1. Type checker may be wrong – Lean and the Curry-Howard correspondence (max-amb.github.io)
Contents The Curry-Howard correspondence How do proof assistants use the CH correspondence A theorem A proof of the theorem The type checker Limitations of the type checker Mathematical consequences (and proof) Your type checker maybe wrong Conclusion When writing code many of us have been saved time and time again by type checkers: the useful piece of software that ensures you aren’t adding a string to an integer 1 or returning a reference to a value instead of the owned value. However, while useful, and sometimes annoying, it seems that the humble type checker has limited capability beyond its noble task of saving our asses…
Type checkers play a critical role in programming by preventing common errors, but they aren’t infallible. This piece discusses the limitations of type checkers, particularly in the context of Lean and the Curry-Howard correspondence, highlighting how these tools might lead developers astray despite their benefits.
