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Logic and Lattices for Distributed Programming Neil Conway, William R. Marczak, Peter Alvaro, Joseph M. Hellerstein UC Berkeley David Maier Portland State University

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Distributed Programming: Key Challenges Asynchrony Partial Failure

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Dealing with Disorder Enforce global order –Paxos, Two-Phase Commit, GCS, … –“Strong Consistency” Tolerate disorder –Programmer must ensure correct behavior for many possible network orders –“Eventual Consistency” Typical goal: replicas converge to same final state

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Dealing with Disorder Enforce global order –Paxos, Two-Phase Commit, GCS, … –“Strong Consistency” Tolerate disorder –Programmer must ensure correct behavior for many possible network orders –“Eventual Consistency” Typical goal: replicas converge to same final state

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Goal: Make it easier to write programs on top of eventual consistency

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This Talk 1.Prior Work –Convergent Modules (CRDTs) –Monotonic Logic (CALM) 2.Bloom L 3.Case Study

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Read: {Alice, Bob} Write: {Alice, Bob, Dave} Write: {Alice, Bob, Carol} Students {Alice, Bob, Dave} Students {Alice, Bob, Carol} Client 0 Client 1 Read: {Alice, Bob} Students {Alice, Bob} How to resolve? Students {Alice, Bob}

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Proble m Replicas perceive different event orders GoalSame final state at all replicas Solutio n Use commutative operations (“merge functions”)

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Students {Alice, Bob, Carol, Dave} Client 0 Client 1 Merge = Set Union

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Commutative Operations Common design pattern Formalized as CRDTs: Convergent and Commutative Replicated Data Types –Shapiro et al., INRIA ( ) –Based on join semilattices

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Lattices hS,t,?i is a bounded join semilattice iff: –S is a set –t is a binary operator (“least upper bound”) Associative, commutative, and idempotent Induces a partial order on S: x · S y if x t y = y Informally, “merge function” for elements of S –? is the “least” element in S 8x 2 S: ? t x = x 12

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Time Set (LUB = Union) Increasing Integer (LUB = Max) Boolean (LUB = Or)

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Client 0 Client 1 Students {Alice, Bob, Carol, Dave} Teams { } Read: {Alice, Bob, Carol, Dave} Read: { } Write: {, } Teams {, } Remove: {Dave} Students {Alice, Bob, Carol} Replica Synchronization Students {Alice, Bob, Carol} Teams {, }

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Client 0 Client 1 Students {Alice, Bob, Carol, Dave} Teams { } Read: {Alice, Bob, Carol} Read: { } Teams { } Remove: {Dave} Students {Alice, Bob, Carol} Replica Synchronization Students {Alice, Bob, Carol} Nondeterministic Outcome! Teams { }

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Problem: Composition of CRDTs can result in non-determinism

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Possible Solution: Encapsulate all distributed state in a single CRDT Hard to design, verify, and test Doesn’t scale with application size

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Goal: Design a language that allows safe composition of CRDTs

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Solution: … Datalog? Concurrent work: distributed programming using Datalog –P2 ( ) –Bloom ( ) Monotonic logic: building block for convergent distributed programs

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Monotonic Logic As input set grows, output set does not shrink –“Retraction-free” Order independent e.g., map, filter, join, union, intersection Non-Monotonic Logic New inputs might retract previous outputs Order sensitive e.g., aggregation, negation

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Monotonicity and Determinism Agents learn strictly more knowledge over time Different learning order, same final outcome Result: Program is deterministic!

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Consistency As Logical Monotonicity CALM Analysis 1.All monotone programs are deterministic 2.Simple syntactic test for monotonicity Result: Whole-program static analysis for eventual consistency

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Problem: CALM only applies to programs over growing sets Version NumbersTimestampsThreshold Tests

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Quorum Vote A coordinator accepts votes from agents Count # of votes –When Count(Votes) > k, send “success” message

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Quorum Vote A coordinator accepts votes from agents Count # of votes –When Count(Votes) > k, send “success” message Aggregation is non-monotonic!

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CRDTs Limited scope (single object) Flexible types (any lattice) CALM Whole program analysis Limited types (only sets) Bloom L Whole program analysis Flexible types (any lattice)

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Bloom L Constructs OrganizationCollection of agents CommunicationMessage passing StateLattices ComputationFunctions over lattices

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Monotone Functions f : S T is a monotone function iff 8a,b 2 S : a · S b ) f(a) · T f(b) 28

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Time Set (LUB = Union) Increasing Integer (LUB = Max) Boolean (LUB = Or) size() >= 5 Monotone function from set increase-int Monotone function from increase-int boolean

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Quorum Vote in Bloom L QUORUM_SIZE = 5 RESULT_ADDR = "example.org" class QuorumVote include Bud state do channel :vote_chn, :voter_id] channel :result_chn, lset :votes lmax :vote_cnt lbool :got_quorum end bloom do votes <= vote_chn {|v| v.voter_id} vote_cnt <= votes.size got_quorum <= vote_cnt.gt_eq(QUORUM_SIZE) result_chn <~ got_quorum.when_true { [RESULT_ADDR] } end Monotone function: set ! max Monotone function: max ! bool Threshold test on bool (monotone) Lattice state declarations 30 Communication interfaces Accumulate votes into set Annotated Ruby class Program state Program logic Merge function for set lattice Monotonic CALM

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Bloom L Features Generalizes logic programming to lattices –Integration of relational-style queries and functions over lattices –Efficient incremental evaluation scheme Library of built-in lattices –Booleans, increasing/decreasing integers, sets, multisets, maps, … API for defining custom lattices

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Case Studies Key-Value Store –Object versioning via vector clocks –Quorum replication Replicated Shopping Cart –Using custom lattice types to encode domain-specific knowledge

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Case Studies Key-Value Store –Object versioning via vector clocks –Quorum replication Replicated Shopping Cart –Using custom lattice types to encode domain-specific knowledge

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Case Study: Shopping Carts 34

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Case Study: Shopping Carts 35

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Case Study: Shopping Carts 36

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Case Study: Shopping Carts 37

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Perspectives on Shopping CRDTs –Individual server replicas converge Bloom –Checkout is non-monotonic requires distributed coordination Built-in Bloom L lattice types –Checkout is not a monotone function of any of the built-in lattices

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Observation: Once a checkout occurs, no more shopping actions can be performed

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Observation: Each client knows when a checkout can be processed “safely”

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Monotone Checkout OPS = [1] Incomplete OPS = [2] Incomplete OPS = [3] Incomplete OPS = [1,2] Incomplete OPS = [2,3] Incomplete OPS = [1,2,3] Complete 41

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Monotone Checkout 42

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Monotone Checkout 43

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Monotone Checkout 44

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Monotone Checkout 45

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Shopping Takeaways Checkout summary is a monotone function of client’s activities Custom lattice type captures application- specific notion of “forward progress” –“Unsafe” state hidden behind ADT interface

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Recap 1.How to build eventually consistent systems –Write disorderly programs 2.Disorderly state –Lattices 3.Disorderly computation –Monotone functions over lattices 4.Bloom L –Type system for deterministic behavior –Support for custom lattice types

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Thank You!

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Backup Slides

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Strong Consistency in Industry “… there was a single overarching theme within the keynote talks… strong synchronization of the sort provided by a locking service must be avoided like the plague… [the key] challenge is to find ways of transforming services that might seem to need locking into versions that … can operate correctly without locking.” -- Birman et al., “Toward a Cloud Computing Research Agenda” (LADIS, 2009) 50

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Bloom Operational Model 51

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QUORUM_SIZE = 5 RESULT_ADDR = "example.org" class QuorumVote include Bud state do channel :vote_chn, :voter_id] channel :result_chn, table :votes, [:voter_id] scratch :cnt, [] => [:cnt] end bloom do votes <= vote_chn {|v| [v.voter_id]} cnt <= votes.group(nil, count(:voter_id)) result_chn = QUORUM_SIZE} end Quorum Vote in Bloom Communication Persistent Storage Transient Storage Accumulate votes Send message when quorum reached Not (set) monotonic! 52 Count votes Annotated Ruby class Program state Program logic

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Built-in Lattices NameDescription?a t bSample Monotone Functions lboolThreshold testfalse a ∨ b when_true() ! v lmaxIncreasing number 1max(a,b ) gt(n) ! lbool +(n) ! lmax -(n) ! lmax lminDecreasing number −1−1min(a,b)lt(n) ! lbool lsetSet of values;a [ bintersect(lset) ! lset product(lset) ! lset contains?(v) ! lbool size() ! lmax lpsetNon-negative set;a [ bsum() ! lmax lbagMultiset of values;a [ bmult(v) ! lmax +(lbag) ! lbag lmapMap from keys to lattice values empty map at(v) ! any-lat intersect(lmap) ! lmap 53

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Failure Handling Great question! 1.Monotone programs handle transient faults very well –Deterministic simple logging –Commutative, idempotent simple recovery 2.Future work: “controlled non-determinism” –Timeout code is fundamentally non-deterministic –But we still want mostly deterministic programs

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Handling Non-Monotonicity … is not the focus of this talk Basic alternatives: 1.Nodes agree on an event order using distributed coordination (e.g., Paxos) 2.Allow non-deterministic outcomes If needed, compensate and apologize

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