Safe Haskell	Safe-Inferred
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 a, JoinSemiLattice b) ⇒ JoinSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods (\/) ∷ (a, b) → (a, b) → (a, b) Source #
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 a, MeetSemiLattice b) ⇒ MeetSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods (/\) ∷ (a, b) → (a, b) → (a, b) Source #
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 a, BoundedJoinSemiLattice b) ⇒ BoundedJoinSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods bottom ∷ (a, b) Source #
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 a, BoundedMeetSemiLattice b) ⇒ BoundedMeetSemiLattice (a, b) Source #
Instance details Defined in PlutusTx.Lattice Methods top ∷ (a, b) Source #
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

BoundedJoinSemiLattice a ⇒ Monoid (Join a) Source #
Instance details Defined in PlutusTx.Lattice Methods mempty ∷ Join a Source #
JoinSemiLattice a ⇒ Semigroup (Join a) Source #
Instance details Defined in PlutusTx.Lattice Methods (<>) ∷ Join a → Join a → 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

BoundedMeetSemiLattice a ⇒ Monoid (Meet a) Source #
Instance details Defined in PlutusTx.Lattice Methods mempty ∷ Meet a Source #
MeetSemiLattice a ⇒ Semigroup (Meet a) Source #
Instance details Defined in PlutusTx.Lattice Methods (<>) ∷ Meet a → Meet a → Meet a Source #