A Mystery Esterel small no type inference subtyping

A Mystery • Esterel – small • • • no type inference, subtyping, … no recursion, functions, … no pointers, malloc, GC, … no complex data structures, libraries, … … – formal semantics [Berry&Cosserat 84, Gonthier 88] well… no! ) compiling Esterel is easy

Motivation • Esterel – small kernel language + formal semantics – for embedded/real-time/safety-critical designs – compiled into C code, automata, digital circuits, VHDL… • Mathematically certified compiler? – YES [Schneider 04] but: ) • for correct programs • for circuit synthesis • for non-optimized circuits • let’s check correctness • let’s think generic • let’s aim at

Why Loops? • Synchronous loops impact – correctness: – performance: instantaneous loops schizophrenia • Specify code generation for loops – check correctness – achieve performance – generic (independent from target language) – amenable to certification

A Key to Many Improvements • Compiler • Semantics – better understanding of determinism + errors • Language – new construct: higher expressivity + lower complexity • Proofs

Outline • Esterel – Synchronous Reactive Language – Syntax and Formal Semantics • Causality and Instantaneous Loops • Schizophrenia • Conclusion

Reactive Approach input output Eventdriven time • 0 -delay abstraction ) reactions • Clock-triggered ) instants inputs outputs time tick Reactiv e

Synchronous Concurrency • Parallel composition • Master clock • Instantaneous Asynchrono us Synchrono us – broadcast of signals – reaction to presence and absence of signals ) deterministic concurrency

Example • pause • local signal declaration • signal emission • test • loop • parallel composition • sequence

Syntax wait for the next tick (in the document)

Non-Reactive Programs • signals INCORRECT • loops INCORRECT

Operational Semantics

Inputs and Outputs

Sequence and Concurrency

Deduction Trees

Loops and Local Signals

Example: Present Signal

Outline • Esterel • Causality and Instantaneous Loops – Deterministic Semantics – Instantaneous Loop Detection • Schizophrenia • Conclusion

Instantaneous Loops - Causality

Instantaneous Loops - Causality Instantaneous Loop [Gonthier 88] Causality

Non-Determinism • INCORRECT

A Deterministic Semantics Logical [Berry 9 6] Deterministic Constructive Semantics 1 0 2 1 1 0 0 0

Determinism + Explicit Errors

Determinism + Explicit Errors

Determinism + Explicit Errors A better semantics – correct programs: unchanged – incorrect programs: more easily handled + error propagation – distinguishes causality errors and instantaneous loops

Instantaneous Loop Detection

Outline • Esterel • Causality and Instantaneous Loops • Schizophrenia – Example and Definition – Diagnosis and Cure • Conclusion

Schizophrenia Are these programs equivalent? [Berry 9 2] NO YES How shall we define, diagnose, and cure

Defining Schizophrenia * * 1 * 2

Diagnosing Schizophrenia

Curing Schizophrenia ) Recursively replicate loop bodies [Mignard 94]

Curing Schizophrenia )

Curing Schizophrenia ) Unfolding using non-instantaneous gotopause

And then… • Extend Esterel with “gotopause” • Specify the cure – proving it preserves the semantics – proving it cures schizophrenia • Combine diagnosis and cure – to achieve performance • Extend the algorithm to full Esterel

Implementation initial size (statements) quadratic rewriting quasi-linear rewriting abro 14 18 14 P 18 28 86 58 tcint 403 725 418 wristwatch 432 833 439 atds 100 890 1372 990 7644 67680 8020 10286 566585 16867 cabine globalopt

Conclusion • Loops – Instantaneous Loop Detection (SAS’ 03) – Schizophrenia (MEMOCODE’ 04) • generic + efficient • Better Language – Deterministic Semantics – gotopause (SOS’ 04) (SLAP’ 04) • makes compiling Esterel much easier (because of schizophrenia) • makes compiling to Esterel much easier (ex: Sync. Charts [And 95]) • makes optimizations much easier (source-to-source PROOFS IMPLEMENTATION transformation)

Future Work • • Mechanize proofs Consider constructive causality Apply gotopause to more optimizations… Make gotopause available • Dynamic well-formedness? • Semantics of signals?