[Haskell-cafe] working my way through Data.Type.Equality...my head hurts...

Nicholls, Mark nicholls.mark at vimn.com
Tue Jan 13 12:39:23 UTC 2015

Full code here…

Lets start at the beginning…

Ø  data a :~: b where

Ø  Refl :: a :~: a

Looks reasonable….” a :~: b” is inhabited by 1 value…of type “a :~: a”

Ø  sym :: (a :~: b) -> (b :~: a)

Ø  sym Refl = Refl

hmmm… (a :~: b) implies that a is b
so (b :~: a)

Ø  -- | Transitivity of equality

Ø  trans :: (a :~: b) -> (b :~: c) -> (a :~: c)

Ø  trans Refl Refl = Refl

Ø  -- | Type-safe cast, using propositional equality

Ø  castWith :: (a :~: b) -> a -> b

Ø  castWith Refl x = x



Ø  -- | Generalized form of type-safe cast using propositional equality

Ø  gcastWith :: (a :~: b) -> ((a ~ b) => r) -> r

Ø  gcastWith Refl x = x

I don’t even understand the signature

What does “~” mean…(it’s something that comes out in error messages when my types are all messed up)….and then there’s a “=>” going on…in the middle of a signature….I know “=>” in the context of “Num a => a -> a -> a”

What would a value of type “((a ~ b) => r)” look like?


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