| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Data.Connection.Property
Synopsis
- connection :: Prd a => Prd b => Conn a b -> a -> b -> Bool
- closed :: Prd a => Prd b => Conn a b -> a -> Bool
- closed' :: Prd a => Prd b => Trip a b -> a -> Bool
- kernel :: Prd a => Prd b => Conn a b -> b -> Bool
- kernel' :: Prd a => Prd b => Trip a b -> b -> Bool
- monotone :: Prd a => Prd b => Conn a b -> b -> b -> Bool
- monotone' :: Prd a => Prd b => Conn a b -> a -> a -> Bool
- idempotent_unit :: Prd a => Prd b => Conn a b -> a -> Bool
- idempotent_counit :: Prd a => Prd b => Conn a b -> b -> Bool
- projective_l :: Prd a => Prd b => Conn a b -> a -> Bool
- projective_r :: Prd a => Prd b => Conn a b -> b -> Bool
Documentation
connection :: Prd a => Prd b => Conn a b -> a -> b -> Bool Source #
\( \forall x, y : f \dashv g \Rightarrow f (x) \leq y \Leftrightarrow x \leq g (y) \)
A monotone Galois connection.
closed :: Prd a => Prd b => Conn a b -> a -> Bool Source #
\( \forall x : f \dashv g \Rightarrow x \leq g \circ f (x) \)
This is a required property.
closed' :: Prd a => Prd b => Trip a b -> a -> Bool Source #
\( \forall x : f \dashv g \Rightarrow x \leq g \circ f (x) \)
This is a required property.
kernel :: Prd a => Prd b => Conn a b -> b -> Bool Source #
\( \forall x : f \dashv g \Rightarrow f \circ g (x) \leq x \)
This is a required property.
kernel' :: Prd a => Prd b => Trip a b -> b -> Bool Source #
\( \forall x : f \dashv g \Rightarrow x \leq g \circ f (x) \)
This is a required property.
monotone :: Prd a => Prd b => Conn a b -> b -> b -> Bool Source #
\( \forall x, y : x \leq y \Rightarrow g (x) \leq g (y) \)
This is a required property.
monotone' :: Prd a => Prd b => Conn a b -> a -> a -> Bool Source #
\( \forall x, y : x \leq y \Rightarrow f (x) \leq f (y) \)
This is a required property.
idempotent_unit :: Prd a => Prd b => Conn a b -> a -> Bool Source #
\( \forall x : f \dashv g \Rightarrow unit \circ unit (x) \sim unit (x) \)
idempotent_counit :: Prd a => Prd b => Conn a b -> b -> Bool Source #
\( \forall x : f \dashv g \Rightarrow counit \circ counit (x) \sim counit (x) \)
projective_l :: Prd a => Prd b => Conn a b -> a -> Bool Source #
\( \forall x: f \dashv g \Rightarrow counit \circ f (x) \sim f (x) \)