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Interfacing with Proof Assistants for Domain Specific Programming Using EventML Vincent Rahli PRL team - Cornell University July 13, 2012 Vincent Rahli EventML July 13, 2012 1/15 Credits Mark Bickford Robert Constable David

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Interfacing with Proof Assistants for Domain Specific Programming Using EventML

Vincent Rahli

PRL team - Cornell University

July 13, 2012

Vincent Rahli EventML July 13, 2012 1/15

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Credits

◮ Mark Bickford ◮ Robert Constable ◮ David Guaspari ◮ Richard Eaton ◮ Vincent Rahli ◮ Robbert Van Renesse ◮ Nicolas Schiper ◮ Jason Wu

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Problem

Problem: unverified protocols are wrong. Goal: automatic synthesis of verified diversifiable distributed systems. Our solution: building tools that cooperate with a Logical Programming Environment (e.g., a constructive theorem prover).

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EventML: specification and programming language

◮ A ML-like functional programming language. ◮ Features logical constructs (Logic of Events combinators). ◮ To specify/code distributed protocols. ◮ EventML translates specifications into event classes.

Logical aspect

◮ EventML synthesizes distributed programs (in the model

underlying the Logic of Events) from specifications. Computational aspect

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Cooperation with a Logical Programming Environment

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Accomplishments

We have specified many distributed protocols. We have proved the correctness of the following protocols:

◮ Leader election in a ring. ◮ Two-thirds consensus protocol. ◮ Paxos (in progress).

The methodology works! Nicolas Schiper (Cornell postdoc) has implemented a replicated database (ShadowDB)

n top of our synthesized

two-thirds consensus protocol. It is used!

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An example: Maximum using Memory

We have defined state machines in the Logic of Events. E.g., Memory1. We have automated some reasoning on state machines.

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Maximum

input i n t : I n t c l a s s Maximum = Memory1 (\ l o c .{0}) (\ l o c .\ x .\ s . imax x s ) i n t ’ b a s e ; ; Intuition: at any event, computes the maximum of the integers received in the past.

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Maximum

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Maximum

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Maximum

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Maximum

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Maximum

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Maximum

One can specify state machine invariants in EventML:

i n v a r i a n t pos max on n in Maximum == n >= 0 ; ; p r ogr e s s inc max on n1 then n2 in Maximum with n in i n t ’ b a s e and s = > n > s == n2 > n1 ; ; memory mem max on n1 then n2 in Maximum with n in i n t ’ b a s e == n2 >= n /\ n2 >= n1 ; ;

Nuprl automatically proves these invariants.

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What’s next?

◮ Automation. ◮ Correct-by-construction optimizations. ◮ More expressive types: refinement types, dependent

types...

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