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Making instance of Applicative
Orphaned instances in HaskellEq instance has some strange comparisonsWhy can I not make String an instance of a typeclass?Good examples of Not a Functor/Functor/Applicative/Monad?Confused by the meaning of the 'Alternative' type class and its relationship to other type classesinstance Alternative ZipList in Haskell?How to test the homomorphism law of an Applicative instance?Partially applying a type in a type constructorInstance applicative on datatype `List`Why is this applicative instance unlawful?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty height:90px;width:728px;box-sizing:border-box;
Still not a hundred percent shure how to make instances of the more complex types. Have this:
data CouldBe a = Is a | Lost deriving (Show, Ord)
Made an instance of Functor, using Maybe as an example:
instance Functor CouldBe where
fmap f (Is x) = Is (f x)
fmap f Lost = Lost
For doing something like this:
tupleCouldBe :: CouldBe a -> CouldBe b -> CouldBe (a,b)
tupleCouldBe x y = (,) <$> x <*> y
CouldBe needs to be an instance of Applicative, but how would you go about that? Sure I can look it up and copy it, but I want to learn the process behind it and finally end up with the instance declaration of CouldBe.
haskell typeclass applicative
asked Mar 9 at 9:06
MadderoteMadderote
350211
|
show 1 more comment
Still not a hundred percent shure how to make instances of the more complex types. Have this:
data CouldBe a = Is a | Lost deriving (Show, Ord)
Made an instance of Functor, using Maybe as an example:
instance Functor CouldBe where
fmap f (Is x) = Is (f x)
fmap f Lost = Lost
For doing something like this:
tupleCouldBe :: CouldBe a -> CouldBe b -> CouldBe (a,b)
tupleCouldBe x y = (,) <$> x <*> y
CouldBe needs to be an instance of Applicative, but how would you go about that? Sure I can look it up and copy it, but I want to learn the process behind it and finally end up with the instance declaration of CouldBe.
haskell typeclass applicative
asked Mar 9 at 9:06
MadderoteMadderote
350211
2
Start by writing down the functions you need to define to makeCouldBean instance ofApplicative, with their type signatures (specialised toCouldBe). You should find there's really only one sensible solution if you let the types guide you. And yourFunctorinstance shows you how to handleLost.
– Robin Zigmond
Mar 9 at 9:15
4
Pattern match as much as possible and then construct the results in the only way that type checks. This works often.
– luqui
Mar 9 at 9:17
2
Logically I'd be definingpureand<*>, correct? I think pure should be simple likepure a = Is a, but doesn't<*>require more variants...
– Madderote
Mar 9 at 9:28
1
Try pattern matching on each side of<*>; this should give four different cases. Then use @RobinZigmond's advice and 'follow the types' for each case. One other thing which could help is typed holes: if you don't know what to put somewhere, use an underscore_, and GHC will give you the type which should be there. They're incredibly useful in these sort of 'follow the types' situations.
– bradrn
Mar 9 at 9:44
1
Note that yourCouldBeis isomorphic to Haskell's built-inMaybetype, so any time you want to know how to write an instance for your type, you can just look how the corresponding instance forMaybeis written.
– Joseph Sible
Mar 9 at 16:43
|
show 1 more comment
Still not a hundred percent shure how to make instances of the more complex types. Have this:
data CouldBe a = Is a | Lost deriving (Show, Ord)
Made an instance of Functor, using Maybe as an example:
instance Functor CouldBe where
fmap f (Is x) = Is (f x)
fmap f Lost = Lost
For doing something like this:
tupleCouldBe :: CouldBe a -> CouldBe b -> CouldBe (a,b)
tupleCouldBe x y = (,) <$> x <*> y
CouldBe needs to be an instance of Applicative, but how would you go about that? Sure I can look it up and copy it, but I want to learn the process behind it and finally end up with the instance declaration of CouldBe.
haskell typeclass applicative
asked Mar 9 at 9:06
MadderoteMadderote
350211
Still not a hundred percent shure how to make instances of the more complex types. Have this:
data CouldBe a = Is a | Lost deriving (Show, Ord)
Made an instance of Functor, using Maybe as an example:
instance Functor CouldBe where
fmap f (Is x) = Is (f x)
fmap f Lost = Lost
For doing something like this:
tupleCouldBe :: CouldBe a -> CouldBe b -> CouldBe (a,b)
tupleCouldBe x y = (,) <$> x <*> y
CouldBe needs to be an instance of Applicative, but how would you go about that? Sure I can look it up and copy it, but I want to learn the process behind it and finally end up with the instance declaration of CouldBe.
haskell typeclass applicative
haskell typeclass applicative
asked Mar 9 at 9:06
MadderoteMadderote
350211
asked Mar 9 at 9:06
MadderoteMadderote
350211
asked Mar 9 at 9:06
MadderoteMadderote
350211
asked Mar 9 at 9:06
MadderoteMadderote
350211
asked Mar 9 at 9:06
MadderoteMadderote
350211
350211
2
Start by writing down the functions you need to define to makeCouldBean instance ofApplicative, with their type signatures (specialised toCouldBe). You should find there's really only one sensible solution if you let the types guide you. And yourFunctorinstance shows you how to handleLost.
– Robin Zigmond
Mar 9 at 9:15
4
Pattern match as much as possible and then construct the results in the only way that type checks. This works often.
– luqui
Mar 9 at 9:17
2
Logically I'd be definingpureand<*>, correct? I think pure should be simple likepure a = Is a, but doesn't<*>require more variants...
– Madderote
Mar 9 at 9:28
1
Try pattern matching on each side of<*>; this should give four different cases. Then use @RobinZigmond's advice and 'follow the types' for each case. One other thing which could help is typed holes: if you don't know what to put somewhere, use an underscore_, and GHC will give you the type which should be there. They're incredibly useful in these sort of 'follow the types' situations.
– bradrn
Mar 9 at 9:44
1
Note that yourCouldBeis isomorphic to Haskell's built-inMaybetype, so any time you want to know how to write an instance for your type, you can just look how the corresponding instance forMaybeis written.
– Joseph Sible
Mar 9 at 16:43
|
show 1 more comment
2
Start by writing down the functions you need to define to makeCouldBean instance ofApplicative, with their type signatures (specialised toCouldBe). You should find there's really only one sensible solution if you let the types guide you. And yourFunctorinstance shows you how to handleLost.
– Robin Zigmond
Mar 9 at 9:15
4
Pattern match as much as possible and then construct the results in the only way that type checks. This works often.
– luqui
Mar 9 at 9:17
2
Logically I'd be definingpureand<*>, correct? I think pure should be simple likepure a = Is a, but doesn't<*>require more variants...
– Madderote
Mar 9 at 9:28
1
Try pattern matching on each side of<*>; this should give four different cases. Then use @RobinZigmond's advice and 'follow the types' for each case. One other thing which could help is typed holes: if you don't know what to put somewhere, use an underscore_, and GHC will give you the type which should be there. They're incredibly useful in these sort of 'follow the types' situations.
– bradrn
Mar 9 at 9:44
1
Note that yourCouldBeis isomorphic to Haskell's built-inMaybetype, so any time you want to know how to write an instance for your type, you can just look how the corresponding instance forMaybeis written.
– Joseph Sible
Mar 9 at 16:43
2
2
Start by writing down the functions you need to define to make
CouldBe an instance of Applicative, with their type signatures (specialised to CouldBe). You should find there's really only one sensible solution if you let the types guide you. And your Functor instance shows you how to handle Lost.– Robin Zigmond
Mar 9 at 9:15
Start by writing down the functions you need to define to make
CouldBe an instance of Applicative, with their type signatures (specialised to CouldBe). You should find there's really only one sensible solution if you let the types guide you. And your Functor instance shows you how to handle Lost.– Robin Zigmond
Mar 9 at 9:15
4
4
Pattern match as much as possible and then construct the results in the only way that type checks. This works often.
– luqui
Mar 9 at 9:17
Pattern match as much as possible and then construct the results in the only way that type checks. This works often.
– luqui
Mar 9 at 9:17
2
2
Logically I'd be defining
pure and <*>, correct? I think pure should be simple like pure a = Is a, but doesn't <*> require more variants...– Madderote
Mar 9 at 9:28
Logically I'd be defining
pure and <*>, correct? I think pure should be simple like pure a = Is a, but doesn't <*> require more variants...– Madderote
Mar 9 at 9:28
1
1
Try pattern matching on each side of
<*>; this should give four different cases. Then use @RobinZigmond's advice and 'follow the types' for each case. One other thing which could help is typed holes: if you don't know what to put somewhere, use an underscore _, and GHC will give you the type which should be there. They're incredibly useful in these sort of 'follow the types' situations.– bradrn
Mar 9 at 9:44
Try pattern matching on each side of
<*>; this should give four different cases. Then use @RobinZigmond's advice and 'follow the types' for each case. One other thing which could help is typed holes: if you don't know what to put somewhere, use an underscore _, and GHC will give you the type which should be there. They're incredibly useful in these sort of 'follow the types' situations.– bradrn
Mar 9 at 9:44
1
1
Note that your
CouldBe is isomorphic to Haskell's built-in Maybe type, so any time you want to know how to write an instance for your type, you can just look how the corresponding instance for Maybe is written.– Joseph Sible
Mar 9 at 16:43
Note that your
CouldBe is isomorphic to Haskell's built-in Maybe type, so any time you want to know how to write an instance for your type, you can just look how the corresponding instance for Maybe is written.– Joseph Sible
Mar 9 at 16:43
|
show 1 more comment
1 Answer
1
active
oldest
votes
You just write it out, following the types:
instance Applicative CouldBe where
-
Minimal complete definition:
pure, ((<*>)
pure a = fa
where
fa = ....
liftA2 abc fa fb = fc
where
fc = ....According to
data CouldBe a = Is a | Lost
our toolset is
Is :: a -> CouldBe a
Lost :: CouldBe a
but we can also use pattern matching, e.g.
couldBe is lost (Is a) = is a
couldBe is lost (Lost) = lost
couldBe :: ? -> ? -> CouldBe a -> b
couldBe :: ? -> b -> CouldBe a -> b
couldBe :: (a -> b) -> b -> CouldBe a -> b
So,
-- pure :: a -> f a
pure :: a -> CouldBe a
matches up with
Is :: a -> CouldBe a
so we define
pure a = Is a
Then, for liftA2, we follow the data cases:
-- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
-- liftA2 :: (a -> b -> c) -> CouldBe a -> CouldBe b -> CouldBe c
liftA2 abc Lost _ = ...
liftA2 abc _ Lost = ...
liftA2 abc (Is a) (Is b) = fc
where
c = abc a b
fc = .... -- create an `f c` from `c`:
-- do we have a `c -> CouldBe c` ?
-- do we have an `a -> CouldBe a` ? (it's the same type)
But in the first two cases we don't have an a or a b; so we have to come up with a CouldBe c out of nothing. We do have this tool in our toolset as well.
Having completed all the missing pieces, we can substitute the expressions directly into the definitions, eliminating all the unneeded interim values / variables.
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
add a comment |
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You just write it out, following the types:
instance Applicative CouldBe where
-
Minimal complete definition:
pure, ((<*>)
pure a = fa
where
fa = ....
liftA2 abc fa fb = fc
where
fc = ....According to
data CouldBe a = Is a | Lost
our toolset is
Is :: a -> CouldBe a
Lost :: CouldBe a
but we can also use pattern matching, e.g.
couldBe is lost (Is a) = is a
couldBe is lost (Lost) = lost
couldBe :: ? -> ? -> CouldBe a -> b
couldBe :: ? -> b -> CouldBe a -> b
couldBe :: (a -> b) -> b -> CouldBe a -> b
So,
-- pure :: a -> f a
pure :: a -> CouldBe a
matches up with
Is :: a -> CouldBe a
so we define
pure a = Is a
Then, for liftA2, we follow the data cases:
-- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
-- liftA2 :: (a -> b -> c) -> CouldBe a -> CouldBe b -> CouldBe c
liftA2 abc Lost _ = ...
liftA2 abc _ Lost = ...
liftA2 abc (Is a) (Is b) = fc
where
c = abc a b
fc = .... -- create an `f c` from `c`:
-- do we have a `c -> CouldBe c` ?
-- do we have an `a -> CouldBe a` ? (it's the same type)
But in the first two cases we don't have an a or a b; so we have to come up with a CouldBe c out of nothing. We do have this tool in our toolset as well.
Having completed all the missing pieces, we can substitute the expressions directly into the definitions, eliminating all the unneeded interim values / variables.
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
add a comment |
You just write it out, following the types:
instance Applicative CouldBe where
-
Minimal complete definition:
pure, ((<*>)
pure a = fa
where
fa = ....
liftA2 abc fa fb = fc
where
fc = ....According to
data CouldBe a = Is a | Lost
our toolset is
Is :: a -> CouldBe a
Lost :: CouldBe a
but we can also use pattern matching, e.g.
couldBe is lost (Is a) = is a
couldBe is lost (Lost) = lost
couldBe :: ? -> ? -> CouldBe a -> b
couldBe :: ? -> b -> CouldBe a -> b
couldBe :: (a -> b) -> b -> CouldBe a -> b
So,
-- pure :: a -> f a
pure :: a -> CouldBe a
matches up with
Is :: a -> CouldBe a
so we define
pure a = Is a
Then, for liftA2, we follow the data cases:
-- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
-- liftA2 :: (a -> b -> c) -> CouldBe a -> CouldBe b -> CouldBe c
liftA2 abc Lost _ = ...
liftA2 abc _ Lost = ...
liftA2 abc (Is a) (Is b) = fc
where
c = abc a b
fc = .... -- create an `f c` from `c`:
-- do we have a `c -> CouldBe c` ?
-- do we have an `a -> CouldBe a` ? (it's the same type)
But in the first two cases we don't have an a or a b; so we have to come up with a CouldBe c out of nothing. We do have this tool in our toolset as well.
Having completed all the missing pieces, we can substitute the expressions directly into the definitions, eliminating all the unneeded interim values / variables.
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
add a comment |
You just write it out, following the types:
instance Applicative CouldBe where
-
Minimal complete definition:
pure, ((<*>)
pure a = fa
where
fa = ....
liftA2 abc fa fb = fc
where
fc = ....According to
data CouldBe a = Is a | Lost
our toolset is
Is :: a -> CouldBe a
Lost :: CouldBe a
but we can also use pattern matching, e.g.
couldBe is lost (Is a) = is a
couldBe is lost (Lost) = lost
couldBe :: ? -> ? -> CouldBe a -> b
couldBe :: ? -> b -> CouldBe a -> b
couldBe :: (a -> b) -> b -> CouldBe a -> b
So,
-- pure :: a -> f a
pure :: a -> CouldBe a
matches up with
Is :: a -> CouldBe a
so we define
pure a = Is a
Then, for liftA2, we follow the data cases:
-- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
-- liftA2 :: (a -> b -> c) -> CouldBe a -> CouldBe b -> CouldBe c
liftA2 abc Lost _ = ...
liftA2 abc _ Lost = ...
liftA2 abc (Is a) (Is b) = fc
where
c = abc a b
fc = .... -- create an `f c` from `c`:
-- do we have a `c -> CouldBe c` ?
-- do we have an `a -> CouldBe a` ? (it's the same type)
But in the first two cases we don't have an a or a b; so we have to come up with a CouldBe c out of nothing. We do have this tool in our toolset as well.
Having completed all the missing pieces, we can substitute the expressions directly into the definitions, eliminating all the unneeded interim values / variables.
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
You just write it out, following the types:
instance Applicative CouldBe where
-
Minimal complete definition:
pure, ((<*>)
pure a = fa
where
fa = ....
liftA2 abc fa fb = fc
where
fc = ....According to
data CouldBe a = Is a | Lost
our toolset is
Is :: a -> CouldBe a
Lost :: CouldBe a
but we can also use pattern matching, e.g.
couldBe is lost (Is a) = is a
couldBe is lost (Lost) = lost
couldBe :: ? -> ? -> CouldBe a -> b
couldBe :: ? -> b -> CouldBe a -> b
couldBe :: (a -> b) -> b -> CouldBe a -> b
So,
-- pure :: a -> f a
pure :: a -> CouldBe a
matches up with
Is :: a -> CouldBe a
so we define
pure a = Is a
Then, for liftA2, we follow the data cases:
-- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
-- liftA2 :: (a -> b -> c) -> CouldBe a -> CouldBe b -> CouldBe c
liftA2 abc Lost _ = ...
liftA2 abc _ Lost = ...
liftA2 abc (Is a) (Is b) = fc
where
c = abc a b
fc = .... -- create an `f c` from `c`:
-- do we have a `c -> CouldBe c` ?
-- do we have an `a -> CouldBe a` ? (it's the same type)
But in the first two cases we don't have an a or a b; so we have to come up with a CouldBe c out of nothing. We do have this tool in our toolset as well.
Having completed all the missing pieces, we can substitute the expressions directly into the definitions, eliminating all the unneeded interim values / variables.
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
edited Mar 11 at 10:46
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
answered Mar 9 at 10:39
Will NessWill Ness
47k469127
47k469127
add a comment |
add a comment |
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2
Start by writing down the functions you need to define to make
CouldBean instance ofApplicative, with their type signatures (specialised toCouldBe). You should find there's really only one sensible solution if you let the types guide you. And yourFunctorinstance shows you how to handleLost.– Robin Zigmond
Mar 9 at 9:15
4
Pattern match as much as possible and then construct the results in the only way that type checks. This works often.
– luqui
Mar 9 at 9:17
2
Logically I'd be defining
pureand<*>, correct? I think pure should be simple likepure a = Is a, but doesn't<*>require more variants...– Madderote
Mar 9 at 9:28
1
Try pattern matching on each side of
<*>; this should give four different cases. Then use @RobinZigmond's advice and 'follow the types' for each case. One other thing which could help is typed holes: if you don't know what to put somewhere, use an underscore_, and GHC will give you the type which should be there. They're incredibly useful in these sort of 'follow the types' situations.– bradrn
Mar 9 at 9:44
1
Note that your
CouldBeis isomorphic to Haskell's built-inMaybetype, so any time you want to know how to write an instance for your type, you can just look how the corresponding instance forMaybeis written.– Joseph Sible
Mar 9 at 16:43