Differential interaction nets

T. Ehrhard, L. Regnier
2006 Theoretical Computer Science  
We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the of course and the why not modalities of linear logic, which is completely similar to the symmetry between the tensor and par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong
more » ... n. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus.
doi:10.1016/j.tcs.2006.08.003 fatcat:fok6l6fct5hcnmikal4gtpukou