Transformations of Software Product Lines: A Generalizing Framework based on Category Theory

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1 Transformations of Software Product Lines: A Generalizing Framework based on Category Theory Gabriele Taentzer, Rick Salay, Daniel Strüber and Marsha Chechik

2 Software Product Lines (SPL) Manage a large number of similar but different artifact variants (products) Washing Machine Co. 2 Transformations of Software Product Lines

3 SPL Structure SPL (annotative) represented by Domain Model combined parts from all products shows possible features and restrictions for products Domain Model Wash Delay excludes 3 Transformations of Software Product Lines

4 SPL Configuration example + product Feature configuration: {Wash, } Wash Delay excludes 4 Transformations of Software Product Lines

5 SPL of models: washing machine state machine Presence Conditions excludes Domain Model Wash Delay Locking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() Delay Delay Delay Waiting exit/eroff() [PRESS_START]/ wash.start() Delay /wash.start() Unlocking Washing entry/tempcheck() ing 5 Transformations of Software Product Lines

6 Example Product: {Wash, } excludes Domain Model Wash Delay Locking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() Delay Delay Delay Waiting exit/eroff() [PRESS_START]/ wash.start() Delay /wash.start() Unlocking Washing entry/tempcheck() ing 6 Transformations of Software Product Lines

7 Example Product: {Wash, } excludes Product: {Wash, } Wash Delay Locking [PRESS_START]/ wash.start() Unlocking Washing ing 7 Transformations of Software Product Lines

8 Outline Software Product Lines Transformations of SPLs What is the problem? Approach (part 1): Category of SPLs Approach (part II): SPL Transformations using graph transformation rules Summary of results and next steps 8 Transformations of Software Product Lines

9 Key types of SPL transformations in the Literature 1. Feature model transformations Supports reasoning about additions, deletions, and modifications of features e.g., Transformation rules to specify high-level feature editing operations [Bürdek et al.] 2. Lifted model transformations Adapts single-product transformation rules to the entire SPL [Salay et al. ] Effect of lifting is same as applying the rule to each product separately. 3. SPL refinement Supports safe evolution SPL by controlling impact on existing products. e.g., Modifications restricted so that only a subset of products change [Sampaio et al.] 9 Lifting Transformations to Product Lines

10 Motivation Types (1) & (3) apply only to feature models; type (2) applies only to domain models None of these types of transformation apply to entire SPL s feature and domain models! But, this is needed in practice: Addition or deletion of features usually entails the corresponding changes in the domain model Research Objective: A formal characterization of SPL transformations that addresses both feature and domain models. 10 Lifting Transformations to Product Lines

11 Approach Build on existing formal theories: category theory and theory of Algebraic Graph Transformations (AGT)[1] Our strategy: given any suitable (to be defined) category MMMMMM of models, 1. Show how to define the category PPLL MMMMMM of SPLs having MMMMMM models as domain models. 2. Use AGT to define transformation rules for SPLs in PPLL MMMMMM Benefits: General, systematic and covers both feature and domain model parts of an SPL Gets formal techniques from AGT that support SPL transformation development e.g., conflict and dependency analysis, confluence analysis, etc. [1] H. Ehrig, K. Ehrig, U. Prange, and G. Taentzer, Fundamentals of Algebraic Graph Transformation, ser. Monographs in Theoretical Computer Science. Springer, Lifting Transformations to Product Lines

12 Outline Software Product Lines Transformations of SPLs What is the problem? Approach (part 1): Category of SPLs Approach (part II): SPL Transformations using graph transformation rules Summary of results and next steps 12 Transformations of Software Product Lines

13 Defining category PPLL MMMMMM objects and morphisms An SPL PP = (FF PP, Φ PP, MM PP, ff PP ) of PPLL MMMMMM consists of: (feature model) Set FF PP of features with set Φ PP of propositional feature constraints over FF PP defining allowable feature configurations (domain model) MMMMMM-model MM PP (presence conditions) Function ff PP assigns a propositional formula over FF PP to each submodel of MM PP defining for which feature configurations the submodel is present An SPL morphism h: PP QQ is a mapping from SPL PP to QQ such that (feature mapping) h maps FF PP to FF QQ (domain mapping) h maps DD PP to DD QQ (using a MMMMMM-morphism) above mappings constrained so that products of PP map into products of QQ 13 Transformations of Software Product Lines

14 Washing machine SPL WWWW in PPLL SSSS Domain Model DD WWWW Locking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() FF WWWW : WWWWWWW, HHHHHHHH, DDDDDDDDDD, DDDDDD Φ WWWW : {WWWWWWW, (DDDDDDDDDD HHHHHHHH)} Waiting exit/eroff() [PRESS_START]/ wash.start() /wash.start() Unlocking Washing entry/tempcheck() ff WWWW Presence condition (example) ing DDDDDD HHHHHHHH 14 Transformations of Software Product Lines

15 Example Product: {Wash, } Product: {WWWWWWW, DDDDDD} Locking [PRESS_START]/ wash.start() ff WWWW Presence condition (example) WWWWWWW DDDDDD HHHHHHHH DDDDDDDDDD Unlocking ing Washing Products are the maximal submodels with presence condition for a configuration 15 Transformations of Software Product Lines

16 Morphisms in PPLL SSSS FF BB : BBBBBBBB Φ BB : { } FF WWWW : WWWWWWW, HHHHHHHH, DDDDDDDDDD, DDDDDD Φ WWWW : {WWWWWWW, HHHHHHHH DDDDDDDDDD } Domain Model DD BB x1 [t]/ a Domain Model DD WWWW Locking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() Waiting exit/eroff() x2 [PRESS_START]/ wash.start() /wash.start() h Unlocking Washing entry/tempcheck() ing 16 Transformations of Software Product Lines

17 Morphisms map products Product:{BBBBBBBB} Product:{WWWWWWW, DDDDDD} x1 x2 [t]/ a Locking [PRESS_START]/ wash.start() h Unlocking Washing ing 17 Transformations of Software Product Lines

18 Key result: Pushout construction in PPLL MMMMMM In PPLL MMMMMM we can use the standard category theory pushout construction to combine two SPLs that are related by a common SPL h PPPP SSSSLL PP h PPPP SSSSLL QQ SSSSLL RR h QQQQ See Paper for Details! h RRRR SSSSLL SS Products of SSSSLL SS are constructed by combining products of SSSSLL QQ and SSSSLL RR according to overlap in SSSSLL PP 18 Transformations of Software Product Lines

19 Outline Software Product Lines Transformations of SPLs What is the problem? Approach (part 1): Category of SPLs Approach (part II): SPL Transformations using graph transformation rules Summary of results and next steps 19 Transformations of Software Product Lines

20 Transformations in PPLL MMMMMM Since we can construct pushouts in PPLL MMMMMM, we can use the double pushout approach from AGT to define transformation rules. Rule: AddBeepFeature FF BB : BBBBBBBB Φ BB : { } LHS RHS Domain Model DD See x1details in the paper. BBBB x1 [t]/ a x2 x2 FF BBBB : BBBBBBBB Φ BB : { } FF BBBB : BBBBBBBB, BBBBBBBB Φ BBBB : { BBBBBBBB BBBBBBBB} Key result: We show the existence and Domain uniqueness Model DD BB of rule applications for PPLL Domain Model DD BBBB MMMMMM. BBBBBBBB Beeping [t]/ a BBBBBBBB BBBBBBBB x1 x2 [t]/ a BBBBBBBB BBBBBBBB Logging BBBBBBBB 20 Transformations of Software Product Lines

21 Washing machine SPL WWWW Domain Model DD WWWW Locking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() Delay Delay FF WWWW : WWWWWWW, HHHHHHHH, DDDDDDDDDD, DDDDDD Φ WWWW : {WWWWWWW, DDDDDDDDDD HHHHHHHH } Delay Waiting exit/eroff() [PRESS_START]/ wash.start() Delay /wash.start() Unlocking Washing entry/tempcheck() ing 21 Transformations of Software Product Lines

22 Applying AddBeepFeature: Match LHS LHS FF BB : BBBBBBBB Φ BB : { } Domain Model DD BB x1 x2 [t]/ a Domain Model DD WWWW Locking [PRESS_START]/ wash.start() Unlocking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() Delay ing Delay Delay Waiting exit/eroff() Delay /wash.start() Washing entry/tempcheck() FF WWWW : WWWWWWW, HHHHHHHH, DDDDDDDDDD, DDDDDD Φ WWWW : {WWWWWWW, DDDDDDDDDD HHHHHHHH } 22 Transformations of Software Product Lines

23 Applying AddBeepFeature: Result SPL WWWWWW of double pushout Domain Model DD WWWWWW [PRESS_START]/ wash.start() Beep Beeping Locking [PRESS_START_WITH_DELAY] [PRESS_START] / eron() [PRESS_START]/ wash.start() Logging Delay Delay [PRESS_START]/ wash.start() Beep FF WWWWWW : WWWWWWW, HHHHHHHH, DDDDDDDDDD, DDDDDD, BBBBBBBB Φ WWWWWW : {WWWWWWW, DDDDDDDDDD HHHHHHHH, BBBBBBBB DDDDDD} Delay Waiting exit/eroff() Delay /wash.start() Unlocking ing Washing model, feature model and entry/tempcheck() Rule application affects domain presence conditions! 23 Transformations of Software Product Lines

24 Summary of Results Given any suitable category MMMMMM of models, 1. Showed how to define the category PPLL MMMMMM of SPLs having MMMMMM models as domain models. 2. Defined the pushout construction for PPLL MMMMMM 3. Showed how to define transformation rules for PPLL MMMMMM using double pushout 4. Proved the existence and uniqueness of rule application. Illustrated how an SPL rule can affect both feature and domain model parts of an SPL i.e., we have exceeded these limitations in the literature 24 Transformations of Software Product Lines

25 Next Steps Have only partially proven that PPLL MMMMMM satisfies the formal requirements for AGT We are completing this task Plan to implement formal analysis techniques from AGT for PPLL MMMMMM e.g., conflict and dependency analysis, confluence analysis, etc. Henshin is likely the platform Want to explore the scope of SPL transformations expressible using our approach. Want to explore the kinds of SPLs obtained by using different model categories for MMMMMM 25 Transformations of Software Product Lines

26 Questions 26 Lifting Transformations to Product Lines

PROPOSED REGULATION OF THE STATE ENVIRONMENTAL COMMISSION. LCB File No. R084-16

PROPOSED REGULATION OF THE STATE ENVIRONMENTAL COMMISSION LCB File No. R084-16 P2016-04 June 7, 2016 EXPLANATION Matter in italics is new; matter in brackets [omitted material] is material to be omitted.