Edit detail for SandBox Category of Graphs 2 revision 1 of 1

This seems to work if the category is defined in the same source file (i.e. same section in MathAction). The code is based on the Spad version SandBox Category of Graphs in Spad

#pile
#include "axiom.as"
--
-- First we define the general category of graphs.
--
GraphCategory(nodes:Type, edges:Type): Category == with
  source:edges->nodes
  target:edges->nodes
--
-- Now we define finite graphs as follows:
--
edges ==> Record(source:nodes,target:nodes)
FiniteGraph(nodes: BasicType):GraphCategory(nodes,edges)
  with
    new: %
    addNode: (%,List nodes) -> List nodes
    addNode: (%,nodes) -> List nodes
    addEdge: (%,nodes,nodes) -> edges
    edgeList: (%) -> List edges
    nodeList: (%) -> List nodes

  == add
    import from NonNegativeInteger

    Rep == Record(node: List nodes, edge: List edges)

    new:% == 
      n:List(nodes):=[]
      e:List(edges):=[]
      per([n,e]$Rep)

    addNode(g:%,n:nodes):List nodes == addNode(g,[n])

    addNode(g:%,n:List nodes):List nodes ==
      G:Rep:=g pretend Rep;
      if #G.node=0 then
        G.node:=n
      else
        concat!(G.node,n)
      n

    addEdge(g:%,source:nodes,target:nodes):edges ==
      G:Rep:=g pretend Rep;
      if #G.edge=0 then
        G.edge:=[[source,target]$edges]
      else
        concat!(G.edge,[[source,target]$edges])
      [source,target]$edges

    edgeList(g:%):List edges ==
      G:Rep:=g pretend Rep;
      G.edge

    nodeList(g:%):List nodes ==
      G:Rep:=g pretend Rep;
      G.node

    source(ed:edges):nodes == ed.source
    target(ed:edges):nodes == ed.target

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1676669208528368195-25px001.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      Use the system command )set compiler args to change these 
      options.
   The )library system command was not called after compilation.

)sh FiniteGraph

 FiniteGraph(S: SetCategory) is a category constructor
 Abbreviation for FiniteGraph is FGRPH 
 This constructor is not exposed in this frame.
------------------------------- Operations --------------------------------

 ?+? : (%, %) -> %                     ?=? : (%, %) -> Boolean
 addObject! : (%, S) -> %              coerce : % -> OutputForm
 flatten : DirectedGraph(%) -> %       hash : % -> SingleInteger
 initial : () -> %                     isAcyclic? : % -> Boolean
 isDirected? : () -> Boolean           isFunctional? : % -> Boolean
 kgraph : (List(S), String) -> %       latex : % -> String
 loopsArrows : % -> List(Loop)         loopsNodes : % -> List(Loop)
 looseEquals : (%, %) -> Boolean       max : % -> NonNegativeInteger
 merge : (%, %) -> %                   min : % -> NonNegativeInteger
 terminal : S -> %                     unit : (List(S), String) -> %
 ?~=? : (%, %) -> Boolean             
 addArrow! : (%, String, S, S) -> %
 addArrow! : (%, String, NonNegativeInteger, NonNegativeInteger, List(NonNegativeInteger)) -> %
 addArrow! : (%, String, NonNegativeInteger, NonNegativeInteger) -> %
 addArrow! : (%, Record(name: String,arrType: NonNegativeInteger,fromOb: NonNegativeInteger,toOb: NonNegativeInteger,xOffset: Integer,yOffset: Integer,map: List(NonNegativeInteger))) -> %
 addObject! : (%, Record(value: S,posX: NonNegativeInteger,posY: NonNegativeInteger)) -> %
 adjacencyMatrix : % -> Matrix(NonNegativeInteger)
 arrowName : (%, NonNegativeInteger, NonNegativeInteger) -> String
 arrowsFromArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 arrowsFromNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 arrowsToArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 arrowsToNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 createWidth : NonNegativeInteger -> NonNegativeInteger
 createX : (NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger
 createY : (NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger
 cycleClosed : (List(S), String) -> %
 cycleOpen : (List(S), String) -> %
 deepDiagramSvg : (String, %, Boolean) -> Void
 diagramHeight : % -> NonNegativeInteger
 diagramSvg : (String, %, Boolean) -> Void
 diagramWidth : % -> NonNegativeInteger
 diagramsSvg : (String, List(%), Boolean) -> Void
 distance : (%, NonNegativeInteger, NonNegativeInteger) -> Integer
 distanceMatrix : % -> Matrix(Integer)
 getArrowIndex : (%, NonNegativeInteger, NonNegativeInteger) -> NonNegativeInteger
 getArrows : % -> List(Record(name: String,arrType: NonNegativeInteger,fromOb: NonNegativeInteger,toOb: NonNegativeInteger,xOffset: Integer,yOffset: Integer,map: List(NonNegativeInteger)))
 getVertexIndex : (%, S) -> NonNegativeInteger
 getVertices : % -> List(Record(value: S,posX: NonNegativeInteger,posY: NonNegativeInteger))
 hashUpdate! : (HashState, %) -> HashState
 inDegree : (%, NonNegativeInteger) -> NonNegativeInteger
 incidenceMatrix : % -> Matrix(Integer)
 isDirectSuccessor? : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean
 isFixPoint? : (%, NonNegativeInteger) -> Boolean
 isGreaterThan? : (%, NonNegativeInteger, NonNegativeInteger) -> Boolean
 laplacianMatrix : % -> Matrix(Integer)
 loopsAtNode : (%, NonNegativeInteger) -> List(Loop)
 map : (%, List(NonNegativeInteger), List(S), Integer, Integer) -> %
 mapContra : (%, List(NonNegativeInteger), List(S), Integer, Integer) -> %
 max : (%, List(NonNegativeInteger)) -> NonNegativeInteger
 min : (%, List(NonNegativeInteger)) -> NonNegativeInteger
 nodeFromArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 nodeFromNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 nodeToArrow : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 nodeToNode : (%, NonNegativeInteger) -> List(NonNegativeInteger)
 outDegree : (%, NonNegativeInteger) -> NonNegativeInteger
 routeArrows : (%, NonNegativeInteger, NonNegativeInteger) -> List(NonNegativeInteger)
 routeNodes : (%, NonNegativeInteger, NonNegativeInteger) -> List(NonNegativeInteger)
 spanningForestArrow : % -> List(Tree(Integer))
 spanningForestNode : % -> List(Tree(Integer))
 spanningTreeArrow : (%, NonNegativeInteger) -> Tree(Integer)
 spanningTreeNode : (%, NonNegativeInteger) -> Tree(Integer)
 subdiagramSvg : (Scene(SCartesian(2)), %, Boolean, Boolean) -> Void

Example 1: create a simple finite graph:

g:FiniteGraph(INT)

   FiniteGraph(Integer) is a category, not a domain, and declarations 
      require domains.