2 research outputs found
Proving Type Class Laws for Haskell
Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way
to ensure both to the programmer and the compiler that a set of functions are
defined for a specific data type. All instances of such type classes are
expected to behave in a certain way and satisfy laws associated with the
respective class. These are however typically just stated in comments and as
such, there is no real way to enforce that they hold. In this paper we describe
a system which allows the user to write down type class laws which are then
automatically instantiated and sent to an inductive theorem prover when
declaring a new instance of a type class.Comment: Presented at the Symposium for Trends in Functional Programming, 201
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 of specifications or abstract
data types (ADTs). Functors and monads are at the core of many applications of
functional programming. This raises the question of what useful ADTs for
verified functors and monads could look like. The functorial map of many
important monads preserves extensional equality. For instance, if are extensionally equal, that is, , then and are also
extensionally equal. This suggests that preservation of extensional equality
could be a useful principle in verified generic programming. We explore this
possibility with a minimalist approach: we deal with (the lack of) extensional
equality in Martin-L\"of's intensional type theories without extending the
theories or using full-fledged setoids. Perhaps surprisingly, this minimal
approach turns out to be extremely useful. It allows one to derive simple
generic proofs of monadic laws but also verified, generic results in dynamical
systems and control theory. In turn, these results avoid tedious code
duplication and ad-hoc proofs. Thus, our work is a contribution towards
pragmatic, verified generic programming.Comment: Manuscript ID: JFP-2020-003