Finding a “free theorem”











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How do I derive the free theorem for the type:



data F a = C1 Nat | C2 Bool Nat a


where Nat is simply data Nat = Z | S Nat?



In principle, this can be answered by the Haskell 'free-theorems' package, but it's too elderly to compile under any GHC version I can reasonably install.






haskell free-theorem







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    Free theorems are usually associated to polymorphic function types. Otherwise, IIRC, you get a trivial theorem, e.g. fmap f = fmap f where fmap :: (a->b)-> F a -> F b is the functor instance.
    – chi
    Nov 17 at 14:39















up vote
2
down vote

favorite
1












How do I derive the free theorem for the type:



data F a = C1 Nat | C2 Bool Nat a


where Nat is simply data Nat = Z | S Nat?



In principle, this can be answered by the Haskell 'free-theorems' package, but it's too elderly to compile under any GHC version I can reasonably install.






haskell free-theorem







share|improve this question


















  • 2




    Free theorems are usually associated to polymorphic function types. Otherwise, IIRC, you get a trivial theorem, e.g. fmap f = fmap f where fmap :: (a->b)-> F a -> F b is the functor instance.
    – chi
    Nov 17 at 14:39













up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





How do I derive the free theorem for the type:



data F a = C1 Nat | C2 Bool Nat a


where Nat is simply data Nat = Z | S Nat?



In principle, this can be answered by the Haskell 'free-theorems' package, but it's too elderly to compile under any GHC version I can reasonably install.






haskell free-theorem







share|improve this question













How do I derive the free theorem for the type:



data F a = C1 Nat | C2 Bool Nat a


where Nat is simply data Nat = Z | S Nat?



In principle, this can be answered by the Haskell 'free-theorems' package, but it's too elderly to compile under any GHC version I can reasonably install.






haskell free-theorem




haskell free-theorem






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asked Nov 17 at 13:58









NietzscheanAI

424415




424415








  • 2




    Free theorems are usually associated to polymorphic function types. Otherwise, IIRC, you get a trivial theorem, e.g. fmap f = fmap f where fmap :: (a->b)-> F a -> F b is the functor instance.
    – chi
    Nov 17 at 14:39














  • 2




    Free theorems are usually associated to polymorphic function types. Otherwise, IIRC, you get a trivial theorem, e.g. fmap f = fmap f where fmap :: (a->b)-> F a -> F b is the functor instance.
    – chi
    Nov 17 at 14:39








2




2




Free theorems are usually associated to polymorphic function types. Otherwise, IIRC, you get a trivial theorem, e.g. fmap f = fmap f where fmap :: (a->b)-> F a -> F b is the functor instance.
– chi
Nov 17 at 14:39




Free theorems are usually associated to polymorphic function types. Otherwise, IIRC, you get a trivial theorem, e.g. fmap f = fmap f where fmap :: (a->b)-> F a -> F b is the functor instance.
– chi
Nov 17 at 14:39












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There is an online generator for free theorems at, and when it was down a little while ago I created an alternative UI that runs completely in the browser (using reflex-dom).



But the deeper problem is that free theorems, in the sense of these packages, are properties of polymorphic functions, so in order to answer your question, you have to give a function (like map) whose free theorem you are interested in.






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    up vote
    4
    down vote













    There is an online generator for free theorems at, and when it was down a little while ago I created an alternative UI that runs completely in the browser (using reflex-dom).



    But the deeper problem is that free theorems, in the sense of these packages, are properties of polymorphic functions, so in order to answer your question, you have to give a function (like map) whose free theorem you are interested in.






    share|improve this answer

























      up vote
      4
      down vote













      There is an online generator for free theorems at, and when it was down a little while ago I created an alternative UI that runs completely in the browser (using reflex-dom).



      But the deeper problem is that free theorems, in the sense of these packages, are properties of polymorphic functions, so in order to answer your question, you have to give a function (like map) whose free theorem you are interested in.






      share|improve this answer























        up vote
        4
        down vote










        up vote
        4
        down vote









        There is an online generator for free theorems at, and when it was down a little while ago I created an alternative UI that runs completely in the browser (using reflex-dom).



        But the deeper problem is that free theorems, in the sense of these packages, are properties of polymorphic functions, so in order to answer your question, you have to give a function (like map) whose free theorem you are interested in.






        share|improve this answer












        There is an online generator for free theorems at, and when it was down a little while ago I created an alternative UI that runs completely in the browser (using reflex-dom).



        But the deeper problem is that free theorems, in the sense of these packages, are properties of polymorphic functions, so in order to answer your question, you have to give a function (like map) whose free theorem you are interested in.







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered Nov 17 at 14:40









        Joachim Breitner

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