Safe Haskell	None
Language	Haskell2010

PlutusTx.Lattice

Synopsis

class JoinSemiLattice a where
- (\/) :: a -> a -> a
class MeetSemiLattice a where
- (/\) :: a -> a -> a
type Lattice a = ( JoinSemiLattice a, MeetSemiLattice a)
class JoinSemiLattice a => BoundedJoinSemiLattice a where
- bottom :: a
class MeetSemiLattice a => BoundedMeetSemiLattice a where
- top :: a
type BoundedLattice a = ( BoundedJoinSemiLattice a, BoundedMeetSemiLattice a)
newtype Join a = Join a
newtype Meet a = Meet a

Documentation

class JoinSemiLattice a where Source #

A join semi-lattice, i.e. a partially ordered set equipped with a binary operation (\/) .

Note that the mathematical definition would require an ordering constraint - we omit that so we can define instances for e.g. (->) .

Methods

(\/) :: a -> a -> a Source #

Instances

Instances details

JoinSemiLattice Bool Source #
Instance details Defined in PlutusTx.Lattice Methods (\/) :: Bool -> Bool -> Bool Source #
JoinSemiLattice b => JoinSemiLattice (a -> b) Source #
Instance details Defined in PlutusTx.Lattice Methods (\/) :: (a -> b) -> (a -> b) -> a -> b Source #
( JoinSemiLattice a, JoinSemiLattice b) => JoinSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods (\/) :: (a, b) -> (a, b) -> (a, b) Source #

class MeetSemiLattice a where Source #

A meet semi-lattice, i.e. a partially ordered set equipped with a binary operation (/\) .

Note that the mathematical definition would require an ordering constraint - we omit that so we can define instances for e.g. (->) .

Methods

(/\) :: a -> a -> a Source #

Instances

Instances details

MeetSemiLattice Bool Source #
Instance details Defined in PlutusTx.Lattice Methods (/\) :: Bool -> Bool -> Bool Source #
MeetSemiLattice b => MeetSemiLattice (a -> b) Source #
Instance details Defined in PlutusTx.Lattice Methods (/\) :: (a -> b) -> (a -> b) -> a -> b Source #
( MeetSemiLattice a, MeetSemiLattice b) => MeetSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods (/\) :: (a, b) -> (a, b) -> (a, b) Source #

type Lattice a = ( JoinSemiLattice a, MeetSemiLattice a) Source #

A lattice.

class JoinSemiLattice a => BoundedJoinSemiLattice a where Source #

A bounded join semi-lattice, i.e. a join semi-lattice augmented with a distinguished element bottom which is the unit of (\/) .

Methods

bottom :: a Source #

Instances

Instances details

BoundedJoinSemiLattice Bool Source #
Instance details Defined in PlutusTx.Lattice Methods bottom :: Bool Source #
BoundedJoinSemiLattice b => BoundedJoinSemiLattice (a -> b) Source #
Instance details Defined in PlutusTx.Lattice Methods bottom :: a -> b Source #
( BoundedJoinSemiLattice a, BoundedJoinSemiLattice b) => BoundedJoinSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods bottom :: (a, b) Source #

class MeetSemiLattice a => BoundedMeetSemiLattice a where Source #

A bounded meet semi-lattice, i.e. a meet semi-lattice augmented with a distinguished element top which is the unit of (/\) .

Methods

top :: a Source #

Instances

Instances details

BoundedMeetSemiLattice Bool Source #
Instance details Defined in PlutusTx.Lattice Methods top :: Bool Source #
BoundedMeetSemiLattice b => BoundedMeetSemiLattice (a -> b) Source #
Instance details Defined in PlutusTx.Lattice Methods top :: a -> b Source #
( BoundedMeetSemiLattice a, BoundedMeetSemiLattice b) => BoundedMeetSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods top :: (a, b) Source #

type BoundedLattice a = ( BoundedJoinSemiLattice a, BoundedMeetSemiLattice a) Source #

A bounded lattice.

newtype Join a Source #

A wrapper witnessing that a join semi-lattice is a monoid with (\/) and bottom .

Constructors

Join a

Instances

Instances details

JoinSemiLattice a => Semigroup ( Join a) Source #
Instance details Defined in PlutusTx.Lattice Methods (<>) :: Join a -> Join a -> Join a Source #
BoundedJoinSemiLattice a => Monoid ( Join a) Source #
Instance details Defined in PlutusTx.Lattice Methods mempty :: Join a Source #

newtype Meet a Source #

A wrapper witnessing that a meet semi-lattice is a monoid with (/\) and top .

Constructors

Meet a

Instances

Instances details

MeetSemiLattice a => Semigroup ( Meet a) Source #
Instance details Defined in PlutusTx.Lattice Methods (<>) :: Meet a -> Meet a -> Meet a Source #
BoundedMeetSemiLattice a => Monoid ( Meet a) Source #
Instance details Defined in PlutusTx.Lattice Methods mempty :: Meet a Source #