Mid-Level IR (MIR)

The Mid-Level IR (MIR) represents the stage in the RunMat compilation pipeline where High-Level IR (HIR) is lowered into a Control-Flow Graph (CFG) of Basic Blocks. While HIR maintains a structure close to the original MATLAB AST (nested loops, if-statements), MIR flattens these into explicit jumps, branch targets, and local variable slots (locals). This representation is used for dataflow analysis, type inference, and as the primary input for bytecode generation.

Lowering HIR to MIR mirrors the approach used by modern compilers such as the Rust compiler. The flattened control-flow graph lets RunMat perform dataflow analysis and type inference, and it serves as the primary input for bytecode generation, enabling static analysis and optimization of runtime branches before execution.

MIR Structure & CFG

A MIR program is organized into a MirAssembly, which contains a collection of MirBody objects indexed by their FunctionId. Each MirBody consists of a list of MirLocal declarations and a graph of BasicBlock nodes.

Basic Blocks and Control Flow

Every BasicBlock contains a sequence of MirStmt and exactly one MirTerminator.

• MirStmt: Linear operations like assignments (Assign), multi-assignments (MultiAssign), or expressions evaluated for side effects (Expr).
• MirTerminator: Dictates the transfer of control out of the block.

The terminator kind makes every exit edge explicit:

pub enum MirTerminatorKind {
    Goto(BasicBlockId),
    Branch { cond, then_block, else_block },
    Switch { discr, cases, otherwise },
    For { binding, iterable, body_block, exit_block },
    TryCatch { try_block, catch_block, catch_binding },
    Return(Vec<MirOperand>),
    Await { future, result, resume },
    Unreachable,
}

MIR Data Entity Mapping

The following diagram bridges the conceptual MATLAB control flow to the internal MIR representation.

MIR Lowering (HIR to MIR)

Lowering is performed by the lower_assembly function, which iterates through HIR functions and utilizes a ControlFlowBuilder to construct the CFG.

ControlFlowBuilder & Continuation Passing

The ControlFlowBuilder handles the conversion of nested HIR structures into flat blocks using a continuation-passing approach. When encountering a branch or an await point, the builder:

1. Allocates a fresh_block() for the continuation.
2. Lowers the "current" block's terminator to point to the new block.
3. Recursively lowers the remaining statements into the continuation block.

MirLocal Slots

MIR replaces HIR BindingId references with MirLocalId slots. Locals are categorized by MirLocalKind:

• Parameter: Input arguments to the function.
• Output: Variables that will be returned.
• Binding: Standard local variables.
• Capture: Variables captured from an outer scope (closures).
• Temporary: Compiler-generated slots for intermediate expression results.

Rvalues and Indexing Plans

MIR expressions are represented as MirRvalue. Unlike HIR expressions, MirRvalue is shallow; its operands are usually MirOperand::Local or MirOperand::Constant.

Indexing Operations

MATLAB indexing is complex (supporting end, :, and logical masks). MIR lowers these into a MirIndexing structure containing MirIndexComponents.

• MirIndexPlan: Determines if the access is Scalar, Slice, or Cell.
• MirRvalue::Index: Represents a read operation.
• MirStmtKind::Assign with MirPlace::Index: Represents a write/mutation operation.

Rvalue Kinds

MIR Dataflow Analysis

Once lowered, the AnalysisStore tracks facts about MirLocal slots across the CFG using a fixed-point iteration engine in compute_simple_local_facts.

Analysis Logic Flow

The diagram below illustrates how the analysis engine processes a MirBody to produce type and shape facts.

Key Analysis Facts

• InitFact: Tracks if a local is Unassigned, MaybeAssigned, or DefinitelyAssigned. Used for definite assignment validation.
• SimpleValueFact: Aggregates TypeFact (e.g., Double, Struct), ShapeFact (dimensions), and ValueFlowFact.
• SpawnSafetyFact: Analyzes if a closure or function is safe to spawn on a background thread based on its captures and effects.