the pattern’s root operation, which must be “bound” to the operation rewrite statement that denotes the rewrite section of the pattern. All non-root variables within the match section must be bound in some way to the “root” operation. To help illustrate the concept, let’s take a look at a quick example. Consider the .mlir snippet below:

func.func @baz(%arg: i32) {
%result = my_dialect.foo %arg, %arg -> i32
}


Say that we want to write a pattern that matches my_dialect.foo and replaces it with its unique input argument. A naive way to write this pattern in PDLL is shown below:

Pattern {
// ** match section ** //
let arg: Value;
let root = op<my_dialect.foo>(arg, arg);

// ** rewrite section ** //
replace root with arg;
}


In the above pattern, the arg variable is “bound” to the first and second operands of the root operation. Every use of arg is constrained to be the same Value, i.e. the first and second operands of root will be constrained to refer to the same input Value. The same is true for the root operation, it is bound to the “root” operation of the pattern as it is used in input of the top-level replace statement of the rewrite section of the pattern. Writing this pattern using the C++ API, the concept of “binding” becomes more clear:

struct Pattern : public OpRewritePattern<my_dialect::FooOp> {
LogicalResult matchAndRewrite(my_dialect::FooOp root, PatternRewriter &rewriter) {
Value arg = root->getOperand(0);
if (arg != root->getOperand(1))
return failure();

rewriter.replaceOp(root, arg);
return success();
}
};


If a variable is not “bound” properly, PDLL won’t be able to identify what value it would correspond to in the IR. As a final example, let’s consider a variable that hasn’t been bound:

Pattern {
// ** match section ** //
let arg: Value;
let root = op<my_dialect.foo>

// ** rewrite section ** //
replace root with arg;
}


If we were to write this exact pattern in C++, we would end up with:

struct Pattern : public OpRewritePattern<my_dialect::FooOp> {
LogicalResult matchAndRewrite(my_dialect::FooOp root, PatternRewriter &rewriter) {
// arg was never bound, so we don't know what input Value it was meant to
// correspond to.
Value arg;

rewriter.replaceOp(root, arg);
return success();
}
};


#### Variable Constraints ¶

// This statement defines a variable value that is constrained to be a Value.
let value: Value;

// This statement defines a variable value that is constrained to be a Value
// *and* constrained to have a single use.
let value: [Value, HasOneUse];


Any number of single entity constraints may be attached directly to a variable upon declaration. Within the matcher section, these constraints may add additional checks on the input IR. Within the rewriter section, constraints are only used to define the type of the variable. There are a number of builtin constraints that correlate to the core MLIR constructs: Attr, Op, Type, TypeRange, Value, ValueRange. Along with these, users may define custom constraints that are implemented within PDLL, or natively (i.e. outside of PDLL). See the general Constraints section for more detailed information.

#### Inline Variable Definition ¶

Along with the let statement, variables may also be defined inline by specifying the constraint list along with the desired variable name in the first place that the variable would be used. After definition, the variable is visible from all points forward. See below for an example:

// value is used as an operand to the operation root:
let value: Value;
let root = op<my_dialect.foo>(value);
replace root with value;

// value could also be defined "inline":
let root = op<my_dialect.foo>(value: Value);
replace root with value;


Note that the point of definition of an inline variable is the point of reference, meaning that an inline variable can be used immediately in the same parent expression within which it was defined:

let root = op<my_dialect.foo>(value: Value, _: Value, value);
replace root with value;

##### Wildcard Variable Definition ¶

Often times when defining a variable inline, the variable isn’t intended to be used anywhere else in the pattern. For example, this may happen if you want to attach constraints to a variable but have no other use for it. In these situations, the “wildcard” variable can be used to remove the need to provide a name, as “wildcard” variables are not visible outside of the point of definition. An example is shown below:

Pattern {
let root = op<my_dialect.foo>(arg: Value, _: Value, _: [Value, I64Value], arg);
replace root with arg;
}


In the above example, the second operand isn’t needed for the pattern but we need to provide it to signal that a second operand does exist (we just don’t care what it is in this pattern).

### Operation Expression ¶

An operation expression in PDLL represents an MLIR operation. In the match section of the pattern, this expression models one of the input operations to the pattern. In the rewrite section of the pattern, this expression models one of the operations to create. The general structure of the operation expression is very similar to that of the “generic form” of textual MLIR assembly:

let root = op<my_dialect.foo>(operands: ValueRange) {attr = attr: Attr} -> (resultTypes: TypeRange);


Let’s walk through each of the different components of the expression:

#### Operation name ¶

The operation name signifies which type of MLIR Op this operation corresponds to. In the match section of the pattern, the name may be elided. This would cause this pattern to match any operation type that satifies the rest of the constraints of the operation. In the rewrite section, the name is required.

// root corresponds to an instance of a my_dialect.foo operation.
let root = op<my_dialect.foo>;

// root could be an instance of any operation type.
let root = op<>;


#### Operands ¶

The operands section corresponds to the operands of the operation. This section of an operation expression may be elided, which within a match section means that the operands are not constrained in any way. If elided within a rewrite section, the operation is treated as having no operands. When present, the operands of an operation expression are interpreted in the following ways:

1. A single instance of type ValueRange:

In this case, the single range is treated as all of the operands of the operation:

// Define an instance with single range of operands.
let root = op<my_dialect.foo>(allOperands: ValueRange);

1. A variadic number of either Value or ValueRange:

In this case, the inputs are expected to correspond with the operand groups as defined on the operation in ODS.

Given the following operation definition in ODS:

def MyIndirectCallOp {
let arguments = (ins FunctionType:$call, Variadic<AnyType>:$args);
}


We can match the operands as so:

let root = op<my_dialect.indirect_call>(call: Value, args: ValueRange);


#### Results ¶

The results section corresponds to the result types of the operation. This section of an operation expression may be elided, which within a match section means that the result types are not constrained in any way. If elided within a rewrite section, the results of the operation are inferred. When present, the result types of an operation expression are interpreted in the following ways:

1. A single instance of type TypeRange:

In this case, the single range is treated as all of the result types of the operation:

// Define an instance with single range of types.
let root = op<my_dialect.foo> -> (allResultTypes: TypeRange);

1. A variadic number of either Type or TypeRange:

In this case, the inputs are expected to correspond with the result groups as defined on the operation in ODS.

Given the following operation definition in ODS:

def MyOp {
let results = (outs SomeType:$result, Variadic<SomeType>:$otherResults);
}


We can match the result types as so:

let root = op<my_dialect.op> -> (result: Type, otherResults: TypeRange);


#### Inferred Results ¶

Within the rewrite section of a pattern, the result types of an operation are inferred if they are elided or otherwise not previously bound. The “variable binding” section above discusses the concept of “binding” in more detail. Below are various examples that build upon this to help showcase how a result type may be “bound”:

op<my_dialect.op> -> (type<"i32">);

• Binding to types within the match section:
Pattern {
replace op<dialect.inputOp> -> (resultTypes: TypeRange)
with op<dialect.outputOp> -> (resultTypes);
}

• Binding to previously inferred types:
Pattern {
rewrite root: Op with {
// resultTypes here is *not* yet bound, and will be inferred when
// creating dialect.op. Any uses of resultTypes after this expression,
// will use the types inferred when creating this operation.
op<dialect.op> -> (resultTypes: TypeRange);

// resultTypes here is bound to the types inferred when creating dialect.op.
op<dialect.bar> -> (resultTypes);
};
}

Rewrite BuildTypes() -> TypeRange;

Pattern {
rewrite root: Op with {
op<dialect.op> -> (BuildTypes());
};
}


Below are the set of contexts in which result type inferrence is supported:

##### Inferred Results of Replacement Operation ¶

Replacements have the invariant that the types of the replacement values must match the result types of the input operation. This means that when replacing one operation with another, the result types of the replacement operation may be inferred from the result types of the operation being replaced. For example, consider the following pattern:

Pattern => replace op<dialect.inputOp> with op<dialect.outputOp>;


This pattern could be written in a more explicit way as:

Pattern {
replace op<dialect.inputOp> -> (resultTypes: TypeRange)
with op<dialect.outputOp> -> (resultTypes);
}

##### Inferred Results with InferTypeOpInterface ¶

InferTypeOpInterface is an interface that enables operations to infer its result types from its input attributes, operands, regions, etc. When the result types of an operation cannot be inferred from any other context, this interface is invoked to infer the result types of the operation.

#### Attributes ¶

The attributes section of the operation expression corresponds to the attribute dictionary of the operation. This section of an operation expression may be elided, in which case the attributes are not constrained in any way. The composition of this component maps exactly to how attribute dictionaries are structured in the MLIR textual assembly format:

let root = op<my_dialect.foo> {attr1 = attrValue: Attr, attr2 = attrValue2: Attr};


Within the {} attribute entries are specified by an identifier or string name, corresponding to the attribute name, followed by an assignment to the attribute value. If the attribute value is elided, the value of the attribute is implicitly defined as a UnitAttr.

let unitConstant = op<my_dialect.constant> {value};

##### Accessing Operation Results ¶

In multi-operation patterns, the result of one operation often feeds as an input into another. The result groups of an operation may be accessed by name or by index via the . operator:

Note: Remember to import the definition of your operation via include to ensure it is visible to PDLL.

Given the following operation definition in ODS:

def MyResultOp {
let results = (outs SomeType:$result); } def MyInputOp { let arguments = (ins SomeType:$input, SomeType:\$input);
}


We can write a pattern where MyResultOp feeds into MyInputOp as so:

// In this example, we use both result(the name) and 0(the index) to refer to
// the first result group of resultOp.
// Note: If we elide the result types section within the match section, it means
let resultOp = op<my_dialect.result_op>;
let inputOp = op<my_dialect.input_op>(resultOp.result, resultOp.0);


Along with result name access, variables of Op type may implicitly convert to Value or ValueRange. If these variables are registered (has ODS entry), they are converted to Value when they are known to only have one result, otherwise they will be converted to ValueRange:

// resultOp may also convert implicitly to a Value for use in inputOp:
let resultOp = op<my_dialect.result_op>;
let inputOp = op<my_dialect.input_op>(resultOp);

// We could also inline resultOp directly:
let inputOp = op<my_dialect.input_op>(op<my_dialect.result_op>);


#### Unregistered Operations ¶

A variable of unregistered op is still available for numeric result indexing. Given that we don’t have knowledge of its result groups, numeric indexing returns a Value corresponding to the individual result at the given index.

// Use the index 0 to refer to the first result value of the unregistered op.
let inputOp = op<my_dialect.input_op>(op<my_dialect.unregistered_op>.0);


### Attribute Expression ¶

An attribute expression represents a literal MLIR attribute. It allows for statically specifying an MLIR attribute to use, by specifying the textual form of that attribute.

let trueConstant = op<arith.constant> {value = attr<"true">};

let applyResult = op<affine.apply>(args: ValueRange) {map = attr<"affine_map<(d0, d1) -> (d1 - 3)>">}


### Type Expression ¶

A type expression represents a literal MLIR type. It allows for statically specifying an MLIR type to use, by specifying the textual form of that type.

let i32Constant = op<arith.constant> -> (type<"i32">);


### Tuples ¶

PDLL provides native support for tuples, which are used to group multiple elements into a single compound value. The values in a tuple can be of any type, and do not need to be of the same type. There is also no limit to the number of elements held by a tuple. The elements of a tuple can be accessed by index:

let tupleValue = (op<my_dialect.foo>, attr<"10 : i32">, type<"i32">);

let opValue = tupleValue.0;
let attrValue = tupleValue.1;
let typeValue = tupleValue.2;


You can also name the elements of a tuple and use those names to refer to the values of the individual elements. An element name consists of an identifier followed immediately by an equal (=).

let tupleValue = (
opValue = op<my_dialect.foo>,
attr<"10 : i32">,
typeValue = type<"i32">
);

let opValue = tupleValue.opValue;
let attrValue = tupleValue.1;
let typeValue = tupleValue.typeValue;


Tuples are used to represent multiple results from a constraint or rewrite.

### Constraints ¶

Constraints provide the ability to inject additional checks on the input IR within the match section of a pattern. Constraints can be applied anywhere within the match section, and depending on the type can either be applied via the constraint list of a variable or via the call operator (e.g. MyConstraint(...)). There are three main categories of constraints:

#### Core Constraints ¶

PDLL defines a number of core constraints that constrain the type of the IR entity. These constraints can only be applied via the constraint list of a variable.

• Attr (< type >)?

A single entity constraint that corresponds to an mlir::Attribute. This constraint optionally takes a type component that constrains the result type of the attribute.

// Define a simple variable using the Attr constraint.
let attr: Attr;
let constant = op<arith.constant> {value = attr};

// Define a simple variable using the Attr constraint, that has its type
// constrained as well.
let attrType: Type;
let attr: Attr<attrType>;
let constant = op<arith.constant> {value = attr};

• Op (< op-name >)?

A single entity constraint that corresponds to an mlir::Operation *.

// Match only when the input is from another operation.
let inputOp: Op;
let root = op<my_dialect.foo>(inputOp);

// Match only when the input is from another my_dialect.foo operation.
let inputOp: Op<my_dialect.foo>;
let root = op<my_dialect.foo>(inputOp);

• Type

A single entity constraint that corresponds to an mlir::Type.

// Define a simple variable using the Type constraint.
let resultType: Type;
let root = op<my_dialect.foo> -> (resultType);

• TypeRange

A single entity constraint that corresponds to a mlir::TypeRange.

// Define a simple variable using the TypeRange constraint.
let resultTypes: TypeRange;
let root = op<my_dialect.foo> -> (resultTypes);

• Value (< type-expr >)?

A single entity constraint that corresponds to an mlir::Value. This constraint optionally takes a type component that constrains the result type of the value.

// Define a simple variable using the Value constraint.
let value: Value;
let root = op<my_dialect.foo>(value);

// Define a variable using the Value constraint, that has its type constrained
// to be same as the result type of the root op.
let valueType: Type;
let input: Value<valueType>;
let root = op<my_dialect.foo>(input) -> (valueType);

• ValueRange (< type-expr >)?

A single entity constraint that corresponds to a mlir::ValueRange. This constraint optionally takes a type component that constrains the result types of the value range.

// Define a simple variable using the ValueRange constraint.
let inputs: ValueRange;
let root = op<my_dialect.foo>(inputs);

// Define a variable using the ValueRange constraint, that has its types
// constrained to be same as the result types of the root op.
let valueTypes: TypeRange;
let inputs: ValueRange<valueTypes>;
let root = op<my_dialect.foo>(inputs) -> (valueTypes);


#### Defining Constraints in PDLL ¶

Aside from the core constraints, additional constraints can also be defined within PDLL. This allows for building matcher fragments that can be composed across many different patterns. A constraint in PDLL is defined similarly to a function in traditional programming languages; it contains a name, a set of input arguments, a set of result types, and a body. Results of a constraint are returned via a return statement. A few examples are shown below:

/// A constraint that takes an input and constrains the use to an operation of
/// a given type.
Constraint UsedByFooOp(value: Value) {
op<my_dialect.foo>(value);
}

/// A constraint that returns a result of an existing operation.
Constraint ExtractResult(op: Op<my_dialect.foo>) -> Value {
return op.result;
}

Pattern {
let value = ExtractResult(op<my_dialect.foo>);
UsedByFooOp(value);
}

##### Constraints with multiple results ¶

Constraints can return multiple results by returning a tuple of values. When returning multiple results, each result can also be assigned a name to use when indexing that tuple element. Tuple elements can be referenced by their index number, or by name if they were assigned one.

// A constraint that returns multiple results, with some of the results assigned
Constraint ExtractMultipleResults(op: Op<my_dialect.foo>) -> (Value, result1: Value) {
return (op.result1, op.result2);
}

Pattern {
// Return a tuple of values.
let result = ExtractMultipleResults(op: op<my_dialect.foo>);

// Index the tuple elements by index, or by name.
replace op<my_dialect.foo> with (result.0, result.1, result.result1);
}

##### Constraint result type inference ¶

In addition to explicitly specifying the results of the constraint via the constraint signature, PDLL defined constraints also support inferring the result type from the return statement. Result type inference is active whenever the constraint is defined with no result constraints:

// This constraint returns a derived operation.
Constraint ReturnSelf(op: Op<my_dialect.foo>) {
return op;
}
// This constraint returns a tuple of two Values.
Constraint ExtractMultipleResults(op: Op<my_dialect.foo>) {
return (result1 = op.result1, result2 = op.result2);
}

Pattern {
let values = ExtractMultipleResults(op<my_dialect.foo>);
replace op<my_dialect.foo> with (values.result1, values.result2);
}

##### Single Line “Lambda” Body ¶

Constraints generally define their body using a compound block of statements, as shown below:

Constraint ReturnSelf(op: Op<my_dialect.foo>) {
return op;
}
Constraint ExtractMultipleResults(op: Op<my_dialect.foo>) {
return (result1 = op.result1, result2 = op.result2);
}


Constraints also support a lambda-like syntax for specifying simple single line bodies. The lambda body of a Constraint expects a single expression, which is implicitly returned:

Constraint ReturnSelf(op: Op<my_dialect.foo>) => op;

Constraint ExtractMultipleResults(op: Op<my_dialect.foo>)
=> (result1 = op.result1, result2 = op.result2);


#### Native Constraints ¶

Constraints may also be defined outside of PDLL, and registered natively within the C++ API.

##### Importing existing Native Constraints ¶

Constraints defined externally can be imported into PDLL by specifying a constraint “declaration”. This is similar to the PDLL form of defining a constraint but omits the body. Importing the declaration in this form allows for PDLL to statically know the expected input and output types.

// Import a single entity value native constraint that checks if the value has a
// single use. This constraint must be registered by the consumer of the
// compiled PDL.
Constraint HasOneUse(value: Value);

// Import a multi-entity type constraint that checks if two values have the same
// element type.
Constraint HasSameElementType(value1: Value, value2: Value);

Pattern {
// A single entity constraint can be applied via the variable argument list.
let value: HasOneUse;

// Otherwise, constraints can be applied via the call operator:
let value: Value = ...;
let value2: Value = ...;
HasOneUse(value);
HasSameElementType(value, value2);
}


External constraints are those registered explicitly with the RewritePatternSet via the C++ PDL API. For example, the constraints above may be registered as:

static LogicalResult hasOneUseImpl(PatternRewriter &rewriter, Value value) {
return success(value.hasOneUse());
}
static LogicalResult hasSameElementTypeImpl(PatternRewriter &rewriter,
Value value1, Value Value2) {
return success(value1.getType().cast<ShapedType>().getElementType() ==
value2.getType().cast<ShapedType>().getElementType());
}

void registerNativeConstraints(RewritePatternSet &patterns) {
patternList.getPDLPatterns().registerConstraintFunction(
"HasOneUse", hasOneUseImpl);
patternList.getPDLPatterns().registerConstraintFunction(
"HasSameElementType", hasSameElementTypeImpl);
}

##### Defining Native Constraints in PDLL ¶

In addition to importing native constraints, PDLL also supports defining native constraints directly when compiling ahead-of-time (AOT) for C++. These constraints can be defined by specifying a string code block after the constraint declaration:

Constraint HasOneUse(value: Value) [{
return success(value.hasOneUse());
}];
Constraint HasSameElementType(value1: Value, value2: Value) [{
return success(value1.getType().cast<ShapedType>().getElementType() ==
value2.getType().cast<ShapedType>().getElementType());
}];

Pattern {
// A single entity constraint can be applied via the variable argument list.
let value: HasOneUse;

// Otherwise, constraints can be applied via the call operator:
let value: Value = ...;
let value2: Value = ...;
HasOneUse(value);
HasSameElementType(value, value2);
}


The arguments of the constraint are accessible within the code block via the same name. See the “type translation” below for detailed information on how PDLL types are converted to native types. In addition to the PDLL arguments, the code block may also access the current PatternRewriter using rewriter. The result type of the native constraint function is implicitly defined as a ::mlir::LogicalResult.

Taking the constraints defined above as an example, these function would roughly be translated into:

LogicalResult HasOneUse(PatternRewriter &rewriter, Value value) {
return success(value.hasOneUse());
}
LogicalResult HasSameElementType(Value value1, Value value2) {
return success(value1.getType().cast<ShapedType>().getElementType() ==
value2.getType().cast<ShapedType>().getElementType());
}


TODO: Native constraints should also be allowed to return values in certain cases.

###### Native Constraint Type Translations ¶

The types of argument and result variables are generally mapped to the corresponding MLIR type of the constraint used. Below is a detailed description of how the mapped type of a variable is determined for the various different types of constraints.

• Attr, Op, Type, TypeRange, Value, ValueRange:

These are all core constraints, and are mapped directly to the MLIR equivalent (that their names suggest), namely:

• Attr -> “::mlir::Attribute”

• Op -> “::mlir::Operation *”

• Type -> “::mlir::Type”

• TypeRange -> “::mlir::TypeRange”

• Value -> “::mlir::Value”

• ValueRange -> “::mlir::ValueRange”

• Op<dialect.name>

A named operation constraint has a unique translation. If the ODS registration of the referenced operation has been included, the qualified C++ is used. If the ODS information is not available, this constraint maps to “::mlir::Operation *”, similarly to the unnamed variant. For example, given the following:

// my_ops.td provides the ODS definition of the my_dialect operations, such as
// my_dialect.bar used below.
#include "my_ops.td"

Constraint Cst(op: Op<my_dialect.bar>) [{
return success(op ... );
}];


The native type used for op may be of the form my_dialect::BarOp, as opposed to the default ::mlir::Operation *. Below is a sample translation of the above constraint:

LogicalResult Cst(my_dialect::BarOp op) {
return success(op ... );
}

• Imported ODS Constraints

Aside from the core constraints, certain constraints imported from ODS may use a unique native type. How to enable this unique type depends on the ODS constraint construct that was imported:

• Attr constraints

• Imported Attr constraints utilize the storageType field for native type translation.
• Type constraints

• Imported Type constraints utilize the cppClassName field for native type translation.
• AttrInterface/OpInterface/TypeInterface constraints

• Imported interfaces utilize the cppInterfaceName field for native type translation.

#### Defining Constraints Inline ¶

In addition to global scope, PDLL Constraints and Native Constraints defined in PDLL may be specified inline at any level of nesting. This means that they may be defined in Patterns, other Constraints, Rewrites, etc:

Constraint GlobalConstraint() {
Constraint LocalConstraint(value: Value) {
...
};
Constraint LocalNativeConstraint(value: Value) [{
...
}];
let someValue: [LocalConstraint, LocalNativeConstraint] = ...;
}


Constraints that are defined inline may also elide the name when used directly:

Constraint GlobalConstraint(inputValue: Value) {
Constraint(value: Value) { ... }(inputValue);
Constraint(value: Value) [{ ... }](inputValue);
}


When defined inline, PDLL constraints may reference any previously defined variable:

Constraint GlobalConstraint(op: Op<my_dialect.foo>) {
Constraint LocalConstraint() {
let results = op.results;
};
}


### Rewriters ¶

Rewriters define the set of transformations to be performed within the rewrite section of a pattern, and, more specifically, how to transform the input IR after a successful pattern match. All PDLL rewrites must be defined within the rewrite section of the pattern. The rewrite section is denoted by the last statement within the body of the Pattern, which is required to be an operation rewrite statement. There are two main categories of rewrites in PDLL: operation rewrite statements, and user defined rewrites.

#### Operation Rewrite statements ¶

Operation rewrite statements are builtin PDLL statements that perform an IR transformation given a root operation. These statements are the only ones able to start the rewrite section of a pattern, as they allow for properly “binding” the root operation of the pattern.

##### erase statement ¶
// A pattern that erases all my_dialect.foo operations.
Pattern => erase op<my_dialect.foo>;


The erase statement erases a given operation.

##### replace statement ¶
// A pattern that replaces the root operation with its input value.
Pattern {
let root = op<my_dialect.foo>(input: Value);
replace root with input;
}

// A pattern that replaces the root operation with multiple input values.
Pattern {
let root = op<my_dialect.foo>(input: Value, _: Value, input2: Value);
replace root with (input, input2);
}

// A pattern that replaces the root operation with another operation.
// Note that when an operation is used as the replacement, we can infer its
// result types from the input operation. In these cases, the result
// types of replacement operation may be elided.
Pattern {
// Note: In this pattern we also inlined the root expression.
replace op<my_dialect.foo> with op<my_dialect.bar>;
}


The replace statement allows for replacing a given root operation with either another operation, or a set of input Value and ValueRange values. When an operation is used as the replacement, we allow infering the result types from the input operation. In these cases, the result types of replacement operation may be elided. Note that no other components aside from the result types will be inferred from the input operation during the replacement.

##### rewrite statement ¶
// A simple pattern that replaces the root operation with its input value.
Pattern {
let root = op<my_dialect.foo>(input: Value);
rewrite root with {
...

replace root with input;
};
}


The rewrite statement allows for rewriting a given root operation with a block of nested rewriters. The root operation is not implicitly erased or replaced, and any transformations to it must be expressed within the nested rewrite block. The inner body may contain any number of other rewrite statements, variables, or expressions.

#### Defining Rewriters in PDLL ¶

Additional rewrites can also be defined within PDLL, which allows for building rewrite fragments that can be composed across many different patterns. A rewriter in PDLL is defined similarly to a function in traditional programming languages; it contains a name, a set of input arguments, a set of result types, and a body. Results of a rewrite are returned via a return statement. A few examples are shown below:

// A rewrite that constructs and returns a new operation, given an input value.
Rewrite BuildFooOp(value: Value) -> Op {
return op<my_dialect.foo>(value);
}

Pattern {
// We invoke the rewrite in the same way as functions in traditional
// languages.
replace op<my_dialect.old_op>(input: Value) with BuildFooOp(input);
}

##### Rewrites with multiple results ¶

Rewrites can return multiple results by returning a tuple of values. When returning multiple results, each result can also be assigned a name to use when indexing that tuple element. Tuple elements can be referenced by their index number, or by name if they were assigned one.

// A rewrite that returns multiple results, with some of the results assigned
Rewrite CreateRewriteOps() -> (Op, result1: ValueRange) {
return (op<my_dialect.bar>, op<my_dialect.foo>);
}

Pattern {
rewrite root: Op<my_dialect.foo> with {
// Invoke the rewrite, which returns a tuple of values.
let result = CreateRewriteOps();

// Index the tuple elements by index, or by name.
replace root with (result.0, result.1, result.result1);
}
}

##### Rewrite result type inference ¶

In addition to explicitly specifying the results of the rewrite via the rewrite signature, PDLL defined rewrites also support inferring the result type from the return statement. Result type inference is active whenever the rewrite is defined with no result constraints:

// This rewrite returns a derived operation.
Rewrite ReturnSelf(op: Op<my_dialect.foo>) => op;
// This rewrite returns a tuple of two Values.
Rewrite ExtractMultipleResults(op: Op<my_dialect.foo>) {
return (result1 = op.result1, result2 = op.result2);
}

Pattern {
rewrite root: Op<my_dialect.foo> with {
let values = ExtractMultipleResults(op<my_dialect.foo>);
replace root with (values.result1, values.result2);
}
}

##### Single Line “Lambda” Body ¶

Rewrites generally define their body using a compound block of statements, as shown below:

Rewrite ReturnSelf(op: Op<my_dialect.foo>) {
return op;
}
Rewrite EraseOp(op: Op) {
erase op;
}


Rewrites also support a lambda-like syntax for specifying simple single line bodies. The lambda body of a Rewrite expects a single expression, which is implicitly returned, or a single operation rewrite statement:

Rewrite ReturnSelf(op: Op<my_dialect.foo>) => op;
Rewrite EraseOp(op: Op) => erase op;


#### Native Rewriters ¶

Rewriters may also be defined outside of PDLL, and registered natively within the C++ API.

##### Importing existing Native Rewrites ¶

Rewrites defined externally can be imported into PDLL by specifying a rewrite “declaration”. This is similar to the PDLL form of defining a rewrite but omits the body. Importing the declaration in this form allows for PDLL to statically know the expected input and output types.

// Import a single input native rewrite that returns a new operation. This
// rewrite must be registered by the consumer of the compiled PDL.
Rewrite BuildOp(value: Value) -> Op;

Pattern {
replace op<my_dialect.old_op>(input: Value) with BuildOp(input);
}


External rewrites are those registered explicitly with the RewritePatternSet via the C++ PDL API. For example, the rewrite above may be registered as:

static Operation *buildOpImpl(PDLResultList &results, Value value) {
// insert special rewrite logic here.
Operation *resultOp = ...;
return resultOp;
}

void registerNativeRewrite(RewritePatternSet &patterns) {
patterns.getPDLPatterns().registerRewriteFunction("BuildOp", buildOpImpl);
}

##### Defining Native Rewrites in PDLL ¶

In addition to importing native rewrites, PDLL also supports defining native rewrites directly when compiling ahead-of-time (AOT) for C++. These rewrites can be defined by specifying a string code block after the rewrite declaration:

Rewrite BuildOp(value: Value) -> (foo: Op<my_dialect.foo>, bar: Op<my_dialect.bar>) [{
return {rewriter.create<my_dialect::FooOp>(value), rewriter.create<my_dialect::BarOp>()};
}];

Pattern {
let root = op<my_dialect.foo>(input: Value);
rewrite root with {
// Invoke the native rewrite and use the results when replacing the root.
let results = BuildOp(input);
replace root with (results.foo, results.bar);
}
}


The arguments of the rewrite are accessible within the code block via the same name. See the “type translation” below for detailed information on how PDLL types are converted to native types. In addition to the PDLL arguments, the code block may also access the current PatternRewriter using rewriter. See the “result translation” section for detailed information on how the result type of the native function is determined.

Taking the rewrite defined above as an example, this function would roughly be translated into:

std::tuple<my_dialect::FooOp, my_dialect::BarOp> BuildOp(Value value) {
return {rewriter.create<my_dialect::FooOp>(value), rewriter.create<my_dialect::BarOp>()};
}

###### Native Rewrite Type Translations ¶

The types of argument and result variables are generally mapped to the corresponding MLIR type of the constraint used. The rules of native Rewrite type translation are identical to those of native Constraints, please view the corresponding native Constraint type translation section for a detailed description of how the mapped type of a variable is determined.

###### Native Rewrite Result Translation ¶

The results of a native rewrite are directly translated to the results of the native function, using the type translation rules described above. The section below describes the various result translation scenarios:

• Zero Result
Rewrite createOp() [{
rewriter.create<my_dialect::FooOp>();
}];


In the case where a native Rewrite has no results, the native function returns void:

void createOp(PatternRewriter &rewriter) {
rewriter.create<my_dialect::FooOp>();
}

• Single Result
Rewrite createOp() -> Op<my_dialect.foo> [{
return rewriter.create<my_dialect::FooOp>();
}];


In the case where a native Rewrite has a single result, the native function returns the corresponding native type for that single result:

my_dialect::FooOp createOp(PatternRewriter &rewriter) {
return rewriter.create<my_dialect::FooOp>();
}

• Multi Result
Rewrite complexRewrite(value: Value) -> (Op<my_dialect.foo>, FunctionOpInterface) [{
...
}];


In the case where a native Rewrite has multiple results, the native function returns a std::tuple<...> containing the corresponding native types for each of the results:

std::tuple<my_dialect::FooOp, FunctionOpInterface>
complexRewrite(PatternRewriter &rewriter, Value value) {
...
}


#### Defining Rewrites Inline ¶

In addition to global scope, PDLL Rewrites and Native Rewrites defined in PDLL may be specified inline at any level of nesting. This means that they may be defined in Patterns, other Rewrites, etc:

Rewrite GlobalRewrite(inputValue: Value) {
Rewrite localRewrite(value: Value) {
...
};
Rewrite localNativeRewrite(value: Value) [{
...
}];
localRewrite(inputValue);
localNativeRewrite(inputValue);
}


Rewrites that are defined inline may also elide the name when used directly:

Rewrite GlobalRewrite(inputValue: Value) {
Rewrite(value: Value) { ... }(inputValue);
Rewrite(value: Value) [{ ... }](inputValue);
}


When defined inline, PDLL rewrites may reference any previously defined variable:

Rewrite GlobalRewrite(op: Op<my_dialect.foo>) {
Rewrite localRewrite() {
let results = op.results;
};
}