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Summary: 2 Lehrstuhl für Informatik 2
Modellierung und Verifikation von Software
Semantics and Verification of Software WS2011/12
Exercise 0 (Hand in until 25.10.2011)
aaAOR Priv.-Doz. Dr. Thomas Noll Christina Jansen, Sabrina von Styp
Exercise 1 (Programming Language WHILE): (1 + 1 Points)
a) Write a program using the WHILE programming language that calculates z := x div y with x,y,z Z.
b) Draw the flow diagram for the program from part a).
Exercise 2 (Evaluation Relations): (1 + 4 Points)
a) Declare a rule for the arithmetic expression a1 div a2 describing the integer division.
b) Evaluate the following arithmetic and boolean expressions using the evaluation relations. You may use your
rule defined in part a).
· a = (10 + x · y) - (z div 3) with (x) = 3, (y) = 4, (z) = 5
· b1 = (true f alse) ¬f alse
· b2 = ((4 + x) = 7) (¬(y > 5)) with (x) = 3, (y) = 7
Exercise 3 (Structural Induction): (3 Points)
Consider the structure of lists of natural numbers l with the following inductive definition:
[] Lists(N)
l Lists(N)
n :: l Lists(N)
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