## Heterogeneous development graphs and heterogeneous borrowing

### Till Mossakowski

To appear at Foundations of Software Science and Computation Structures (FOSSACS02), Grenoble, France, 6-14 April, 2002

## Abstract

Development graphs are a tool for dealing with structured specifications in a formal program development in order to ease the management of change and reusing proofs. Often, different aspects of a software system have to be specified in different logics, since the construction of a huge logic covering all needed features would be too complex to be feasible. Therefore, we introduce {\em heterogeneous development graphs} as a means to cope with heterogeneous specifications. We cover both the semantics and the proof theory of heterogeneous development graphs A proof calculus can be obtained either by combining proof calculi for the individual logics, or by representing these in some universal'' logic like higher-order logic in a coherent way and then borrowing'' its calculus for the heterogeneous language. Last but not least, we sketch how these results can also be applied to programming languages.

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