SPIRAL (Stratified Progressive Intermediate Representation Architecture Language)

SPIRAL is a JSON-first intermediate representation spanning AIR, CIR, EIR, PIR, and LIR. All layers support expression and CFG block forms (hybrid documents).

Layers & Computational Classes

Layer	Name	Computational Class	Key Feature
AIR	Algebraic IR	Primitive Recursive (bounded)	Pure, no recursion, always terminates
CIR	Computational IR	Turing-Complete	Lambdas, fix combinator for recursion
EIR	Execution IR	Turing-Complete	Sequencing, mutation, loops, effects
PIR	Parallel IR	Turing-Complete	Async/parallel primitives (spawn, await, channels)
LIR	Low-Level IR	Turing-Complete	CFG-based, SSA with phi nodes

See wiki/Architecture.md for details.

Quick start

pnpm install
pnpm build
pnpm test

Run examples (folder or file stem):

pnpm run-example air/basics/arithmetic
pnpm run-example air/basics/arithmetic/arithmetic

Wiki

• Wiki home & navigation: wiki/Home.md
• Quick start: wiki/Quick-Start.md
• Examples & learning path: wiki/Examples.md
• Architecture (layers, expression/CFG hybrids): wiki/Architecture.md
• Specification (sections): wiki/Specification.md
• Appendices: wiki/Appendices.md
• Schemas and references: wiki/Schemas-and-References.md