14 Foundation of Programming Languages and Software Engineering: Summer Term 2010
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1 14 Foundation of Programming Languages and Software Engineering: Abstract Data Types Summer Term 2010 Robert Elsässer
2 Abstract data types Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 2
3 ADTs are special signatures Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 3
4 Examples Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 4
5 Datatypes are -Algebras Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 5
6 Implementations of the ADT for Naturals Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 6
7 Implementations of the ADT for Naturals Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 7
8 Implementations of the ADT for Integers (1) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 8
9 Implementations of the ADT for Integers (2) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 9
10 Implementations of the ADT for Integers (3) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 10
11 Fixing the Problems Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 11
12 Equivalence Classes Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 12
13 Congruence Relations Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 13
14 Syntactic Quotient Algebras Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 14
15 Equational Theory Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 15
16 Example Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 16
17 Revised Definition for ADT Implementations Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 17
18 Syntactic Implementations of ADTs Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 18
19 Proof (cont.) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 19
20 Example Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 20
21 Example Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 21
22 Example Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 22
23 Equivalence Classes for Terms Representing Integers Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 23
24 Proof Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 24
25 Equivalence Classes for Terms Representing Integers Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 25
26 Example Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 26
27 Summary Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 27
28 Richer ADTs Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 28
29 Lists Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 29
30 Lists (cont.) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 30
31 Abstract Data Types Ht Heterogeneous Signatures Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 31
32 Dealing with Partial Operations Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 32
33 Search for Representatives Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 33
34 Proof (cont.) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 34
35 Another Example Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 35
36 Arrays Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 36
37 Arrays (cont.) Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 37
38 Examples Theory 1 - Foundation of Programming Languages and Software Engineering: Abstract data types 38
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