Revisions to What is the mathematical name for Haskell's Alternative Functor

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edited Jan 9, 2017 at 13:17

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Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation of type f a -> f a -> f a and empty is the identity of type f a. Uncurrying the type of <|>, we get $$f\ a \times f\ a \rightarrow f\ a$$ and empty can be equivalently defined to have type $$1 \rightarrow f\ a$$ In the Haskell definition, the type variable a is universally quantified. As far as I know, this translates to the requirement that they are natural in a.

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation of type f a -> f a -> f a and empty is the identity of type f a. Uncurrying the type of <|>, we get $$f\ a \times f\ a \rightarrow f\ a$$ and empty can be equivalently defined to have type $$1 \rightarrow f\ a$$ In the Haskell definition, a is universally quantified. As far as I know, this translates to the requirement that they are natural in a.

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation of type f a -> f a -> f a and empty is the identity of type f a. Uncurrying the type of <|>, we get $$f\ a \times f\ a \rightarrow f\ a$$ and empty can be equivalently defined to have type $$1 \rightarrow f\ a$$ In the Haskell definition, the type variable a is universally quantified. As far as I know, this translates to the requirement that they are natural in a.

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edited Jan 9, 2017 at 13:11

xuh

89
3

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation of type f a -> f a -> f a and empty is the identity of type f a.

Edit 2: Uncurrying the type of <|> and, we get $$f\ a \times f\ a \rightarrow f\ a$$ and empty can be equivalently defined to have type $$1 \rightarrow f\ a$$ In the Haskell definition, a is universally quantified. As far as I know, this translates to the requirement that they are natural in a.

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation and empty is the identity.

Edit 2: <|> and empty are natural in a.

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation of type f a -> f a -> f a and empty is the identity of type f a. Uncurrying the type of <|>, we get $$f\ a \times f\ a \rightarrow f\ a$$ and empty can be equivalently defined to have type $$1 \rightarrow f\ a$$ In the Haskell definition, a is universally quantified. As far as I know, this translates to the requirement that they are natural in a.

added 192 characters in body

Source Link

edited Jan 9, 2017 at 13:01

xuh

89
3

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation and empty is the identity.

Edit 2: <|> and empty are natural in a.

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation and empty is the identity.

Haskell's Applicative Functor is called Lax Monoidal Functor in mathematics.

What is Haskell's Alternative Functor called in mathematics?

Recall that Haskell's Alternative Functor is defined as follows:

class Applicative f => Alternative f where -- | The identity of '<|>' empty :: f a -- | An associative binary operation (<|>) :: f a -> f a -> f a

Edit: In other words, an Alternative Functor f is an Applicative Functor such that for every type a, f a is a monoid, where <|> is the binary operation and empty is the identity.

Edit 2: <|> and empty are natural in a.