The Key monad: Type-safe unconstrained dynamic typing
Paper in proceeding, 2016

We present a small extension to Haskell called the Key monad. With the Key monad, unique keys of different types can be created and can be tested for equality. When two keys are equal, we also obtain a concrete proof that their types are equal. This gives us a form of dynamic typing, without the need for Typeable constraints. We show that our extension allows us to safely do things we could not otherwise do: it allows us to implement the ST monad (inefficiently), to implement an embedded form of arrow notation, and to translate parametric HOAS to typed de Bruijn indices, among others. Although strongly related to the ST monad, the Key monad is simpler and might be easier to prove safe. We do not provide such a proof of the safety of the Key monad, but we note that, surprisingly, a full proof of the safety of the ST monad also remains elusive to this day. Hence, another reason for studying the Key monad is that a safety proof for it might be a stepping stone towards a safety proof of the ST monad.


Arrow notation

Parametric HOAS

Higher-order state

Functional programming

ST monad


Atze van der Ploeg

Chalmers, Computer Science and Engineering (Chalmers), Software Technology (Chalmers)

Koen Claessen

Software Technology, Group A

Pablo Buiras

Harvard University

Haskell 2016 - Proceedings of the 9th International Symposium on Haskell, co-located with ICFP 2016

9781450344340 (ISBN)

9th International Symposium on Haskell, Haskell 2016, co-located with ICFP 2016
Nara, Japan,

Subject Categories

Embedded Systems

Computer Science



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