License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	Safe
Language	Haskell2010

Data.Category.Fix

Description

Synopsis

Documentation

newtype Fix f a b Source #

Constructors

Fix (f (Fix f) a b)

Instances

Category (f (Fix f)) => Category (Fix f) Source #	`Fix f` is the fixed point category for a category combinator `f`.
Methods src :: Fix f a b -> Obj (Fix f) a Source # tgt :: Fix f a b -> Obj (Fix f) b Source # (.) :: Fix f b c -> Fix f a b -> Fix f a c Source #
HasBinaryCoproducts (f (Fix f)) => HasBinaryCoproducts (Fix f) Source #	`Fix f` inherits its (co)limits from `f (Fix f)`.
Associated Types type BinaryCoproduct (Fix f :: * -> * -> ) x y :: Source # Methods inj1 :: Obj (Fix f) x -> Obj (Fix f) y -> Fix f x (BinaryCoproduct (Fix f) x y) Source # inj2 :: Obj (Fix f) x -> Obj (Fix f) y -> Fix f y (BinaryCoproduct (Fix f) x y) Source # (\|\|\|) :: Fix f x a -> Fix f y a -> Fix f (BinaryCoproduct (Fix f) x y) a Source # (+++) :: Fix f a1 b1 -> Fix f a2 b2 -> Fix f (BinaryCoproduct (Fix f) a1 a2) (BinaryCoproduct (Fix f) b1 b2) Source #
HasBinaryProducts (f (Fix f)) => HasBinaryProducts (Fix f) Source #	`Fix f` inherits its (co)limits from `f (Fix f)`.
Associated Types type BinaryProduct (Fix f :: * -> * -> ) x y :: Source # Methods proj1 :: Obj (Fix f) x -> Obj (Fix f) y -> Fix f (BinaryProduct (Fix f) x y) x Source # proj2 :: Obj (Fix f) x -> Obj (Fix f) y -> Fix f (BinaryProduct (Fix f) x y) y Source # (&&&) :: Fix f a x -> Fix f a y -> Fix f a (BinaryProduct (Fix f) x y) Source # (***) :: Fix f a1 b1 -> Fix f a2 b2 -> Fix f (BinaryProduct (Fix f) a1 a2) (BinaryProduct (Fix f) b1 b2) Source #
HasInitialObject (f (Fix f)) => HasInitialObject (Fix f) Source #	`Fix f` inherits its (co)limits from `f (Fix f)`.
Associated Types type InitialObject (Fix f :: * -> * -> ) :: Source # Methods initialObject :: Obj (Fix f) (InitialObject (Fix f)) Source # initialize :: Obj (Fix f) a -> Fix f (InitialObject (Fix f)) a Source #
HasTerminalObject (f (Fix f)) => HasTerminalObject (Fix f) Source #	`Fix f` inherits its (co)limits from `f (Fix f)`.
Associated Types type TerminalObject (Fix f :: * -> * -> ) :: Source # Methods terminalObject :: Obj (Fix f) (TerminalObject (Fix f)) Source # terminate :: Obj (Fix f) a -> Fix f a (TerminalObject (Fix f)) Source #
CartesianClosed (f (Fix f)) => CartesianClosed (Fix f) Source #	`Fix f` inherits its exponentials from `f (Fix f)`.
Associated Types type Exponential (Fix f :: * -> * -> ) y z :: Source # Methods apply :: Obj (Fix f) y -> Obj (Fix f) z -> Fix f (BinaryProduct (Fix f) (Exponential (Fix f) y z) y) z Source # tuple :: Obj (Fix f) y -> Obj (Fix f) z -> Fix f z (Exponential (Fix f) y (BinaryProduct (Fix f) z y)) Source # (^^^) :: Fix f z1 z2 -> Fix f y2 y1 -> Fix f (Exponential (Fix f) y1 z1) (Exponential (Fix f) y2 z2) Source #
type InitialObject (Fix f) Source #
type InitialObject (Fix f) = InitialObject (f (Fix f))
type TerminalObject (Fix f) Source #
type TerminalObject (Fix f) = TerminalObject (f (Fix f))
type BinaryCoproduct (Fix f) a b Source #
type BinaryCoproduct (Fix f) a b = BinaryCoproduct (f (Fix f)) a b
type BinaryProduct (Fix f) a b Source #
type BinaryProduct (Fix f) a b = BinaryProduct (f (Fix f)) a b
type Exponential (Fix f) a b Source #
type Exponential (Fix f) a b = Exponential (f (Fix f)) a b

data Wrap f Source #

Constructors

Wrap

Instances

Category (f (Fix f)) => Functor (Wrap f) Source #	The `Wrap` functor wraps `Fix` around `f (Fix f)`.
Associated Types type Dom (Wrap f) :: * -> * -> * Source # type Cod (Wrap f) :: * -> * -> * Source # type (Wrap f) :% a :: * Source # Methods (%) :: Wrap f -> Dom (Wrap f) a b -> Cod (Wrap f) (Wrap f :% a) (Wrap f :% b) Source #
type Dom (Wrap f) Source #
type Dom (Wrap f) = f (Fix f)
type Cod (Wrap f) Source #
type Cod (Wrap f) = Fix f
type (Wrap f) :% a Source #
type (Wrap f) :% a = a

type Omega = Fix ((:>>:) Unit) Source #

Take the Omega category, add a new disctinct object, and an arrow from that object to every object in Omega, and you get Omega again.