Model-versioning-in-the-large: Algebraic foundations and the tile - PowerPoint PPT Presentation

Model-versioning-in-the-large: Algebraic foundations and the tile notation Work in progress Zinovy Diskin, Krzysztof Czarnecki and Michal Antkiewicz Generative Software Development Lab University of Waterloo, Canada

A “very large” picture: ! ! Pictures/diagrams are good but informal (no formal semantics) ! ! Formulas are bad (mind boggling) but precise ! ! The best of the two worlds: precise diagrams with formal semantics 9/4/11 CVSM-2009, Vancouver 2

Versioning: small vs. large Replicas Carol … and matches Bob Ann Plan of the talk: Model ! ! R M1 … 1. ! Inside a tile A B C t Model ! T ! M2 2. ! Tile composition " " " t " A " B " B " " Typical setting: 3. ! Reconciliation 1D and Small 4. ! Sample “large” t !! A "" " " B " C " "" "" … scenario 5. ! Summary/discussion … Our setting: Time 2D and Large and updates 9/4/11 CVSM-2009, Vancouver 3

Example: Relational tile Green refers to heuristic activity; Frame denotes elements’ ID s Ann’s model, A Bob’s model, B = P:Person Q:Person = name : Jo nickname : Jo # pho: 222 pho: 111 = age: 30 # # # # # # # model A ! model B ! = P " :Person Q " :Person = name : Jo name : Jon # = mPho: 222 hPho: 111 # # 9/4/11 CVSM-2009, Vancouver 4

Versioning-in-the-small: Deltas are tiles Bob Ann m Replicas B A m B A t u /v* v u v " A " B " m " " t " A " " " B " " m " A tile as a revision Time of update m B A Blue elements are v u derived /m* (computed) " B " A " m " A tile as a revision of match 9/4/11 CVSM-2009, Vancouver 5

Special cases: Idle/identity tiles 1 A m 1 A A A A B A A 1 m 1 u 1 A 1 B u 1 A u 1 A " A B A " " A " A A m 1 A’ 1 A (b1) Horizontal (a1) Vertical (ab) 1 1A =1 1A identity identity 9/4/11 CVSM-2009, Vancouver 6

Metamodel of tiles $ 0 (src model) Node Horizontal Arrow $ 1 (trg model) (Model) (Match spec) " h (identical match) $ 0 (src $ 1 (trg h $ 0 (src h $ 1 (trg " (idle " v (idle model) model) match) match) 2-update) update) " (identical 2-match) v $ 0 (src update) Vertical Arrow Square (Update spec) (Tile) v $ 1 (trg update) 9/4/11 CVSM-2009, Vancouver 7

Model versioning-in-the-large. Tile composition & interchange law Ann Bob Carol % $ Replica AC "" 1 = ( # ! ! ) % % ( $ ! ! ) ! #! ! $! # % s m n B C A t AC "" 2 = ( # % % $ ) ! ! ( &" % % $! ) u v w # $ Interchange law: " ! ! " C " ! ! " B " A " " " AC "" 1 = AC "" 2 m " n " ! ! #! $! " w " " u " v " " " " " B " C " t " A " "" "" "" "" " " m " n " "" "" Time ! ! % #! % $! 9/4/11 CVSM-2009, Vancouver 8

Model versioning-in-the-large. Definition of tile system (double category) ! ! Collection of nodes, vertical and horizontal arrows, and squares (tiles) ! ! V-arrows can be composed (assoc. and units) and h-arrows can be composed (assoc. and units). ! ! Tiles can be composed vertically (assoc. and units) and horizontally (assoc. and units), and work together under the interchange law. 9/4/11 CVSM-2009, Vancouver 9

Model versioning-in-the-large. Pasting lemma: Any tile system has the following property: {( & % & 12 )[ ' 1 % % ( & 22 & 32 )]} % % ( ' 3 & 33 ) = & 11 % ( & & 11 ' 1 ) % % ( & 12 & 22 & 32 ) % % ( ' 3 & 33 ) = ( & & 11 ' 1 ) % % {[( & 12 & 22 ) % % ' 3 ]( & 32 % % & 33 )} 9/4/11 CVSM-2009, Vancouver 10

Optimistic versioning and reconciliation Standard view Tile view O O O u v Input m rec B B A A m A B u ! Output v ! ! ! AB B! A! B! A! m ! Algebraic laws: (1) ( & % ' )! = & ! % ' ! (2) ( & " &" )! = &" ! (optional) 9/4/11 CVSM-2009, Vancouver 11

Use case: “large” versioning scenario via tiles Ann Bob Carol O O authors Mon 1 O u v R • • • Tue 1 v! u! v! v! • • • Tue + R m • • • • Wed m! • • Wed + R • • Thu Thu + • • 12 time

Summary ! ! The elementary unit (molecule) of model versioning is a 2D-structure -- tile. Complex scenarios are composed from tiles. ! ! Tile composition is regulated by algebraic laws of double categories (associativity, interchange law, pasting lemma). ! ! Complex scenarios are terms built from tiles in some signature of tile operations. Hence, ! ! Algebraic machineries of category theory become applicable (diagram chasing/diagrammatic calculus). 9/4/11 CVSM-2009, Vancouver 13

Even bigger picture ! ! Engineering (e.g., mechanical and electrical) Software Engineering ! ! Physics ! ! Mathematics ! ! Category theory (abstract nonsense) • Higher-dimensional category theory 9/4/11 CVSM-2009, Vancouver 14

Thank you! Questions/Comments? 9/4/11 CVSM-2009, Vancouver 15