Pattern Rewriting : Generic DAG-to-DAG Rewriting

This document details the design and API of the pattern rewriting infrastructure present in MLIR, a general DAG-to-DAG transformation framework. This framework is widely used throughout MLIR for canonicalization, conversion, and general transformation.

For an introduction to DAG-to-DAG transformation, and the rationale behind this framework please take a look at the Generic DAG Rewriter Rationale.


The pattern rewriting framework can largely be decomposed into two parts: Pattern Definition and Pattern Application.

Defining Patterns

Patterns are defined by inheriting from the RewritePattern class. This class represents the base class of all rewrite patterns within MLIR, and is comprised of the following components:


This is the expected benefit of applying a given pattern. This benefit is static upon construction of the pattern, but may be computed dynamically at pattern initialization time, e.g. allowing the benefit to be derived from domain specific information (like the target architecture). This limitation allows for performing pattern fusion and compiling patterns into an efficient state machine, and Thier, Ertl, and Krall have shown that match predicates eliminate the need for dynamically computed costs in almost all cases: you can simply instantiate the same pattern one time for each possible cost and use the predicate to guard the match.

Root Operation Name (Optional)

The name of the root operation that this pattern matches against. If specified, only operations with the given root name will be provided to the match and rewrite implementation. If not specified, any operation type may be provided. The root operation name should be provided whenever possible, because it simplifies the analysis of patterns when applying a cost model. To match any operation type, a special tag must be provided to make the intent explicit: MatchAnyOpTypeTag.

match and rewrite implementation

This is the chunk of code that matches a given root Operation and performs a rewrite of the IR. A RewritePattern can specify this implementation either via separate match and rewrite methods, or via a combined matchAndRewrite method. When using the combined matchAndRewrite method, no IR mutation should take place before the match is deemed successful. The combined matchAndRewrite is useful when non-trivially recomputable information is required by the matching and rewriting phase. See below for examples:

class MyPattern : public RewritePattern {
  /// This overload constructs a pattern that only matches operations with the
  /// root name of `MyOp`.
  MyPattern(PatternBenefit benefit, MLIRContext *context)
      : RewritePattern(MyOp::getOperationName(), benefit, context) {}
  /// This overload constructs a pattern that matches any operation type.
  MyPattern(PatternBenefit benefit)
      : RewritePattern(benefit, MatchAnyOpTypeTag()) {}

  /// In this section, the `match` and `rewrite` implementation is specified
  /// using the separate hooks.
  LogicalResult match(Operation *op) const override {
    // The `match` method returns `success()` if the pattern is a match, failure
    // otherwise.
    // ...
  void rewrite(Operation *op, PatternRewriter &rewriter) {
    // The `rewrite` method performs mutations on the IR rooted at `op` using
    // the provided rewriter. All mutations must go through the provided
    // rewriter.

  /// In this section, the `match` and `rewrite` implementation is specified
  /// using a single hook.
  LogicalResult matchAndRewrite(Operation *op, PatternRewriter &rewriter) {
    // The `matchAndRewrite` method performs both the matching and the mutation.
    // Note that the match must reach a successful point before IR mutation may
    // take place.


Within the match section of a pattern, the following constraints apply:

  • No mutation of the IR is allowed.

Within the rewrite section of a pattern, the following constraints apply:

  • All IR mutations, including creation, must be performed by the given PatternRewriter. This class provides hooks for performing all of the possible mutations that may take place within a pattern. For example, this means that an operation should not be erased via its erase method. To erase an operation, the appropriate PatternRewriter hook (in this case eraseOp) should be used instead.
  • The root operation is required to either be: updated in-place, replaced, or erased.

Pattern Rewriter

A PatternRewriter is a special class that allows for a pattern to communicate with the driver of pattern application. As noted above, all IR mutations, including creations, are required to be performed via the PatternRewriter class. This is required because the underlying pattern driver may have state that would be invalidated when a mutation takes place. Examples of some of the more prevalent PatternRewriter API is shown below, please refer to the class documentation for a more up-to-date listing of the available API:

  • Erase an Operation : eraseOp

This method erases an operation that either has no results, or whose results are all known to have no uses.

  • Notify why a match failed : notifyMatchFailure

This method allows for providing a diagnostic message within a matchAndRewrite as to why a pattern failed to match. How this message is displayed back to the user is determined by the specific pattern driver.

  • Replace an Operation : replaceOp/replaceOpWithNewOp

This method replaces an operation's results with a set of provided values, and erases the operation.

  • Update an Operation in-place : (start|cancel|finalize)RootUpdate

This is a collection of methods that provide a transaction-like API for updating the attributes, location, operands, or successors of an operation in-place within a pattern. An in-place update transaction is started with startRootUpdate, and may either be canceled or finalized with cancelRootUpdate and finalizeRootUpdate respectively. A convenience wrapper, updateRootInPlace, is provided that wraps a start and finalize around a callback.

  • OpBuilder API

The PatternRewriter inherits from the OpBuilder class, and thus provides all of the same functionality present within an OpBuilder. This includes operation creation, as well as many useful attribute and type construction methods.

Pattern Application

After a set of patterns have been defined, they are collected and provided to a specific driver for application. A driver consists of several high levels parts:

  • Input OwningRewritePatternList

The input patterns to a driver are provided in the form of an OwningRewritePatternList. This class provides a simplified API for building a list of patterns.

  • Driver-specific PatternRewriter

To ensure that the driver state does not become invalidated by IR mutations within the pattern rewriters, a driver must provide a PatternRewriter instance with the necessary hooks overridden. If a driver does not need to hook into certain mutations, a default implementation is provided that will perform the mutation directly.

  • Pattern Application and Cost Model

Each driver is responsible for defining its own operation visitation order as well as pattern cost model, but the final application is performed via a PatternApplicator class. This class takes as input the OwningRewritePatternList and transforms the patterns based upon a provided cost model. This cost model computes a final benefit for a given rewrite pattern, using whatever driver specific information necessary. After a cost model has been computed, the driver may begin to match patterns against operations using PatternApplicator::matchAndRewrite.

An example is shown below:

class MyPattern : public RewritePattern {
  MyPattern(PatternBenefit benefit, MLIRContext *context)
      : RewritePattern(MyOp::getOperationName(), benefit, context) {}

/// Populate the pattern list.
void collectMyPatterns(OwningRewritePatternList &patterns, MLIRContext *ctx) {
  patterns.insert<MyPattern>(/*benefit=*/1, ctx);

/// Define a custom PatternRewriter for use by the driver.
class MyPatternRewriter : public PatternRewriter {
  MyPatternRewriter(MLIRContext *ctx) : PatternRewriter(ctx) {}

  /// Override the necessary PatternRewriter hooks here.

/// Apply the custom driver to `op`.
void applyMyPatternDriver(Operation *op,
                          const OwningRewritePatternList &patterns) {
  // Initialize the custom PatternRewriter.
  MyPatternRewriter rewriter(op->getContext());

  // Create the applicator and apply our cost model.
  PatternApplicator applicator(patterns);
  applicator.applyCostModel([](const RewritePattern &pattern) {
    // Apply a default cost model.
    // Note: This is just for demonstration, if the default cost model is truly
    //       desired `applicator.applyDefaultCostModel()` should be used
    //       instead.
    return pattern.getBenefit();

  // Try to match and apply a pattern.
  LogicalResult result = applicator.matchAndRewrite(op, rewriter);
  if (failed(result)) {
    // ... No patterns were applied.
  // ... A pattern was successfully applied.

Common Pattern Drivers

MLIR provides several common pattern drivers that serve a variety of different use cases.

Dialect Conversion Driver

This driver provides a framework in which to perform operation conversions between, and within dialects using a concept of “legality”. This framework allows for transforming illegal operations to those supported by a provided conversion target, via a set of pattern-based operation rewriting patterns. This framework also provides support for type conversions. More information on this driver can be found here.

Greedy Pattern Rewrite Driver

This driver performs a post order traversal over the provided operations and greedily applies the patterns that locally have the most benefit. The benefit of a pattern is decided solely by the benefit specified on the pattern, and the relative order of the pattern within the pattern list (when two patterns have the same local benefit). Patterns are iteratively applied to operations until a fixed point is reached, at which point the driver finishes. This driver may be used via the following: applyPatternsAndFoldGreedily and applyOpPatternsAndFold. The latter of which only applies patterns to the provided operation, and will not traverse the IR.

Note: This driver is the one used by the canonicalization pass in MLIR.