Formal Methods for Software Development

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1 Formal Methods for Software Development Till Mossakowski, Lutz Schröder

2 2 Overview of this Lecture MMISS Software Development and Formal Specification Overview of the course Scheinkriterien

3 3 MMISS MMISS = multimedia instructions in safe and secure systems aim: multimedia Internet-based adaptive educational system repository of lectures (in english) glossary with central notions translated to German See

educational system repository of lectures (in english)

4 Software Development and Formal Specification

5 Software Development and Formal Specification 5 Software Development and Formal Specification Goals to understand the basic principles of software development to understand the role of formal methods in software development to understand the basic principles of functional programs and their formal specification

development to understand the role of formal methods in software development

6 Software Development and Formal Specification 6 Software Engineering deals with the technical and organisational aspects of the development and maintenance of large software systems. State of the Art natural language documentations diagrammatic modeling languages (e.g. UML) CASE Tools (Computer Aided Software Engineering) formal methods (for safety critical systems)

7 Software Development and Formal Specification 7 Formal Methods based on mathematics (set theory, algebra, math. logics) advantages: unambiguous interpretation of syntactic constructs verification of properties (of specifications, models, programs) verification of the correctness of development steps difficulties: knowledge of formal notations and their meaning additional development costs

logics) advantages: unambiguous interpretation of syntactic constructs verification of properties

8 Software Development and Formal Specification 8 waterfall model Process Models iterative model, V-model, spiral model, XP/agile... Formal software development uses additionally formal specifications in the different phases. Verification of the correctness of a development step is only possible on the basis of formal specifications.

.. Formal software development uses additionally formal specifications in the

9 Software Development and Formal Specification 9 Proving the Correctness of the Implementation a) Verification of the implementation against the requirements specification (post mortem) OR b) Verification of each realization step (verification conditions) Remarks Testing can only show the existence of errors. Verification can show the absence of errors. The adequateness of a (formal) specification w.r.t. the desires of the user can not be verified.

step (verification conditions) Remarks Testing can only show the existence of errors.

10 Software Development and Formal Specification 10 Verification Success Stories complete formal verification of Pentium 4 arithmetic NASA uses formal specification of physical units verification of the Java bytecode verifier found 12 deadlocks in occam code for international space station

formal specification of physical units verification of the Java

11 Software Development and Formal Specification 11 Haskell is a purely functional programming language therefore it is well-suited for application of formal methods side-effects are encapsulated via monads Haskell specification logic P-logic specifications can be used for both testing and verification

application of formal methods side-effects are encapsulated via monads

12 Software Development and Formal Specification 12 Sorting in Haskell insert :: Ord a => (a,[a]) -> [a] insert(x,[]) = [x] insert(x,y:l) = if x <= y then x:y:l else y:insert(x,l) insert_sort :: Ord a => [a] -> [a] insert_sort([]) = [] insert_sort(x:l) = insert(x,insert_sort(l))

if x <= y then x:y:l else y:insert(x,l) insert_sort :: Ord a => [a]

13 Software Development and Formal Specification 13 Test Cases testsorting = TestCase (do let list = [7,2,6,3,5] sortedlist = [2,3,5,6,7] assertbool "insert_sort is faulty" (insert_sort list == sortedlist) )

14 Software Development and Formal Specification 14 Test Case Generation propsorted [] = True propsorted [x] = True propsorted (x:y:xs) = x <= y && propsorted (y:xs) instance Arbitrary [Int] where arbitrary = do len <- choose (0,20) l <- mapm (\x -> choose (0,20)) [1..len] return l

$len <- choose (0,20) l <- mapm (\x -> choose (0,20)) [1..len] return l$

15 Software Development and Formal Specification 15

16 Software Development and Formal Specification 16 Specification {-# AXIOMS "issorted" forall l l1 l2 x y -> insert_sort l == l1++[x,y]++l2 = #-}

17 This Course

18 This Course 18 Overview of the course Testing with user-defined test cases (HUnit) Testing with automated test-case generation (QuickCheck) Testing monadic programs P-logic specification logic Isabelle/HOL: verification of simple functional programs ISabelle/HOLCF: verification of general functional programs From P-logic to HOLCF

P-logic specification logic Isabelle/HOL: verification of simple functional

19 This Course 19 Scheinkriterien two big exercises (one in December, one at the end of the lecture) successful solution of the exercises and presentation in the course in groups of at most three students

20 This Course 20 Mon h: MZH 7230 Wed h: MZH 7250 Dates + Rooms Lectures and, from time to time, exercises (please bring your laptops) Web:

Formal Methods for Software Development

Formal Methods for Software Development Till Mossakowski, Lutz Schröder 03./08.11.2004 2 Monadic QuickCheck extension of QuickCheck for monadic (= imperative) programs specifications are equations between