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Formal Methods in Software Engineering

Formal Methods in Software Engineering

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Formal Methods in Software Engineering

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  1. Formal Methods in Software Engineering “And they made their lives bitter with hard bondage … all their service … was with rigour.” Ex 1:14

  2. A Spectrum of Methods More Formal OCL and Z Cleanroom Traditional Models: Waterfall, Spiral, Incremental Agile Methods: FDD and SCRUM Less Formal

  3. Characteristics of Formal Methods • Well-defined specification language • Typically based on set-theoretical concepts • Specifies by indicating operational conditions: • pre-conditions, post-conditions, and invariants • Composed of three components: • syntax, semantics, and relations (operational statements) • Emphasis on verification • Of program correctness • Of completeness of description • Of refinements to different abstractions • Testing De-emphasized

  4. Advantages of Formal Methods • Consistency (fewer contradictions) • Precision (less ambiguity) • Completeness (extent of definitions more clearly defined, so all cases handled) • Descriptive Uniformity (less mixture among levels of detail)

  5. Set Theoretical Foundation for Formal Methods • See Section 28.3 • Set Operators: , ∩, \, and x • Logic Operators: and, or, not, implication • Sequences: <a, b, c, d>, head, tail, front, last, concatenation • See Examples for Block Handler: pgs 775 and 788-790 (section 28.6.2) • OCL Notation Summary (Table28.1), pg 785 • Z Notation Summary (Table 28.2), pg 789

  6. Block Handler Example: Constraints • No block will be marked as both free and used • All the sets of blocks in the queue are subsets of currently used blocks • No elements of the queue contain the same block numbers • The collection of used and free blocks make up the total collection of all blocks • There are no duplicates among the free blocks • There are no duplicates among the used blocks

  7. OCL Example: Block Handler Free • Context BlockHandler inv: (used->intersection(free))-> isEmpty() • Context BlockHandler inv: blockQ->forAll(aBlockSet | used->includesAll(aBlockSet)) • Context BlockHandler inv: allBlocks = used->union(free) • Context BlockHandler::remove() pre: blockQ->size() > 0 post: used = used@pre – blockQ@pre->first() AND free = free@pre->union(blockQ@pre-> first()) AND blockQ = blockQ@pre-> excluding(blockQ@pre->first()) 1 3 4 6 9 Used 2 5 7 8 10 11 12 released 2 5 8 11 7 Block Queue

  8. Z Example: Block Handler Free • used, free: powerSet BLOCKS • blockQ: seq powerSet BLOCKS • used ∩ free = Ø • used U free = allBlocks • forAll i: dom blockQ : blockQ i subset used • forAll i, j: dom blockQ : i ≠ j → blockQ i ∩ blockQ j = Ø • removes(): • Pre: #blockQ > 0 • Post: used’=used–head blockQ AND free’=free U head blockQ AND blockQ’=tail blockQ 1 3 4 6 9 Used 2 5 7 8 10 11 12 released 2 5 8 11 7 Block Queue

  9. Additional Points of Emphasis • Why completeness is difficult to achieve (pg 771) • Controversy over formal methods (pg 771) • Areas in which formal methods may apply (pg 770 – “Why is it important”) • Area in which formal methods are difficult to apply (pg 792)