Re: [Haskell-cafe] A commutative diagram conjecture about applicative functors

2007-12-31 Thread Isaac Dupree
Twan van Laarhoven wrote: Robin Green wrote: I am proving various statements relating to applicative functors, using the Coq proof assistant (I am considering only Coq terms, which always terminate so you don't have to worry about _|_). However, I'm not sure how to go about proving a certain

Re: [Haskell-cafe] A commutative diagram conjecture about applicative functors

2007-12-31 Thread Twan van Laarhoven
Isaac Dupree wrote: Unfortunately, I get puzzling type errors if I annotate either one of them with their type (e.g. (Applicative f) = f (a - b) - f a - f (Int, b) ) in an expression. The very answer doesn't seem to typecheck. :t \f x - fmap ((,) (0::Int)) (f * x) :: (Applicative f) = f (a1

Re: [Haskell-cafe] A commutative diagram conjecture about applicative functors

2007-12-31 Thread Isaac Dupree
Twan van Laarhoven wrote: Isaac Dupree wrote: Unfortunately, I get puzzling type errors if I annotate either one of them with their type (e.g. (Applicative f) = f (a - b) - f a - f (Int, b) ) in an expression. The very answer doesn't seem to typecheck. :t \f x - fmap ((,) (0::Int)) (f * x)

[Haskell-cafe] A commutative diagram conjecture about applicative functors

2007-12-30 Thread Robin Green
I am proving various statements relating to applicative functors, using the Coq proof assistant (I am considering only Coq terms, which always terminate so you don't have to worry about _|_). However, I'm not sure how to go about proving a certain conjecture, which, translated back into Haskell

Re: [Haskell-cafe] A commutative diagram conjecture about applicative functors

2007-12-30 Thread Twan van Laarhoven
Robin Green wrote: I am proving various statements relating to applicative functors, using the Coq proof assistant (I am considering only Coq terms, which always terminate so you don't have to worry about _|_). However, I'm not sure how to go about proving a certain conjecture, which,