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Towards Using Constructive Type Theory for Verifiable Modular Transformations

Towards Using Constructive Type Theory for Verifiable Modular Transformations. Steffen Zschaler , Iman Poernomo , Jeffrey Terrell FREECO’11 Lancaster, 26 July 2011. Motivation. Object-Relational Mappings Classes & Attributes: A Table for every Class A column for every attribute

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Towards Using Constructive Type Theory for Verifiable Modular Transformations

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  1. Towards Using Constructive Type Theory for VerifiableModular Transformations Steffen Zschaler, ImanPoernomo, Jeffrey Terrell FREECO’11 Lancaster, 26 July 2011

  2. Motivation Object-Relational Mappings • Classes & Attributes: • A Table for every Class • A column for every attribute • Associations • Model with foreign keys • Many-to-many: Additional table • One-to-one: May merge tables • Inheritance • Model with foreign keys  use joins for every query • Model with one global table  denormalisation • Would like choice • Require modular transformation • Require contracts to make composition safe (c) Steffen Zschaler

  3. Constructive Type Theory 101 a : T • Example types • Basic types: int, String, ... • Function types: T1 -> T2 • Dependent types: •  x : T1. T2(x) •  x : T1. T2(x) • Curry–Howard isomorphism: • Can interpret instances of types as proofs (c) Steffen Zschaler

  4. Model Transformations • Transform source models into target models • Source model instance of MMS • Target model instance of MMT • Can specify as a forall-exists type: •  s: MMS. Pre s   t : MMT. Post s t (c) Steffen Zschaler

  5. Composing Transformations  trans : MMS  MMT  Prop.  proof : ( s: MMS.  t: MMT. trans s t  ...).  s: MMS. Pre s   t : MMT. Post s t  trans s t Formal description of dependencies between transformations – contract (c) Steffen Zschaler

  6. Structure of Contracts Three types of statements • Requirements on what trans must ensure • Conjoin statements that refer to properties of t and no further  clauses  s: MMS.  t: MMT. trans s t  SID s = TID t • Requirements on what trans must not constrain • Conjoin statements that equate properties of t with all-quantified variables  s: MMS.  n: NAT. t: MMT. trans s t  TID t = n • Assumptions trans may make • Precedent of an implication  s: MMS.  t: MMT. assume s t  trans s t (c) Steffen Zschaler

  7. Conclusions & Outlook • Contracts are important to make composition safe • Higher-order type theory can be used to express such contracts for transformations • Initial work, more research needed • Larger, more complex examples • Different composition strategies • Integration with main-stream transformation languages (c) Steffen Zschaler

  8. Thank you for your Attention! (c) Steffen Zschaler

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