The P-Calculus Supratik Mukhopadhyay PEMWS-2 April 6 th 2011

Introduction & Motivation Next generation data-intensive exascale computing architectures will have significantly different execution models: –Instead of data moving to work, work should move to data –Execution should be message-driven –Need to expose different granularities of parallelism: determinism, non-determinism, dataflow, globally asynchronous locally synchronous (GALS) semantics, … –Security & Reliability –Fault-tolerance

Motivation (Contd.) Communicating Sequential Processes (CSP: Hoare 1978) served as the foundation for MPI Limitations of CSP limit existing models with respect to expressiveness in terms of fine granularities of parallelism, fault-tolerance, security, localities, hierarchical partitioning of address spaces, … Next generation ubiquitous high performance computing needs new execution models What is the CSP for next generation exascale computing? –Abstract formal specification of parallel execution

Existing Specification Formalisms Petri Nets -calculus, CSP, CCS, Pi Calculus, Ambient Calculus, Actors, Kahn Process Networks, … –Do not support globally asynchronous locally synchronous semantics –Not message driven –Cannot expose different granularities of parallelism (deterministic/dataflow, nondeterministic, fine-grained, coarse-grained) –Does not support work moving to data

The P-calculus: A Specifcation Formalism for Exascale Computation Nominal process calculus as a formal execution model for future-generation exascale computation –Has formal operational semantics involving interactions of external and internal actions Allows answering questions about the execution models unambigously Allows (automatic) checking for inconsistencies and incompleteness in the execution model Allows checking (automatically) whether a claimed implementation of an execution model such as ParalleX or Codelets really implements it

The P-calculus (contd.) Uniform representation of synchronous and asynchronous semantics Has an equational theory that allows comparison of different implementations of an execution model Equipped with a type system (the first order P-calculus) for correctness, security, …

The Untyped P-calculus Chromosomes: Primitive computing elements in the P-calculus –Internal Actions –External Actions Chromatins Regulators Boards Nucleus

Chromosomes Chromosomes are the most basic kind of computational entity defined in the P- Calculus. Their role is to execute fundamental computations.

Chromosomes (Contd.) Chromosomes may also declare methods: –The set of declared methods is partitioned into private and public methods. Formal Parameters

Internal Actions A chromosome may perform either an internal or external action.

Chromatins Chromosomes are only capable of performing sequential computations. A Chromatin is defined as a group of coexisting chromosomes organized together by parallel composition.

Regulators Aside from being executed computations need to be managed. Managing computations involves: –Controlling and synchronizing data access –Moving work to data y

Regulators – Guarded Commands Each regulator is denoted by a deterministic state machine that is defined by a set of guarded commands. Each guard is denoted by an event which triggers an action. At most one of the guards can be triggered by an event

Regulators – Event Language Each event can be an atomic event (extending Parnas). Or an event could also be a complex event. An action (for now) is the creation of a chromosome.

Board Regulators can coexist may be composed A “parallel” composition of regulators is known as a @F(z)

Nucleus We can perform computations (via chromatins and chromosomes) We can manage computations (via boards and regulators). A nucleus is a composition of coexisting chromatins and @F(z) Nucleus

Activity Space Computations need a context i.e. a place in which they take place. An Activity Space is the context in which a cooperating and coexisting chromatin and a board interacts (i.e., a nucleus exists).

AS1 Example – Activity Spaces and Nuclei let z = …. > let x = ….let y = @F(z)

System A System is a composition of Activity Spaces Multilevel hierarchy

External Actions Boards and chromatins were capable of performing and coordinating/managing internal computations. External actions coordinate computations across Activity Spaces.

Example – External Actions AS1 let z = …. > let x = ….let y = @F(z) > (foo) AS3 In AS3 out AS1.in AS2

Operational Semantics – Visual let x = getInput() let y = sort(x)^f(sort,cont) >^cont’^^ ’ (y^cont) let z = shuffle(y) >^cont^^ ’’ ’

Example – Operational Semantics

Example (Cont’d)

Future Work First Order P-calculus Confluence Properties Tool Building Query Languages

Questions?