Either returns with its parameters, reversed, but Maybe did not. That's my main question. On Sat, Sep 18, 2021 at 5:43 PM Francesco Ariis wrote:

Il 18 settembre 2021 alle 17:30 Galaxy Being ha scritto:

...

...

:t Just True Just True :: Maybe Bool :t Left True Left True :: Either Bool b :t Right False Right False :: Either a Bool

What am I being told here? It seems are both straightforward parameterized types, but Maybe doesn't give me a type parameter back, while Either does, and in different order, different names (a becomes b; b becomes a) depending on which variable I invoke. What deeper lore am I not seeing here?

When you ask the type of

λ> :t Just True

the interpreter *knows* that that `Maybe` is not just a `Maybe a` (so type constructor and its type parameter) but the /concrete/ type `Maybe Bool`. This would not be the case if we did

λ> :t Nothing Nothing :: Maybe a

Same story with `Either`. Each of the two data constructors (`Left` and `Right`) let the interpreter infer just *one* of the type parameters (the `a` and `b` in `Either a b`). Does this answer your question? _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

-- ⨽ Lawrence Bottorff Grand Marais, MN, USA borgauf@gmail.com

I hope the wizards will forgive a down-to-earth analogy. Either a b is a knapsack with two pockets, the one on the Left (which must hold an "a") and the one on the Right (which must hold a "b"). But you can only use one pocket at a time. So when there's a specific case of Either a b such as Left True, all that can be concluded is that this is a case of an Either whose left pocket must be able to handle a Bool; there's not enough information to know what could have been put in the Right pocket. So only the left-pocket type ("a") can be replaced with something specific. Similarly, for a specific case of Right False, it's clear that the right pocket holds a value of type Bool (replacing the general "b"), but there's no information to identify what type might be in the left pocket. So it remains unspecified. I hope that helps. -jn- On Sat, Sep 18, 2021 at 9:21 PM Galaxy Being wrote:

Either returns with its parameters, reversed, but Maybe did not. That's my main question.

On Sat, Sep 18, 2021 at 5:43 PM Francesco Ariis wrote:

...

Il 18 settembre 2021 alle 17:30 Galaxy Being ha scritto:

...

...

:t Just True Just True :: Maybe Bool :t Left True Left True :: Either Bool b :t Right False Right False :: Either a Bool

What am I being told here? It seems are both straightforward parameterized types, but Maybe doesn't give me a type parameter back, while Either does, and in different order, different names (a becomes b; b becomes a) depending on which variable I invoke. What deeper lore am I not seeing here?

When you ask the type of

λ> :t Just True

the interpreter *knows* that that `Maybe` is not just a `Maybe a` (so type constructor and its type parameter) but the /concrete/ type `Maybe Bool`. This would not be the case if we did

λ> :t Nothing Nothing :: Maybe a

Same story with `Either`. Each of the two data constructors (`Left` and `Right`) let the interpreter infer just *one* of the type parameters (the `a` and `b` in `Either a b`). Does this answer your question? _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

-- ⨽ Lawrence Bottorff Grand Marais, MN, USA borgauf@gmail.com _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

are both straightforward parameterized types, but Maybe doesn't give me a type parameter back, while Either does, and in different order, different names (a becomes b; b becomes a) depending on which variable I invoke.

Try these diagnostics: --- Diagnostic 1 Given that the type of "const" is "a -> b -> a" and the type of "True" is "Bool": :t const const :: a -> b -> a :t True True :: Bool What do you expect the type of "const True" to be? :t const True const True :: - If you answer "b -> Bool", you are correct, so you may be confused by the data type definition syntax (see below). - If you answer something else, you may be missing some basic understanding of the type system. --- Diagnostic 2 Consider this case: :t id id :: a -> a :t (id, id) (id, id) :: (a1 -> a1, a2 -> a2) - If you think that the type of "(id, id)" should be "(a -> a, a -> a)", you may be unaware of the implicit universal quantifiers. --- If you are confused by the data type definition syntax: data Either a b = Left a | Right b then, consider the GADT (generalized algebraic data type) definition syntax for saying the same thing: data Either a b where Left :: a -> Either a b Right :: b -> Either a b The problem becomes less confusing: The GADT definition syntax is screaming that "Left" is a function like "id", "const", etc. --- If you're still unsure, try thinking aloud here: Write your expectations and why you think so (your thought process, what steps you took to arrive at your expectations).