Summary: 2 Lehrstuhl für Informatik 2
Modellierung und Verifikation von Software
Semantics and Verification of Software WS2011/12
Exercise 5 (Hand in until 06.12.2011)
aaAOR Priv.-Doz. Dr. Thomas Noll Christina Jansen, Sabrina von Styp
Exercise 1 (Continuity): (1+2 Points)
Show that the following propositions hold:
1. The identity function idD on a cpo D is continuous.
2. Let f : D E and g : E F be continuous functions on cpos D, E, F. Then their composition g f :
D F is continuous.
Exercise 2 (Fixpoint Approximation): (4 Points)
C z := 0; while x > 0 do (x := x - 1; z := z + y)
in analogy to the factorial example 7.9 given in lecture 7.
Exercise 3 (Three-Valued Denotation Semantics): (1+1+2 Points)
Define a three-valued denotational semantics for the WHILE language as follows:
1. Assume that at the beginning of a programm evaluation, all variables have unknown values. To model this,
extend the variable domain by , and let with (x) = for all x Var be the initial state of all
programs. Define A · in analogy to Definition 5.1 and evaluate 3 + x and 0 x for .
2. In addition to true and false, a third truth-value ? is needed to express uncertainty about the result of a