Slimmer Formal Proofs for Mathematical Libraries

Short of being able to exhaustively test all the inputs, writing a formal proof offers the highest possible confidence in the correctness of a mathematical library. This comes at a large cost though, since formal proofs require taking into account all the details, even the seemingly insignificant ones, which makes them tedious to write. This issue is compounded by the fact that the objects whose properties we need to verify (floating-point numbers) are not the ones we would like to reason about (real numbers and integers). This short paper explores some ways of reducing the overhead of formal proofs in the setting of mathematical libraries, so as to let the user focus on the details that really matter.