Understanding MLIR Fold Mechanisms: Design, Implementation, and Rationale

As a result of our more general interest in MLIR’s impact upon AI optimization, we found that after looking at much of the most impactful work in this realm, our interest was drawn toward MLIR fold mechanisms.

Folding, in the context of compiler design, typically refers to the compile-time evaluation of expressions or subexpressions whose values can be determined statically. Of course, this concept is hardly new or all that revolutionary, but has been a fundamental optimization technique in compilers for decades.

To understand exactly what folding is or how it has been incorporated in traditional compilers, we can think about the simplest possible example

Consider the following code snippet in C++

int result = 2 * 5 + 10 / 2;

A compiler with constant folding enabled could replace the above line with:

int result = 15;

In other words, at compile time or when the folding is done, the expression 2 * 5 + 10 / 2 is evaluated and replaced with just 15 … that example is almost too obvious, but it furnishes the gist of what is done. Beyond such constant folding or evaluating expressions composed entirely of constants at compile time rather than runtime, other variants or simplistic examples of folding techniques include algebraic simplification or applying algebraic identities to simplify expressions (e.g., x + 0 = x) OR strength reduction or replacing expensive operations with equivalent cheaper ones (e.g., replacing multiplication by powers of 2 with shifts).

In most traditional compilers, these optimizations are typically implemented as part of larger passes, ie there’s basically zero additional computational cost … in fact, folding likely even reduces compile time computational cost, ie like like eliminating the easy stuff to free up resources or shrink the size of the todo list … and thus our reason for interest in what might be an area where there is more low hanging fruit, or perhaps fruit that is hanging just a weensy bit higher than the previous low-hanging fruit.

Fundamentally, it’s about eliminating busy work … even if computers make automating busy work so easy that nobody ever bothers to eliminate the extra overhead of more busywork, ie the most important lesson from DeepSeek.

Since, we are especially curious about doing a lot more with fold mechanisms, or perhaps other compilier or pre-compiler simplification strategies things that are very similar to fold mechanisms, we want to look at the evolution and future directions for fold mechanisms, but FIRST it is probably well worth our while if we first understand more of the background on fold mechanisms; thus, that is what this post is about.

Introduction
1. The Concept of Folding in Compiler Design
- 1.1 Folding in Traditional Compilers
- 1.2 Folding’s Place in MLIR’s Ecosystem
2. The MLIR Fold Mechanism
3. Fold Method Implementation
4. Fold Mechanism Use Cases
5. Comparison with Other Transformation Mechanisms
6. Design Rationale for Fold’s Limitations
7. Practical Implementation Examples
8. Fold Mechanism in the Dialect Conversion Infrastructure
9. Advanced Considerations and Edge Cases
10. Evolution and Future Directions
Conclusion
References

Introduction

The fold mechanism is one of MLIR’s core transformation capabilities, providing a powerful yet intentionally limited approach to operation simplification. This document provides a comprehensive background on the fold mechanism in MLIR, examining its design philosophy, implementation details, and the rationale behind its intentional limitations to gain greater insight on exactly why fold mechanism are so powerful, thus dangerous.

We will explore how this seemingly constrained system becomes a versatile and widely applicable tool throughout the MLIR compilation process.

MLIR (Multi-Level Intermediate Representation) distinguishes itself through its multi-level design, allowing representation and transformation of code at various levels of abstraction. Within this flexible ecosystem, the fold mechanism plays a crucial role as a fundamental building block for program transformation, despite—or perhaps because of—its carefully designed limitations.

This document will explore why the fold mechanism was designed the way it was, how it compares to other transformation approaches, and how it can be effectively utilized across different contexts in the MLIR infrastructure.

1. The Concept of Folding in Compiler Design

1.1 Folding in Traditional Compilers

Folding, in the context of compiler design, typically refers to the compile-time evaluation of expressions or subexpressions whose values can be determined statically. This concept has been a fundamental optimization technique in compilers for decades. Traditional compilers incorporate several folding techniques:

Constant Folding: Evaluating expressions composed entirely of constants at compile time rather than runtime.
Algebraic Simplification: Applying algebraic identities to simplify expressions (e.g., x + 0 = x).
Strength Reduction: Replacing expensive operations with equivalent cheaper ones (e.g., replacing multiplication by powers of 2 with shifts).

In most traditional compilers, these optimizations are typically implemented as part of larger passes. For example, LLVM has several passes that include folding capabilities, such as “instcombine” and “dag combine.” These passes operate on specific representations and typically include a mixture of pattern matching and algebraic evaluation.

1.2 Folding’s Place in MLIR’s Ecosystem

MLIR’s approach to folding is distinguished by its integration into the core infrastructure rather than being confined to specific passes. This reflects MLIR’s design philosophy of providing reusable infrastructure components that can be leveraged across different dialects and abstraction levels.

Within MLIR’s ecosystem, the fold mechanism serves multiple purposes:

Foundation for Canonicalization: The canonicalization pass uses fold methods as one of its primary transformation mechanisms.
Support for Dialect Conversion: When converting between dialects, fold provides a way to legalize operations.
On-the-fly Simplification: Tools like OpBuilder::createOrFold allow for immediate folding during IR construction.

This ubiquity across different contexts makes fold a cornerstone of MLIR’s transformation infrastructure, despite its deliberately limited scope.

2. The MLIR Fold Mechanism

2.1 Definition and Key Characteristics

At its core, the MLIR fold mechanism is a transformation system that allows operations to define how they might be simplified or evaluated at compile time. The fold method is implemented on a per-operation basis and follows a specific contract with the compiler infrastructure.

The key characteristics of the fold mechanism include:

Operation-centric: Each operation type can define its own folding logic through a fold method.
Declarative: Operations can define their folding behavior declaratively through the Operation Definition Specification (ODS) framework.
Conservative: Folding is designed to be safe and predictable, with clear constraints on what kinds of transformations it can perform.
Widely applicable: Despite its limitations, fold can be used in numerous contexts throughout the compilation process.

These characteristics make the fold mechanism both powerful and reliable, allowing it to serve as a foundational building block for more complex transformations.

2.2 Intentional Limitations of Fold

The fold mechanism in MLIR is intentionally limited in what it can do. These limitations are not weaknesses but deliberate design choices that enhance its versatility and reliability. The primary limitations include:

No New Operation Creation: A fold method cannot create new operations. It can only return existing values or attributes.
Only Root Operation Replacement: Only the operation being folded can be replaced; other operations cannot be directly modified or erased.
In-place Updates Only: Beyond replacement, a fold can only update the operation in place without changing the rest of the IR.

These restrictions might initially seem overly constraining. However, they serve important purposes:

Simplicity: The limited behavior makes fold methods easier to implement correctly.
Composability: The narrow contract allows fold to be safely used in diverse contexts.
Predictability: Clear constraints on fold’s behavior make its effects more predictable.
Efficiency: Limited behaviors enable optimized implementation in the compiler infrastructure.

As we’ll see throughout this document, these intentional limitations enable the fold mechanism to be a versatile tool that can be applied reliably across different compilation stages.

2.3 OpFoldResult: The Building Block of Folding

The OpFoldResult class is a fundamental component of MLIR’s folding infrastructure. It represents a single result from folding an operation and can hold either:

A Value representing an existing SSA value in the IR, or
An Attribute representing a constant result.

This dual-purpose design allows fold methods to either:

Replace an operation with an existing value already in the IR, or
Indicate that an operation’s result is constant (which will be materialized as needed).

The OpFoldResult type’s design is intentionally simple yet flexible, providing just enough capability to support fold’s limited but powerful transformation model. It forms the foundation upon which fold’s more complex behaviors are built.

3. Fold Method Implementation

3.1 Interface and Signature

The fold method is implemented as a member function of an operation class. It can take one of two forms, depending on whether the operation produces a single result or multiple results:

For single-result operations, the signature is typically:

OpFoldResult MyOp::fold(FoldAdaptor adaptor)

For multi-result operations, or as an alternative for single-result operations:

LogicalResult MyOp::fold(FoldAdaptor adaptor, SmallVectorImpl<OpFoldResult> &results)

Operations can opt-in to providing a fold method by setting the hasFolder bit in their ODS definition, which generates the necessary declarations.

The fold method is expected to adhere to specific behavioral constraints:

It can leave the operation unchanged and return failure/nullptr.
It can mutate the operation in place and return the operation itself or success.
It can return existing values or attributes to replace the operation’s results.

These constraints form the contract between fold methods and the infrastructure that invokes them.

3.2 FoldAdaptor and Operand Handling

The FoldAdaptor passed to fold methods provides access to the operation’s operands, with a key twist: operands that are produced by constant operations are presented as attributes rather than values. This allows fold methods to directly access the constant values of their inputs, simplifying constant folding logic.

For example, if op has two operands where the first comes from a constant operation and the second doesn’t, then:

adaptor.getOperands()[0] would be an Attribute representing the constant value
adaptor.getOperands()[1] would be a null Attribute

This automatic conversion from constant operations to attributes eliminates the need for fold methods to manually extract constant values, making them more concise and less error-prone.

Beyond operands, the FoldAdaptor also provides access to the operation’s attributes, regions, and other properties, allowing fold methods to consider all relevant information when determining whether folding is possible.

3.3 Return Values and Operation Replacement

The return value of a fold method determines what happens to the operation being folded:

Failure/nullptr: The operation remains unchanged.
Success/this: The operation has been modified in place.
OpFoldResult(s): The operation will be replaced with the provided value(s) or materialized constant(s).

When a fold method returns an Attribute as an OpFoldResult, it indicates that the result is a constant. The infrastructure will use the dialect’s materializeConstant hook to create a constant operation for this value.

This replacement mechanism, while limited, provides sufficient flexibility for many common transformations while maintaining the safety and composability that fold methods promise.

4. Fold Mechanism Use Cases

4.1 Canonicalization

One of the primary applications of the fold mechanism is in MLIR’s canonicalization pass. This pass iteratively applies folding and rewrite patterns to transform the IR into a more canonical form.

The canonicalizer invokes the fold method on operations to see if they can be simplified or replaced. If folding succeeds, the operation is updated or replaced accordingly, and dependent operations are added to the worklist for further processing.

The canonicalization pass prefers to use fold methods when possible because:

Fold methods are typically simpler and more efficient than full rewrite patterns.
Fold’s limited behavior reduces the risk of pattern interaction issues.
Using fold allows certain optimizations to be applied in other contexts beyond the canonicalizer.

This preference for fold-based canonicalization is reflected in MLIR’s documentation, which suggests that “a canonicalization should always be implemented as a fold method if it can be.”

4.2 Constant Folding and Propagation

Constant folding and propagation is another key application of the fold mechanism. When operations have constant inputs, their fold methods can often compute their results at compile time, eliminating runtime computation.

For example, an addi operation with two constant inputs could be folded into a single constant. Similarly, operations with identities (like x + 0 = x) can be simplified even when only some inputs are constant.

MLIR’s sparse conditional constant propagation (SCCP) pass uses fold methods to determine when operations can be replaced with constants. It propagates this constant information through the IR, potentially enabling additional folding opportunities.

The constant materialization aspect of fold is particularly important here, as it allows fold methods to return attribute values representing constants, which the infrastructure can then materialize as actual constant operations in the IR.

4.3 Dialect Conversion and Legalization

The fold mechanism plays a crucial role in MLIR’s dialect conversion infrastructure, which is used to transform operations from one dialect to another or to legalize operations within a dialect.

During dialect conversion, operations that are considered “illegal” in the target representation need to be replaced with legal alternatives. The conversion framework attempts to legalize operations using multiple strategies, including:

Using operation-specific conversion patterns
Applying generic type conversion
Invoking the operation’s fold method

If an operation can be folded into existing legal operations or constants, it effectively becomes legalized without requiring a specific conversion pattern. This makes fold a valuable legalization mechanism, especially for operations with straightforward equivalents in the target representation.

The limitations of fold actually make it particularly well-suited for legalization, as it can only replace the operation being considered without introducing new potentially illegal operations.

4.4 Direct Invocation via OpBuilder

Beyond passes that automatically apply folding, MLIR also allows direct invocation of the fold mechanism through the OpBuilder::createOrFold method. This method attempts to fold an operation before it’s even inserted into the IR.

For example, instead of unconditionally creating an addi operation, code can use createOrFold to potentially get a constant or simplified value instead:

Value result = builder.createOrFold<AddIOp>(loc, lhs, rhs);

This capability allows IR construction code to automatically apply folding optimizations on the fly, potentially reducing the need for separate optimization passes.

The limitation that fold cannot create new operations is particularly important here, as it ensures that createOrFold either creates exactly one new operation or returns an existing value, making its behavior predictable in IR construction contexts.

5. Comparison with Other Transformation Mechanisms

5.1 Fold vs. RewritePatterns

Both fold methods and rewrite patterns can transform MLIR operations, but they have different capabilities and constraints:

Aspect	Fold Method	Rewrite Pattern
Creation	Cannot create new operations	Can create arbitrary new operations
Scope	Only affects the root operation	Can modify multiple operations
Complexity	Typically simpler	Can be more complex
Applicability	Used in multiple contexts	Primarily used in specific passes
Implementation	Member function of operation	Standalone pattern class

RewritePatterns are more powerful and can express transformations that fold methods cannot, such as:

Replacing an operation with multiple new operations
Modifying or deleting operations other than the root
Creating entirely new subgraphs of operations

However, this power comes with increased complexity and reduced reusability. Fold methods, with their intentional limitations, can be more reliably used across different compilation contexts.

The MLIR documentation advises that “a canonicalization should always be implemented as a fold method if it can be, otherwise it should be implemented as a RewritePattern.” This guidance reflects the preference for the simpler fold mechanism when it’s sufficient for the transformation.

5.2 Fold vs. Trait-Based Folding

In addition to operation-specific fold methods, MLIR also supports trait-based folding through the foldTrait hook. This allows common folding patterns to be encapsulated in traits that can be shared across multiple operation types.

Trait-based folding complements operation-specific folding:

Operation-specific fold: Implements folding logic unique to a particular operation.
Trait-based fold: Implements folding logic common to all operations with a given trait.

For example, a Commutative trait might implement folding for canonical ordering of operands, applying to all commutative operations without each having to implement this logic individually.

The infrastructure tries operation-specific folding first, and if that fails, it attempts trait-based folding. This layered approach allows for both specialized and generalized folding behaviors.

5.3 Fold vs. Transform Dialect

The Transform dialect represents a more recent development in MLIR’s transformation infrastructure. It provides a way to express transformations in a declarative, composable manner using operations in a “transform IR” that guide transformations of the “payload IR”.

While fold methods and the Transform dialect serve different purposes, they represent different points in the spectrum of transformation approaches:

Aspect	Fold Method	Transform Dialect
Granularity	Operation-level	Can operate at multiple levels
Expressivity	Limited, predefined behaviors	Highly expressive and composable
Integration	Integral to operations	Separate IR layer
Control Flow	No control flow	Supports structured control flow
User Interface	Implementation detail	Exposed as user-visible IR

The Transform dialect allows for expressing complex transformation sequences that are far beyond what fold methods can do. However, fold methods serve as efficient, reliable building blocks that can be composed into higher-level transformations, potentially including those expressed through the Transform dialect.

Rather than competing approaches, fold methods and the Transform dialect represent complementary layers in MLIR’s transformation ecosystem, with fold providing low-level, reliable transformation primitives and the Transform dialect offering high-level, user-controllable transformation orchestration.

6. Design Rationale for Fold’s Limitations

6.1 Simplicity and Reliability

The intentional limitations of the fold mechanism significantly contribute to its simplicity and reliability. By restricting what fold methods can do, MLIR reduces the scope for errors and unexpected behaviors.

This simplicity manifests in several ways:

Implementation simplicity: Fold methods are generally straightforward to implement, with clear input-output behavior.
Reasoning simplicity: The restricted behavior makes it easier to reason about what a fold method will do.
Integration simplicity: Systems that use fold methods can make strong assumptions about their behavior.

The reliability benefits are equally significant:

Reduced interaction issues: Limited behavior means less chance of unexpected interactions with other transformations.
Predictable results: Clear constraints on what fold can do lead to more predictable transformation outcomes.
Easier verification: Simpler transformations are easier to validate and test.

These simplicity and reliability benefits are particularly valuable in a compiler infrastructure that must support a diverse ecosystem of dialects and transformation passes.

6.2 Composability

The limited behavior of fold methods makes them highly composable. They can be safely combined with other transformations without concern for complex interactions.

This composability is evident in how fold is used across different contexts in MLIR:

In canonicalization: Fold methods work alongside rewrite patterns.
In dialect conversion: Fold serves as one of multiple legalization strategies.
In IR construction: createOrFold seamlessly integrates folding into IR building.

The restrictions that fold cannot create new operations and can only replace the root operation are particularly important for composability. They ensure that fold’s effects are localized and predictable, making it safe to compose with other transformations that might have broader effects.

6.3 Reusability across Compilation Stages

The intentional limitations of fold enable its reuse across different stages of the compilation process. Because fold methods have a narrow, well-defined contract, they can be safely invoked in various contexts without concern for unexpected side effects.

This reusability manifests in how fold is used at different compilation stages:

During IR construction: Via createOrFold
During optimization: In the canonicalization pass
During lowering: As part of dialect conversion

The ability to reuse the same folding logic across these different contexts is valuable for several reasons:

Code reuse: The same implementation serves multiple purposes.
Consistency: The same folding transformations are applied consistently.
Maintenance: Improvements to fold methods benefit multiple compilation stages.

This cross-stage reusability is a direct consequence of fold’s intentional limitations, which constrain its behavior to a subset that is safe and meaningful in all these contexts.

6.4 Performance Considerations

The limited behavior of fold methods also brings performance benefits. By constraining what fold can do, the infrastructure can implement it more efficiently than more general transformation mechanisms.

These performance benefits include:

Reduced overhead: Simpler behaviors require less infrastructure support.
More predictable performance: Limited behaviors lead to more consistent execution times.
Optimization opportunities: Known constraints allow for specialized implementation strategies.

For example, because fold methods cannot create new operations, the infrastructure doesn’t need to manage complex worklists of newly created operations. Similarly, because fold only affects the root operation, the infrastructure can make stronger assumptions about what parts of the IR remain valid after folding.

These performance considerations are particularly important for fold methods used in contexts like createOrFold, where folding happens during the initial IR construction and should add minimal overhead.

7. Practical Implementation Examples

7.1 Simple Constant Folding

A classic example of folding is evaluating operations with constant inputs. Here’s how a fold method for a constant operation might look:

OpFoldResult ConstantOp::fold(ConstantOp::FoldAdaptor adaptor) {
  // Simply return the constant value
  return adaptor.getValue();
}

This trivial example demonstrates the pattern for constant operations: they simply return their constant value as an attribute, allowing the infrastructure to either reuse an existing constant or create a new one as needed.

For binary operations with constant inputs, the pattern is slightly more complex:

OpFoldResult AddIOp::fold(AddIOp::FoldAdaptor adaptor) {
  // If both operands are constants, compute the result
  if (auto lhs = adaptor.getLhs().dyn_cast<IntegerAttr>()) {
    if (auto rhs = adaptor.getRhs().dyn_cast<IntegerAttr>()) {
      APInt result = lhs.getValue() + rhs.getValue();
      return IntegerAttr::get(getType(), result);
    }
  }
  return {};
}

This implementation checks if both inputs are constants, and if so, computes the result at compile time and returns it as an attribute.

7.2 Operation Identity Folding

Another common folding pattern is applying algebraic identities. For example, adding zero to a value results in the original value:

OpFoldResult AddIOp::fold(AddIOp::FoldAdaptor adaptor) {
  // x + 0 = x
  if (auto rhs = adaptor.getRhs().dyn_cast<IntegerAttr>()) {
    if (rhs.getValue().isZero()) {
      return getOperand(0);
    }
  }
  
  // 0 + x = x
  if (auto lhs = adaptor.getLhs().dyn_cast<IntegerAttr>()) {
    if (lhs.getValue().isZero()) {
      return getOperand(1);
    }
  }
  
  // ... other folding logic ...
  
  return {};
}

This example demonstrates returning an existing value (one of the operands) rather than a constant attribute. This is the other primary capability of fold methods: replacing an operation with an existing value.

7.3 Complex Folding with Attribute Computation

For more complex operations, folding might involve non-trivial computation on attributes. Here’s an example of how polynomial multiplication might be folded:

OpFoldResult MulOp::fold(MulOp::FoldAdaptor adaptor) {
  // Ensure both operands are constants
  auto lhs = adaptor.getOperands()[0].dyn_cast<DenseIntElementsAttr>();
  auto rhs = adaptor.getOperands()[1].dyn_cast<DenseIntElementsAttr>();
  if (!lhs || !rhs) return {};
  
  auto degree = getResult().getType().cast<PolynomialType>().getDegreeBound();
  auto maxIndex = lhs.size() + rhs.size() - 1;
  
  // Compute polynomial multiplication
  SmallVector<APInt, 8> result(maxIndex, APInt(32, 0));
  for (int i = 0; i < lhs.size(); ++i) {
    for (int j = 0; j < rhs.size(); ++j) {
      // index is modulo degree because poly's semantics are defined modulo x^N = 1
      result[(i + j) % degree] += 
        lhs.getValues<APInt>()[i] * rhs.getValues<APInt>()[j];
    }
  }
  
  return DenseIntElementsAttr::get(
    RankedTensorType::get(result.size(), IntegerType::get(getContext(), 32)),
    result);
}

This example demonstrates how fold methods can perform complex computations on constant inputs, as long as the result can be represented as an attribute. The polynomial multiplication logic is executed at compile time, potentially eliminating significant runtime computation.

8. Fold Mechanism in the Dialect Conversion Infrastructure

8.1 Fold as a Legalization Strategy

The dialect conversion infrastructure in MLIR is responsible for transforming operations from one dialect to another, or for ensuring operations conform to a specific legality criteria. Within this infrastructure, the fold mechanism serves as one of several strategies for legalizing operations.

When attempting to legalize an operation, the conversion framework follows a sequence of steps:

It first attempts to apply specific conversion patterns registered for the operation.
If no patterns apply, it tries to legalize the operation using its fold method.
If folding fails, it may attempt other strategies like materialization.

Using fold for legalization has several advantages:

Reuse: It leverages existing folding logic for legalization.
Simplicity: Fold’s limited behavior makes it a safe legalization mechanism.
Fallback: It provides a generic fallback when specific patterns aren’t available.

A common scenario is when an operation can be expressed in terms of simpler operations that are already legal in the target dialect. If the fold method can expose this simplification, it effectively legalizes the operation without requiring a specific conversion pattern.

8.2 Interaction with Type Conversion

Type conversion is a critical aspect of dialect conversion, as operations often need to adapt to new type systems when moving between dialects. The fold mechanism’s role in legalization intersects with type conversion in important ways.

When folding is used as a legalization strategy, the operation’s fold method operates on the original types before conversion. This means that the fold method itself doesn’t need to be aware of type conversion. However, the results returned by the fold method are still subject to type conversion:

If the fold method returns attributes, they may need to be materialized as constants with converted types.
If the fold method returns values, those values must themselves be legal in the target context.

This interaction highlights a limitation of using fold for legalization in the presence of complex type conversions. The fold method’s inability to create new operations means it cannot directly create operations with converted types. Instead, it must rely on existing values that have already been converted or on the infrastructure to materialize constants with appropriate types.

8.3 Partial vs. Full Conversion

MLIR’s dialect conversion infrastructure supports both partial and full conversion modes:

Partial conversion: Legalizes what it can but allows unconverted operations to remain.
Full conversion: Requires all operations to be legalized to be successful.

The fold mechanism’s role differs slightly between these modes:

In partial conversion, fold provides an additional opportunity to legalize operations beyond what dedicated patterns cover.
In full conversion, fold serves as a fallback that might prevent conversion failures when dedicated patterns are missing.

The debug output from dialect conversion illustrates this process, showing how operations are first attempted to be legalized through folding before moving on to pattern-based approaches:

Legalizing operation : 'func.return'(0x608000002e20) {
  * Fold { } -> FAILURE : unable to fold
  * Pattern : 'func.return -> ()' {
    ** Insert : 'spirv.Return'(0x6070000453e0)
    ** Replace : 'func.return'(0x608000002e20)
  } -> SUCCESS : pattern applied successfully
} -> SUCCESS

This example shows that the conversion framework first tried to legalize a ‘func.return’ operation through folding, which failed. It then successfully applied a specific conversion pattern.

9. Advanced Considerations and Edge Cases

9.1 Handling Multi-result Operations

While the basic fold pattern works well for single-result operations, multi-result operations present additional challenges. MLIR provides a different signature for folding multi-result operations:

LogicalResult MyMultiResultOp::fold(
    FoldAdaptor adaptor,
    SmallVectorImpl<OpFoldResult> &results) {
  // Fill 'results' with folded values if folding is possible
  // Return success or failure
}

With this signature, the fold method must populate the results vector with precisely one OpFoldResult for each result of the operation. The method must either:

Return failure() to indicate that the operation cannot be folded, or
Return success() and completely fill the results vector.

Importantly, MLIR does not support partial folding within this mechanism. This is a deliberate design decision that reflects fold’s all-or-nothing philosophy and simplifies the integration of fold methods with other compiler components.

This limitation is particularly significant for operations with many results or when only some results can be determined through folding. In such cases, developers often need to fall back to using RewritePatterns that have more flexibility but less reusability across the compilation pipeline.

The lack of partial folding capabilities is a trade-off that prioritizes simplicity and predictability over optimization coverage. It ensures that fold methods maintain a clear, consistent contract with the rest of the MLIR infrastructure.

9.2 Folding with Side Effects

Operations with side effects present special considerations for folding. In MLIR, operations can explicitly model their side effects through interfaces like MemoryEffectsOpInterface, which indicates when operations read from or write to resources such as memory.

The fold mechanism generally works best with pure operations (those without side effects), as they can be safely evaluated at compile time or replaced with equivalent operations without changing program semantics. For operations with side effects, several considerations come into play:

Preservation of semantics: Folding must not eliminate essential side effects or change their ordering, as this could alter program behavior.
Controlling fold eligibility: MLIR infrastructure components like createOrFold often check if an operation has side effects before attempting to fold it, preventing unexpected behavior changes.
Partial folding of computational aspects: In some cases, the pure computational portion of an operation can be folded while preserving the side-effecting behavior. However, this typically requires custom RewritePatterns rather than fold methods.
Memory-reading operations: Operations that read but don’t write memory might be safely folded if the memory contents are known constants, but this requires careful analysis.

MLIR’s side effect modeling system complements the fold mechanism by providing metadata that helps the compiler make appropriate decisions about when folding is safe. This integration helps maintain program correctness while still enabling optimizations where possible.

9.3 Constant Materialization

When a fold method returns an attribute value through an OpFoldResult, it signals that the operation’s result can be represented as a constant. However, the attribute itself is not directly usable as a value in the IR. Instead, the compiler infrastructure must materialize this attribute as a proper constant operation.

This materialization process is handled through the dialect’s materializeConstant hook:

Operation *MyDialect::materializeConstant(OpBuilder &builder, 
                                          Attribute value, 
                                          Type type, 
                                          Location loc) {
  // Create and return a constant-like operation
}

Dialects opt into this behavior by setting the hasConstantMaterializer bit in their ODS definition. The implementation should create and return a “constant-like” operation that produces the specified attribute value as its result.

Several nuanced behaviors are important to understand in this process:

Laziness: Constant materialization only occurs when folding actually replaces an operation, not when fold is just called to check folding possibility.
Constant hoisting: The infrastructure typically hoists materialized constants to optimal positions, such as the entry block of the nearest “barrier region,” to avoid redundant execution.
Constant uniquing: To reduce code size, the compiler attempts to reuse existing constants rather than creating duplicates.
Cross-dialect cooperation: The constant to be materialized might belong to a different dialect than the operation being folded, requiring coordination between dialect interfaces.

This materialization mechanism is what allows fold methods to indicate constant results without directly creating new operations, thus preserving the fold mechanism’s intentionally limited contract while still enabling powerful constant propagation optimizations.

10. Evolution and Future Directions

10.1 Historical Evolution of Fold

The fold mechanism has evolved significantly throughout MLIR’s development history. Understanding this evolution provides valuable insights into the design decisions and trade-offs that have shaped it.

Initially, the fold interface was simpler but less powerful. Key evolutionary steps include:

Introduction of the FoldAdaptor: Earlier versions required operations to manually extract constant values from operands. The FoldAdaptor simplified this by automatically converting constant-producing operands to attributes and providing a unified interface for accessing them.
Support for multi-result operations: The fold interface was extended with the vector-based signature to accommodate operations that produce multiple results.
Integration with dialect conversion: Fold became an integral part of the dialect conversion infrastructure, serving as one of several legalization strategies.
Trait-based folding: The addition of foldTrait hooks allowed common folding behaviors to be encapsulated in traits and shared across operation types.
Enhanced constant materialization: The constant materialization process has been refined to better handle hoisting, uniquing, and cross-dialect scenarios.
OpFoldResult improvements: The OpFoldResult class has evolved to better support both values and attributes, with clearer semantics around their usage.

These evolutionary steps reflect MLIR’s pragmatic approach to compiler infrastructure development: starting with clean, simple mechanisms and gradually enhancing them based on practical experience while preserving their core design principles.

10.2 Known Limitations and Challenges

Despite its utility, the fold mechanism has several known limitations that developers should be aware of:

No partial folding: As discussed earlier, fold methods must either completely fold an operation or not at all, which can limit optimization opportunities.
No new operation creation: While this is an intentional limitation, it does prevent implementing certain transformations that conceptually feel like “folding” but require creating new operations.
Limited context awareness: Fold methods operate on individual operations with minimal visibility of the surrounding IR, limiting the scope of possible optimizations.
Challenges with type conversion: In dialect conversion scenarios, fold methods can’t directly handle type conversion requirements since they can’t create new operations with converted types.
Timing issues in dialect conversion: When used for legalization, fold methods might be invoked at a point where operands are in an intermediate state of conversion, causing unexpected behavior.
Implementation boilerplate: The constraints of the fold interface sometimes lead to repetitive code structures, especially for complex folding logic.
Debugging challenges: The minimal interface and limited behaviors can make diagnosing failures in fold methods more difficult than with more verbose pattern-based approaches.

These limitations are generally accepted as reasonable trade-offs for the simplicity, reliability, and versatility that the fold mechanism provides. Many of them are direct consequences of the intentional design choices that make fold useful across so many contexts.

10.3 Future Enhancement Possibilities

While preserving the fundamental principles that make fold valuable, several potential enhancements could address its current limitations:

Limited partial folding support: A carefully designed extension could allow fold methods to partially succeed for multi-result operations without compromising the mechanism’s predictability.
Enhanced contextual awareness: Providing fold methods with more information about their context (e.g., dominating definitions or constant propagation facts) could enable more sophisticated folding decisions.
Better integration with the Transform dialect: Creating bidirectional communication between fold methods and the Transform dialect could combine fold’s efficiency with Transform’s expressivity.
Improved dialect conversion handling: Better coordination between fold and type conversion could make fold more effective as a legalization mechanism.
Specialized folding frameworks: Domain-specific extensions to the fold mechanism (e.g., for tensor operations or control flow) could enable more powerful folding without compromising the core mechanism.
Tooling improvements: Better debugging support and developer tools could make implementing and testing fold methods easier and less error-prone.
Performance optimizations: Specialized implementations for common folding patterns could improve compilation speed for frequently used operations.

These potential enhancements would need to be carefully balanced against the risk of complicating the fold mechanism and undermining its key strengths of simplicity and broad applicability. MLIR’s community-driven development model ensures that any evolution will likely be guided by practical needs rather than theoretical ideals.

Conclusion

The fold mechanism in MLIR represents a masterclass in compiler infrastructure design. By deliberately constraining its capabilities, the MLIR team created a transformation system that is both powerful enough to enable significant optimizations and limited enough to be safely used across diverse contexts.

Key insights from this exploration include:

Intentional limitations create versatility: The restricted behavior of fold methods enables their use in many different contexts throughout the compilation pipeline.
Simplicity enhances reliability: The straightforward fold interface reduces implementation complexity and potential for errors.
Constraints enable composability: Fold’s limited behavior makes it safely composable with other transformation mechanisms.
Focused capabilities maximize reusability: By solving a specific, well-defined problem, fold methods can be reused across compilation stages from IR construction to optimization to lowering.
Trade-offs are deliberately chosen: The limitations of fold reflect careful design decisions that prioritize broad applicability over maximum power in any single context.

The fold mechanism exemplifies MLIR’s broader design philosophy: creating modular, composable building blocks that each solve specific problems well rather than monolithic systems that attempt to solve everything at once. This approach enables the flexible, extensible compiler infrastructure that makes MLIR valuable across diverse domains from machine learning to embedded systems to high-performance computing.

As MLIR continues to evolve, the fold mechanism will likely remain a fundamental component of its transformation infrastructure. Its design represents a valuable case study in how thoughtfully applied constraints can sometimes be more enabling than unlimited flexibility.

References

MLIR Canonicalization Documentation, https://mlir.llvm.org/docs/Canonicalization/
MLIR Dialect Conversion Documentation, https://mlir.llvm.org/docs/DialectConversion/
MLIR Transform Dialect Documentation, https://mlir.llvm.org/docs/Dialects/Transform/
MLIR Traits Documentation, https://mlir.llvm.org/docs/Traits/
MLIR Rationale: Generic DAG Rewriter Infrastructure, https://mlir.llvm.org/docs/Rationale/RationaleGenericDAGRewriter/
MLIR: A Compiler Infrastructure for the End of Moore’s Law, https://arxiv.org/abs/2002.11054
MLIR: Incremental Application to Graph Algorithms in ML Frameworks, https://mlir.llvm.org/docs/Rationale/MLIRForGraphAlgorithms/
MLIR Glossary, https://mlir.llvm.org/getting_started/Glossary/
MLIR Language Reference, https://mlir.llvm.org/docs/LangRef/
MLIR — Folders and Constant Propagation, https://www.jeremykun.com/2023/09/11/mlir-folders/
MLIR — Canonicalizers and Declarative Rewrite Patterns, https://www.jeremykun.com/2023/09/20/mlir-canonicalizers-and-declarative-rewrite-patterns/
MLIR — Dialect Conversion, https://www.jeremykun.com/2023/10/23/mlir-dialect-conversion/
MLIR: The case for a simplified polyhedral form, https://mlir.llvm.org/docs/Rationale/RationaleSimplifiedPolyhedralForm/
Linalg Dialect Rationale: The Case For Compiler-Friendly Custom Operations, https://mlir.llvm.org/docs/Rationale/RationaleLinalgDialect/
Chapter 3: High-level Language-Specific Analysis and Transformation - MLIR, https://mlir.llvm.org/docs/Tutorials/Toy/Ch-3/
MLIR Side Effects & Speculation, https://mlir.llvm.org/docs/Rationale/SideEffectsAndSpeculation/
Defining Dialects - MLIR, https://mlir.llvm.org/docs/DefiningDialects/