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No More, No Less
A Formal Model for Serverless Computing
Maurizio Gabbrielli, Ivan Lanese, Stefano Pio Zingaro
INRIA, France / Università di Bologna, Italy
Coordination 2019
Saverio Giallorenzo, Fabrizio Montesi, Marco Peressotti
University of Southern Denmark, Denmark
A gentle introduction to “serverless”...
...
Adapted from “Serverless Architecture Patterns” by Abby Fuller, AWS
Event Source Function Cloud Architecture
A gentle introduction to “serverless”...
Monolith Microservices Serverless
provisioned,
pay-per-deployment
on-demand,
pay-per-execution
A gentle introduction to “serverless”...
Monolith Microservices Serverless
A gentle introduction to “serverless”...
Monolith Microservices Serverless
?!
Still rough
around theedges
A gentle introduction to “serverless”...
https://aws.amazon.com/serverless/
Tailor
A gentle introduction to “serverless”...
https://github.com/alanwill/aws-tailor
Tailor
an excerpt
… and its current limitations (non-exhaustive)
● Currently ~15’ execution timeout;
● No function-to-function invocation. Functions need an in-between
stateful service to call each other;
● Sparse coordination logic.
… and its current limitations (non-exhaustive)
● Traffic-dependent scaling of
functions implies:
○ complex cost model;
○ complex system load
estimations.
● Poor performance for
standard communication
patterns
Jonas, Eric, et al. "Cloud Programming Simplified: A Berkeley View on Serverless Computing."
Block
Storage
Object
Storage
File
System
Elastic
Database
Memory
Store
Function access
Transparent
Provisioning
Availability and
persistence
Latency
Costs
… and its current limitations (non-exhaustive)
Lock-in due to absence of standards on:
● function support/execution environments;
● function call semantics;
● semantics of stateful services.
Direction
● We want to study S.C. avoiding any vendor/technology specifics
● We need a formal model for Serverless Computing that
○ Captures current incarnations of S.C.
(e.g. event-based, storage-mediated as in AWS)
○ Supports proposed approaches/features
(e.g. function-to-function invocation, updatable function definitions)
Serverless Kernel Calculus (SKC)
● Systems: ⟨S,𝒟⟩
● Function definitions: f↦M
● Running functions: c◂M
Repository of function definitionsNetwork of running functions
λ-termFunction name
λ-termPromise
Serverless Kernel Calculus (SKC)
● Systems: ⟨S,𝒟⟩
● Function definitions: f↦M
● Running functions: c◂M
Repository of function definitionsNetwork of running functions
λ-termFunction name
λ-termPromise
Serverless Kernel Calculus (SKC)
● Systems: ⟨S,𝒟⟩
● Function definitions: f↦M
● Running functions: c◂M
Repository of function definitionsNetwork of running functions
λ-termFunction name
λ-termPromise
Serverless Kernel Calculus (SKC)
● Systems: ⟨S,𝒟⟩
● Function definitions: f↦M
● Running functions: c◂M
Repository of function definitionsNetwork of running functions
λ-termFunction name
λ-termPromise
SKC function terms
M ::= M M' ∣ V
∣ f
∣ async M
∣ set f M
∣ take f
V ::= x ∣ λx.M
∣ c
⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩
⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩
⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩
Function invocation
Asynchronous eval
Function Repository
Updates
⟨ℰ[f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟⟩
Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
SKC function terms
M ::= M M' ∣ V
∣ f
∣ async M
∣ set f M
∣ take f
V ::= x ∣ λx.M
∣ c
⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩
⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩
⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩
Function invocation
Asynchronous eval
Function Repository
Updates
⟨ℰ[f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟⟩
Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
SKC function terms
M ::= M M' ∣ V
∣ f
∣ async M
∣ set f M
∣ take f
V ::= x ∣ λx.M
∣ c
⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩
⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩
⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩
Function invocation
Asynchronous eval
Function Repository
Updates
Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
SKC function terms
M ::= M M' ∣ V
∣ f
∣ async M
∣ set f M
∣ take f
V ::= x ∣ λx.M
∣ c
⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩
⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩
Function invocation
Asynchronous eval
Function Repository
Updates
Futures
SKC function terms
M ::= M M' ∣ V
∣ f
∣ async M
∣ set f M
∣ take f
V ::= x ∣ λx.M
∣ c
⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩
⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩
⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩
Function invocation
Asynchronous eval
Function Repository
Updates
⟨ℰ[f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟⟩
Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
λ + Futures + Function Repository
Programmable events in SKC
● Store handlers for event e in the definition repository 𝒟:
install_handler ↦ λe.λhandler.
let old_handler = take e
let new_handler = λv.do async (handler v)
(current_handler v)
set e new_handler
● Raise event e (with v) by invoking its handlers in 𝒟:
e v
● ( See the paper for Tailor in SKC )
Programmable events in SKC
● Store handlers for event e in the definition repository 𝒟:
install_handler ↦ λe.λhandler.
let old_handler = take e
let new_handler = λv.do async (handler v)
(current_handler v)
set e new_handler
● Raise event e (with v) by invoking its handlers in 𝒟:
e v
● ( See the paper for Tailor in SKC )
Updatable function
definitions
Programmable events in SKC
● Store handlers for event e in the definition repository 𝒟:
install_handler ↦ λe.λhandler.
let old_handler = take e
let new_handler = λv.do async (handler v)
(current_handler v)
set e new_handler
● Raise event e (with v) by invoking its handlers in 𝒟:
e v
● ( See the paper for Tailor in SKC )
Updatable function
definitions
Function-to-function
invocation
Conclusions and future work
We introduced SKC a Kernel Calculus for Serverless Computing:
● Build on established models (λ-calculus + futures + function repository)
● captures current programming models
● supports next-gen features e.g. function-to-function invocation
Serverless: current challenges SKC: research direction
The coordination logic is spare and
loosely-consistent
Choreographic Programming
targeting SKC.
Estimation of performance and
costs is complex
Quantitative SKC
No More, No Less
λ + Futures + Function Repository
=
A formal model for Serverless Computing
Thanks for your attention

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No More, No Less: A Formal Model for Serverless Computing

  • 1. No More, No Less A Formal Model for Serverless Computing Maurizio Gabbrielli, Ivan Lanese, Stefano Pio Zingaro INRIA, France / Università di Bologna, Italy Coordination 2019 Saverio Giallorenzo, Fabrizio Montesi, Marco Peressotti University of Southern Denmark, Denmark
  • 2. A gentle introduction to “serverless”... ... Adapted from “Serverless Architecture Patterns” by Abby Fuller, AWS Event Source Function Cloud Architecture
  • 3. A gentle introduction to “serverless”... Monolith Microservices Serverless provisioned, pay-per-deployment on-demand, pay-per-execution
  • 4. A gentle introduction to “serverless”... Monolith Microservices Serverless
  • 5. A gentle introduction to “serverless”... Monolith Microservices Serverless ?! Still rough around theedges
  • 6. A gentle introduction to “serverless”... https://aws.amazon.com/serverless/ Tailor
  • 7. A gentle introduction to “serverless”... https://github.com/alanwill/aws-tailor Tailor an excerpt
  • 8. … and its current limitations (non-exhaustive) ● Currently ~15’ execution timeout; ● No function-to-function invocation. Functions need an in-between stateful service to call each other; ● Sparse coordination logic.
  • 9. … and its current limitations (non-exhaustive) ● Traffic-dependent scaling of functions implies: ○ complex cost model; ○ complex system load estimations. ● Poor performance for standard communication patterns Jonas, Eric, et al. "Cloud Programming Simplified: A Berkeley View on Serverless Computing." Block Storage Object Storage File System Elastic Database Memory Store Function access Transparent Provisioning Availability and persistence Latency Costs
  • 10. … and its current limitations (non-exhaustive) Lock-in due to absence of standards on: ● function support/execution environments; ● function call semantics; ● semantics of stateful services.
  • 11. Direction ● We want to study S.C. avoiding any vendor/technology specifics ● We need a formal model for Serverless Computing that ○ Captures current incarnations of S.C. (e.g. event-based, storage-mediated as in AWS) ○ Supports proposed approaches/features (e.g. function-to-function invocation, updatable function definitions)
  • 12. Serverless Kernel Calculus (SKC) ● Systems: ⟨S,𝒟⟩ ● Function definitions: f↦M ● Running functions: c◂M Repository of function definitionsNetwork of running functions λ-termFunction name λ-termPromise
  • 13. Serverless Kernel Calculus (SKC) ● Systems: ⟨S,𝒟⟩ ● Function definitions: f↦M ● Running functions: c◂M Repository of function definitionsNetwork of running functions λ-termFunction name λ-termPromise
  • 14. Serverless Kernel Calculus (SKC) ● Systems: ⟨S,𝒟⟩ ● Function definitions: f↦M ● Running functions: c◂M Repository of function definitionsNetwork of running functions λ-termFunction name λ-termPromise
  • 15. Serverless Kernel Calculus (SKC) ● Systems: ⟨S,𝒟⟩ ● Function definitions: f↦M ● Running functions: c◂M Repository of function definitionsNetwork of running functions λ-termFunction name λ-termPromise
  • 16. SKC function terms M ::= M M' ∣ V ∣ f ∣ async M ∣ set f M ∣ take f V ::= x ∣ λx.M ∣ c ⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩ ⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩ ⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩ Function invocation Asynchronous eval Function Repository Updates ⟨ℰ[f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟⟩ Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
  • 17. SKC function terms M ::= M M' ∣ V ∣ f ∣ async M ∣ set f M ∣ take f V ::= x ∣ λx.M ∣ c ⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩ ⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩ ⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩ Function invocation Asynchronous eval Function Repository Updates ⟨ℰ[f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟⟩ Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
  • 18. SKC function terms M ::= M M' ∣ V ∣ f ∣ async M ∣ set f M ∣ take f V ::= x ∣ λx.M ∣ c ⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩ ⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩ ⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩ Function invocation Asynchronous eval Function Repository Updates Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩
  • 19. SKC function terms M ::= M M' ∣ V ∣ f ∣ async M ∣ set f M ∣ take f V ::= x ∣ λx.M ∣ c ⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩ ⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩ Function invocation Asynchronous eval Function Repository Updates Futures
  • 20. SKC function terms M ::= M M' ∣ V ∣ f ∣ async M ∣ set f M ∣ take f V ::= x ∣ λx.M ∣ c ⟨ℰ[async M],𝒟⟩ ⟶ ⟨ℰ[c] ∣ c◂M,𝒟⟩ ⟨ℰ[set f M],𝒟⟩ ⟶ ⟨ℰ[f],𝒟[f↦M]⟩ ⟨ℰ[take f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟∖f⟩ Function invocation Asynchronous eval Function Repository Updates ⟨ℰ[f],𝒟[f↦M]⟩ ⟶ ⟨ℰ[M],𝒟⟩ Futures ⟨c◂V ∣ S,𝒟⟩ ⟶ ⟨S[V/c],𝒟⟩ λ + Futures + Function Repository
  • 21. Programmable events in SKC ● Store handlers for event e in the definition repository 𝒟: install_handler ↦ λe.λhandler. let old_handler = take e let new_handler = λv.do async (handler v) (current_handler v) set e new_handler ● Raise event e (with v) by invoking its handlers in 𝒟: e v ● ( See the paper for Tailor in SKC )
  • 22. Programmable events in SKC ● Store handlers for event e in the definition repository 𝒟: install_handler ↦ λe.λhandler. let old_handler = take e let new_handler = λv.do async (handler v) (current_handler v) set e new_handler ● Raise event e (with v) by invoking its handlers in 𝒟: e v ● ( See the paper for Tailor in SKC ) Updatable function definitions
  • 23. Programmable events in SKC ● Store handlers for event e in the definition repository 𝒟: install_handler ↦ λe.λhandler. let old_handler = take e let new_handler = λv.do async (handler v) (current_handler v) set e new_handler ● Raise event e (with v) by invoking its handlers in 𝒟: e v ● ( See the paper for Tailor in SKC ) Updatable function definitions Function-to-function invocation
  • 24. Conclusions and future work We introduced SKC a Kernel Calculus for Serverless Computing: ● Build on established models (λ-calculus + futures + function repository) ● captures current programming models ● supports next-gen features e.g. function-to-function invocation Serverless: current challenges SKC: research direction The coordination logic is spare and loosely-consistent Choreographic Programming targeting SKC. Estimation of performance and costs is complex Quantitative SKC
  • 25. No More, No Less λ + Futures + Function Repository = A formal model for Serverless Computing Thanks for your attention