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Institutions
Investigate the relationship between specifications and models at a general, theoretical level
Implementation Specification
Institutions , Property-Aware Programming and Testing Ali Alnajjar - - PowerPoint PPT Presentation
Institutions , Property-Aware Programming and Testing Ali Alnajjar - - PowerPoint PPT Presentation
Institutions , Property-Aware Programming and Testing Ali Alnajjar Supervisor:Magne Haveraaen Investigate the relationship between Institutions specifications and models at a general, theoretical level Implementation Specification Run the
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Testing
Run the algorithms on selected data sets in
- rder to increase our belief in their
correctness.
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Property-Aware Programming (institutions)
Declaring syntactic and semantic properties
- n generic parameters.
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Sophus
- A medium-sized C++ software library developed for solving coordinate-free
partial differential equations.
- Developed using algebraic specifications (with a focus on reusability).
- Axiomatic specification.
- Implementation were targeted to be as general as possible.
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Sophus
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Sophus
CartShape CartPoint ContShape ContPoint BNShape BNPoint extends uses satisfies satisfies uses extends MeshPoint MeshShape uses
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Sophus
When a specification B in Sophus uses another specification A, it means that specification A defines operations and axioms on a sort-set and B on another sort-set, even though the sorts of A may be used by operations in B. When a specification B in Sophus extends another specification A, it means that specification A defines operations and axioms on a sort-set and B provides more functiins and axioms on the same set.
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Institutions: Signatures
- Sorts (Types).
- Operations (functions,methods) + arities (arguments and return types).
- Variables.
- Terms (expressions).
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Institutions: Signature Morphism
S1 S2
(renaming and combining)
S’
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Institutions: Specification
Signatures Axioms
- Can be combined and renamed.
Equational Axioms Conditional Axioms
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Institutions: Models
- Provide the semantic for each signature.
- For each sort define a data structure.
- For each function define an algorithm.
S int
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Institutions: Satisfaction
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Implementation
- Sorts
data structures (data invariants)
- Functions
Algorithms
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Implementation
- Every algorithm must preserve the data invariants: if the input data satisfies
the data invariant, so must the output data.
- Every algorithm must preserve equality
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Testing
- Preservation of the data invariants
- Preservation of the equality. (provided data needed)
- Checking of axioms. (provided data needed)
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Testing : Test Set
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Testing : test reduction hypothesis.
- Random selection hypothesis
- Domain partitioning hypothesis (Discontinuity hypothesis)
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Random selection hypothesis
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Domain partitioning hypothesis (Discontinuity hypothesis)
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Domain partitioning hypothesis (Discontinuity hypothesis)
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Questions
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Reference to specifications as models
Models Models provide the semantics for each signature. Models transform in the
- pposite direction of signatures. That is, one may think of a signature renaming as
- ne signature pointing at compo- nents of another signature. Then the latter
components are used as models for the former.
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