FiniteBiCPO SΒΆ

logic.spad line 1687 [edit on github]

Holds a complete set together with a structure to codify the partial order. For more documentation see: http://www.euclideanspace.com/prog/scratchpad/mycode/discrete/logic/index.htm Date Created: Aug 2015 Basic Operations: Related packages: UserDefinedPartialOrdering in setorder.spad Related categories: PartialOrder in catdef.spad Related Domains: DirectedGraph in graph.spad Also See: AMS Classifications:

+: (%, %) -> %

from FiniteGraph S

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> 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, NonNegativeInteger, NonNegativeInteger) -> %

from FiniteGraph S

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

from FiniteGraph S

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

from FiniteGraph S

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

from FiniteGraph S

addObject!: (%, S) -> %

from Poset 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

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

from FiniteGraph S

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

from FiniteGraph S

diagramWidth: % -> NonNegativeInteger

from FiniteGraph S

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

from FiniteGraph S

distanceMatrix: % -> Matrix Integer

from FiniteGraph S

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

from Poset S

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

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

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

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

from Poset S

incidenceMatrix: % -> Matrix Integer

from FiniteGraph S

inDegree: (%, NonNegativeInteger) -> NonNegativeInteger

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

isDirected?: () -> Boolean

from FiniteGraph S

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

BasicType

BiCPO S

CoDcpo S

CoercibleTo OutputForm

Dcpo S

FiniteGraph S

Poset S

Preorder S

SetCategory