Intermediate Representation Design

• Intermediate representation design is the development of abstract, machine-friendly models that bridge high-level program specifications and low-level execution details.
• Modern IR designs employ graph-based hierarchical models with multi-level dialect stacks to enable both structured and unstructured control flows along with modular optimizations.
• IR design is critical in domains such as quantum-classical computing and heterogeneous parallelism, ensuring semantic preservation and interoperability through precise type systems.

Intermediate representation (IR) design refers to the principled construction of abstract, machine-friendly formalisms that sit between high-level program descriptions and low-level execution artifacts in a compilation, static analysis, or transformation pipeline. Modern IR design requires precise attention to type systems, extensibility, semantics preservation, multi-level lowering, optimization, and interoperability, especially in domains such as quantum-classical computing, hardware, static analysis, and heterogeneous parallelism. The following sections synthesize key technical concepts and recent advancements in IR design, illustrated by contemporary research.

1. Core Structural Frameworks and Hierarchy

A central trend in recent IR research is the adoption of graph-based, hierarchical models that unify dataflow and control abstractions. In HUGR—Hierarchical Unified Graph Representation—a program is modeled as a directed dataflow graph $G$ whose edges are either classical values (e.g., integers, floats, tuples) or quantum values (qubits). Nodes represent “ops,” each with ordered, statically-typed input/output ports, supporting both nesting (for structured control) and flat wiring (for unstructured control) (Koch et al., 13 Oct 2025).

IRs such as HUGR, RVSDG (Reissmann et al., 2019), and multi-level dialect stacks in MLIR-inspired compilers (Gysi et al., 2020, Majumder et al., 2021) reflect this "region hierarchy" model:

• Nodes may embed child graphs, enabling multi-level reasoning (structured control as subgraphs, unstructured control as Control-Flow Graphs (CFGs)).
• Multiple abstraction layers—high-level domain-specific operations, mid-level language cores, and low-level target-specific representations—are encoded as stacks or dialects, enabling progressive lowering.
• For hardware and parallel domains, mid-level dialects such as HIR (Majumder et al., 2021), LLHD (Schuiki et al., 2020), UPIR (Wang et al., 2022), and Tydi IR (Reukers et al., 2023, Reukers, 2022) exploit program structure for modular lowering and reuse, each emphasizing different forms of graph structure or data-centric