Dcpo S¶
logic.spad line 1556 [edit on github]
S: SetCategory
Directed-complete partial order, partial order that is guaranteed to have a join of any two elements. For more documentation see: http://www.euclideanspace.com/prog/scratchpad/mycode/discrete/logic/index.htm
- +: (%, %) -> %
from FiniteGraph S
- 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
- 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
- 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
- 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
- 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
- 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
returns the join of ‘a’ and
'b'In this version of join nodes are represented as index values. Not every poset will have a join but DCPO will.
- 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
- 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
- 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
- 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
- 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
- zetaMatrix: % -> IncidenceAlgebra(Integer, S)
from Poset S
Poset S
Preorder S