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Using Constructive Type Theory for Safe Verifiable Modular Transformations

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This paper explores the application of Constructive Type Theory (CTT) in creating verifiable modular transformations for Object-Relational Mappings (ORMs). It discusses class and attribute representations, associations, and inheritance modeling, advocating for modular transformation strategies that ensure safety and reliability through contracts. The authors present model transformations from source to target forms, establishing formal dependencies among transformations and the necessary requirements on these transformations. The work highlights the potential of higher-order type theory for expressing transformation contracts and calls for further research into complex examples and integration with mainstream transformation languages.

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Using Constructive Type Theory for Safe 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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