Contents of Report

[Data of Report]

1	Introduction	.... 2
2	Program Term	.... 3
2.1	Syntax	.... 3
2.2	Operational Semantics	.... 4
2.3	Some Termination Properties on Program Term	.... 6
3	Expression of Process	.... 8
3.1	Expressions of Input and Output	.... 8
3.2	Parallelism and Nondeterminism	.... 9
3.3	Problem and Extension of Logic	.... 9
4	Logic	.... 10
4.1	Syntax	.... 10
4.2	Inference Rules	.... 13
4.3	Axiom	.... 14
5	Realizability Interpretation	.... 15
5.1	Definition of the Realizability	.... 15
5.2	Program Extraction Rules	.... 20
6	Example	.... 22
7	Acknowledgment	.... 23
8	Reference	.... 23
9	Appendix 1 Soundness	.... 24
9.1	Appendix 2 Consistency of Logic u	.... 36
9.2	Appendix 3 Proof	.... 37
9.3	Appendix 4 Program	.... 40
	End	.... 41

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