By effect

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By effect describe a way how one program leads to its result. If a program is executed by effect, we emphasize on the change between initial and final state.


  • numpy routines such as sin, cos, tan, etc, we does not focus on detailed implementation of the routines but focus on the effect of the routines.
  • A Möbius transformations, we emphasize on the effect even they can be implemented by a flow

Leibniz theorem

The fundamental theorem of calculus by Leibniz, is an example to relate a "program" by effect with the other "program" by trace.