Contents of Report

[Data of Report]

	Abstract	.... 2
1	Introduction	.... 2
2	The Language of QPC	.... 3
2.1	Term of QPC2	.... 3
2.2	Type of QPC2	.... 4
2.3	Formula of QPC2	.... 5
2.4	Scheme	.... 5
3	The Rules of QPC2	.... 6
3.1	Rules on Scheme Calculus	.... 6
3.2	Type Rules	.... 7
3.3	Logical Rules	.... 9
3.4	Some Properties	.... 10
4	Program Extraction	.... 11
4.1	qpc-realizability	.... 11
4.2	Properties of qpc-realizability	.... 12
4.3	Optimization	.... 16
5	Writing Specifications	.... 16
5.1	Map Function	.... 16
5.2	Sorting program	.... 18
5.3	Use Defined Rules of Inference	.... 18
6	Examples of Program Extraction	.... 19
7	Discussion and Conclusion	.... 21
	Acknowledgement	.... 22
	References	.... 22
	End	.... 23

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