Extensional equality preservation and verified generic programming

In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets specifications or abstract (ADTs). Functors and monads are at core many applications functional programming. This raises question what useful ADTs for functors could look like. The functorial map important preserves extensional equality. For instance, if $f, g : A \rightarrow B$ extensionally equal, that is, $\forall x \in A, \ f = x$, then $map List g$ also equal. suggests preservation equality be a principle in We explore this possibility with minimalist approach: we deal (the lack of) Martin-L\"of's intensional type theories without extending using full-fledged setoids. Perhaps surprisingly, minimal approach turns out extremely useful. It allows derive simple proofs monadic laws verified, results dynamical systems control theory. turn, these avoid tedious code duplication ad-hoc proofs. Thus, our work is contribution towards pragmatic,