FiniteBiCPO(S)

logic.spad line 1688 [edit on github]

• S : SetCategory

Holds a complete set together with a structure to codify the partial order. For more documentation see: htm

+ : (%, %) -> %

from FiniteGraph(S)

= : (%, %) -> Boolean

from BasicType

addArrow! : (%, NonNegativeInteger, NonNegativeInteger) -> %

from Poset(S)

addArrow! : (%, Record(name : String, arrType : NonNegativeInteger, fromOb : NonNegativeInteger, toOb : NonNegativeInteger, xOffset : Integer, yOffset : Integer, map : List(NonNegativeInteger))) -> %

from FiniteGraph(S)

addArrow! : (%, String, S, S) -> %

from FiniteGraph(S)

addArrow! : (%, String, NonNegativeInteger, NonNegativeInteger) -> %

from FiniteGraph(S)

addArrow! : (%, String, NonNegativeInteger, NonNegativeInteger, List(NonNegativeInteger)) -> %

from FiniteGraph(S)

addObject! : (%, S) -> %

from Poset(S)

addObject! : (%, Record(value : S, posX : NonNegativeInteger, posY : NonNegativeInteger)) -> %

from FiniteGraph(S)

adjacencyMatrix : % -> Matrix(NonNegativeInteger)

from FiniteGraph(S)

arrowName : (%, NonNegativeInteger, NonNegativeInteger) -> String

from FiniteGraph(S)

arrowsFromArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

arrowsFromNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

arrowsToArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

arrowsToNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

completeReflexivity : % -> %

from Poset(S)

completeTransitivity : % -> %

from Poset(S)

coverMatrix : % -> IncidenceAlgebra(Integer, S)

from Poset(S)

createWidth : NonNegativeInteger -> NonNegativeInteger

from FiniteGraph(S)

createX : (NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

createY : (NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

cycleClosed : (List(S), String) -> %

from FiniteGraph(S)

cycleOpen : (List(S), String) -> %

from FiniteGraph(S)

deepDiagramSvg : (String, %, Boolean) -> Void

from FiniteGraph(S)

diagramHeight : % -> NonNegativeInteger

from FiniteGraph(S)

diagramSvg : (String, %, Boolean) -> Void

from FiniteGraph(S)

diagramWidth : % -> NonNegativeInteger

from FiniteGraph(S)

diagramsSvg : (String, List(%), Boolean) -> Void

from FiniteGraph(S)

distance : (%, NonNegativeInteger, NonNegativeInteger) -> Integer

from FiniteGraph(S)

distanceMatrix : % -> Matrix(Integer)

from FiniteGraph(S)

finitePoset : (List(S), List(List(Boolean))) -> %

from Poset(S)

finitePoset : (List(S), Mapping(Boolean, S, S)) -> %

from Poset(S)

flatten : DirectedGraph(%) -> %

from FiniteGraph(S)

getArr : % -> List(List(Boolean))

from Poset(S)

getArrowIndex : (%, NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

getArrows : % -> List(Record(name : String, arrType : NonNegativeInteger, fromOb : NonNegativeInteger, toOb : NonNegativeInteger, xOffset : Integer, yOffset : Integer, map : List(NonNegativeInteger)))

from FiniteGraph(S)

getVert : % -> List(S)

from Poset(S)

getVertexIndex : (%, S) -> NonNegativeInteger

from FiniteGraph(S)

getVertices : % -> List(Record(value : S, posX : NonNegativeInteger, posY : NonNegativeInteger))

from FiniteGraph(S)

glb : (%, List(NonNegativeInteger)) -> Union(NonNegativeInteger, "failed")

from Poset(S)

implies : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean

from Poset(S)

inDegree : (%, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

incidenceMatrix : % -> Matrix(Integer)

from FiniteGraph(S)

indexToObject : (%, NonNegativeInteger) -> S

from Poset(S)

initial : () -> %

from FiniteGraph(S)

isAcyclic? : % -> Boolean

from FiniteGraph(S)

isAntiChain? : % -> Boolean

from Poset(S)

isAntisymmetric? : % -> Boolean

from Poset(S)

isChain? : % -> Boolean

from Poset(S)

isDirectSuccessor? : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean

from FiniteGraph(S)

isDirected? : () -> Boolean

from FiniteGraph(S)

isFixPoint? : (%, NonNegativeInteger) -> Boolean

from FiniteGraph(S)

isFunctional? : % -> Boolean

from FiniteGraph(S)

isGreaterThan? : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean

from FiniteGraph(S)

join : (%, NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from Dcpo(S)

joinIfCan : (%, List(NonNegativeInteger)) -> Union(NonNegativeInteger, "failed")

from Poset(S)

joinIfCan : (%, NonNegativeInteger, NonNegativeInteger) -> Union(NonNegativeInteger, "failed")

from Poset(S)

kgraph : (List(S), String) -> %

from FiniteGraph(S)

laplacianMatrix : % -> Matrix(Integer)

from FiniteGraph(S)

latex : % -> String

from SetCategory

le : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean

from Preorder(S)

loopsArrows : % -> List(Loop)

from FiniteGraph(S)

loopsAtNode : (%, NonNegativeInteger) -> List(Loop)

from FiniteGraph(S)

loopsNodes : % -> List(Loop)

from FiniteGraph(S)

looseEquals : (%, %) -> Boolean

from FiniteGraph(S)

lowerSet : % -> %

from Poset(S)

lub : (%, List(NonNegativeInteger)) -> Union(NonNegativeInteger, "failed")

from Poset(S)

map : (%, List(NonNegativeInteger), List(S), Integer, Integer) -> %

from FiniteGraph(S)

mapContra : (%, List(NonNegativeInteger), List(S), Integer, Integer) -> %

from FiniteGraph(S)

max : % -> NonNegativeInteger

from FiniteGraph(S)

max : (%, List(NonNegativeInteger)) -> NonNegativeInteger

from FiniteGraph(S)

meet : (%, NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger

from CoDcpo(S)

meetIfCan : (%, List(NonNegativeInteger)) -> Union(NonNegativeInteger, "failed")

from Poset(S)

meetIfCan : (%, NonNegativeInteger, NonNegativeInteger) -> Union(NonNegativeInteger, "failed")

from Poset(S)

merge : (%, %) -> %

from FiniteGraph(S)

min : % -> NonNegativeInteger

from FiniteGraph(S)

min : (%, List(NonNegativeInteger)) -> NonNegativeInteger

from FiniteGraph(S)

moebius : % -> IncidenceAlgebra(Integer, S)

from Poset(S)

nodeFromArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

nodeFromNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

nodeToArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

nodeToNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

objectToIndex : (%, S) -> NonNegativeInteger

from Poset(S)

opposite : % -> %

from Poset(S)

outDegree : (%, NonNegativeInteger) -> NonNegativeInteger

from FiniteGraph(S)

powerSetStructure : S -> %

from Poset(S)

routeArrows : (%, NonNegativeInteger, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

routeNodes : (%, NonNegativeInteger, NonNegativeInteger) -> List(NonNegativeInteger)

from FiniteGraph(S)

setArr : (%, List(List(Boolean))) -> Void

from Poset(S)

setVert : (%, List(S)) -> Void

from Poset(S)

spanningForestArrow : % -> List(Tree(Integer))

from FiniteGraph(S)

spanningForestNode : % -> List(Tree(Integer))

from FiniteGraph(S)

spanningTreeArrow : (%, NonNegativeInteger) -> Tree(Integer)

from FiniteGraph(S)

spanningTreeNode : (%, NonNegativeInteger) -> Tree(Integer)

from FiniteGraph(S)

subdiagramSvg : (Scene(SCartesian(2)), %, Boolean, Boolean) -> Void

from FiniteGraph(S)

terminal : S -> %

from FiniteGraph(S)

unit : (List(S), String) -> %

from FiniteGraph(S)

upperSet : % -> %

from Poset(S)

zetaMatrix : % -> IncidenceAlgebra(Integer, S)

from Poset(S)

~= : (%, %) -> Boolean

from BasicType

SetCategory

FiniteGraph(S)

Poset(S)

Dcpo(S)

CoDcpo(S)

CoercibleTo(OutputForm)

Preorder(S)

BiCPO(S)

BasicType