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(#mod self org.aiddl.common.math.graph)

(#req EVAL org.aiddl.eval.namespace)
(#nms nms-basic basic-ops@EVAL)
(#nms nms-type  type-ops@EVAL)
(#nms nms-logic logic-ops@EVAL)
(#nms nms-collection collection-ops@EVAL)


(#type Node term)
(#type UndirectedEdge (set-of ^$Node constraint:(lambda ?X (= 2 (size ?X)))))
(#type DirectedEdge (sig [^$Node ^$Node]))
(#type Edge (union [^$UndirectedEdge ^$DirectedEdge]))

(#type (TypedGraph ?NodeType)
       (dict [V:(set-of ?NodeType) E:(set-of ^$Edge)]
        constraint:(lambda ?X 
          (let [?V:(get-key V ?X) ?E:(get-key E ?X)]
              (forall ?e ?E (contains-all ?V ?e) )))))

(#type (TypedDiGraph ?NodeType)
       (dict [V:(set-of ?NodeType) E:(set-of ^$DirectedEdge)]
        constraint:(lambda ?X 
          (let [?V:(get-key V ?X) ?E:(get-key E ?X)]
              (forall (?u ?v) ?E (and (contains ?V ?u) (contains ?V ?v)))))))

(#type Graph ($TypedGraph ^$Node))
(#type DiGraph ($TypedDiGraph ^$Node))

(#type Path (list-of ^$Node))
(#type WeightMap (col-of (typed-kvp ^$Edge:^numerical)))
(#type DistanceMap (union {(enum {NIL}) (col-of (typed-kvp ^$Node:^numerical))}))
(#type PredecessorMap (union {(enum {NIL}) (col-of (typed-kvp ^$Node:^$Node))}))

(#type sssp-out (dict [distance:^$DistanceMap predecessor:^$PredecessorMap]))

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;; Interfaces
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(#interface single-source-shortest-path (
  uri    :  org.aiddl.common.math.graph.single-source-shortest-path
  input  : (sig [^$DiGraph (union [^fun-ref ^$WeightMap]) ^$Node])
  output : ^$sssp-out
))

(#interface depth-first-search (
  uri    : org.aiddl.common.math.graph.depth-first-search
  input  : ^$DiGraph
  output : (dict [
    pi:(set-of (typed-kvp ^$Node:^$Node))
    distances:(set-of (typed-kvp ^$Node:^numerical))
    finish-times:(set-of (typed-kvp ^$Node:^numerical))
    components:(set-of (set-of ^$Node)) ]
  )
))

(#interface strongly-connected-components (
  uri    : org.aiddl.common.math.graph.scc-computer
  input  : ^$DiGraph
  output : (set-of (set-of ^$Node)) 
))

(#interface transpose (
  uri    : org.aiddl.common.math.graph.transpose
  input  : ^$DiGraph
  output : ^$DiGraph
))

(#interface path-extractor (
  uri    : org.aiddl.common.math.graph.path-extractor
  input  : ^$PredecessorMap
  output : ^$Path
))