libretto-lambda
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libretto-lambda/libretto.lambda/InversiveSemigroupalCategory

InversiveSemigroupalCategory

libretto.lambda.InversiveSemigroupalCategory
trait InversiveSemigroupalCategory[->[_, _], |*|[_, _], -[_]] extends ClosedSymmetricSemigroupalCategory[->, |*|, [x, y] =>> -[x] |*| y]

Attributes

Graph
Supertypes
trait ClosedSymmetricSemigroupalCategory[->, |*|, [x, y] =>> -[x] |*| y]
trait ClosedSemigroupalCategory[->, |*|, [x, y] =>> -[x] |*| y]
trait SemigroupalCategory[->, |*|]
trait Category[->]
trait Semigroupoid[->]
class Object
trait Matchable
class Any
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Known subtypes
trait InversiveMonoidalCategory[->, |*|, One, -]

Members list

Value members

Abstract methods

def contrapositive[A, B](f: A -> B): -[B] -> -[A]
def die[A]: -[-[A]] -> A

Double inversion elimination.

Double inversion elimination.

Attributes

def dii[A]: A -> -[-[A]]

Double inversion introduction.

Double inversion introduction.

Attributes

def portLR[A, B, C](f: (A |*| B) -> C): A -> (-[B] |*| C)
def portRL[A, B, C](f: A -> (B |*| C)): (A |*| -[B]) -> C

Concrete methods

override def curry[A, B, C](f: (A |*| B) -> C): A -> (-[B] |*| C)

Attributes

Definition Classes
override def eval[A, B]: (-[A] |*| B |*| A) -> B

Attributes

Definition Classes

Inherited methods

def fst[X, Y, Z](f: X -> Y): (X |*| Z) -> (Y |*| Z)

Attributes

Inherited from:
SemigroupalCategory
def ix[A, B, C]: (A |*| B |*| C) -> (A |*| C |*| B)

Attributes

Inherited from:
SymmetricSemigroupalCategory
def ixi[A, B, C, D]: (A |*| B |*| (C |*| D)) -> (A |*| C |*| (B |*| D))

Attributes

Inherited from:
SymmetricSemigroupalCategory
def snd[X, Y, Z](f: Y -> Z): (X |*| Y) -> (X |*| Z)

Attributes

Inherited from:
SemigroupalCategory
def uncurry[A, B, C](f: A -> (-[B] |*| C)): (A |*| B) -> C

Attributes

Inherited from:
ClosedSemigroupalCategory
def xi[A, B, C]: (A |*| (B |*| C)) -> (B |*| (A |*| C))

Attributes

Inherited from:
SymmetricSemigroupalCategory

Inherited and Abstract methods

def andThen[A, B, C](f: A -> B, g: B -> C): A -> C

Attributes

Inherited from:
Semigroupoid
def assocLR[A, B, C]: (A |*| B |*| C) -> (A |*| (B |*| C))

Attributes

Inherited from:
SemigroupalCategory
def assocRL[A, B, C]: (A |*| (B |*| C)) -> (A |*| B |*| C)

Attributes

Inherited from:
SemigroupalCategory
def id[A]: A -> A

Attributes

Inherited from:
Category
def par[A1, A2, B1, B2](f1: A1 -> B1, f2: A2 -> B2): (A1 |*| A2) -> (B1 |*| B2)

Attributes

Inherited from:
SemigroupalCategory
def swap[A, B]: (A |*| B) -> (B |*| A)

Attributes

Inherited from:
SymmetricSemigroupalCategory

Extensions

Inherited extensions

extension [A, B](f: A -> B)
def >[C](g: B -> C): A -> C

Attributes

Inherited from:
Semigroupoid
def from[Z](using Z =:= A): Z -> B

Attributes

Inherited from:
Semigroupoid
def to[C](using B =:= C): A -> C

Attributes

Inherited from:
Semigroupoid
extension [A, B](f: A -> B)
def inFst[X]: (A |*| X) -> (B |*| X)

Attributes

Inherited from:
SemigroupalCategory
def inSnd[X]: (X |*| A) -> (X |*| B)

Attributes

Inherited from:
SemigroupalCategory
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