;;;
;;; graph.egi
;;;

(define $graph
  (lambda [$a]
    (multiset (nodeInfo a))))

(define $nodeInfo
  (lambda [$a]
    (algebraic-data-matcher
      {<node a (multiset a) (multiset a)>})))

(define $hamilton-cycle
  (pattern-function [$a]
    (& $g
       <cons <node (& a_1 $h_1) <cons (& a_2 $h_2) _> _>
             (loop $i (between 3 (size g))
               <cons <node ,h_(- i 1) <cons (& a_i $h_i) _> _>
                     ...>
               <cons <node ,h_(size g) <cons ,h_1 _> _>
                     <nil>>)>)))

(define $hamilton-path
  (pattern-function [$a]
    (& $g
       <cons <node (& a_1 $h_1) <cons (& a_2 $h_2) _> _>
             (loop $i (between 3 (size g))
               <cons <node ,h_(- i 1) <cons (& a_i $h_i) _> _>
                     ...>
               <cons <node ,h_(size g) _ _>
                     <nil>>)>)))

(define $hamilton-path2
  (pattern-function [$a]
    (& $g
       (let {[$n (size g)]}
         <cons <node (& a_1 $h_1) <cons (& a_2 $h_2) _> _>
               (loop $i (between 3 n)
                 <cons <node ,h_(- i 1) <cons (& a_i $h_i) _> _>
                       ...>
                 <cons <node ,h_n _ _>
                       <nil>>)>)
       )))

(define $all-paths
  (pattern-function [$s $e $p $rest]
    (| <cons <node (& s p_1) <cons (& e p_2) _> _> rest>
       <cons <node (& s p_1)  <cons (& p_2 $h_2) _> _>
          (loop $i (from 2) ;; TEMPORARY
            <cons <node ,h_(- i 1) <cons (& p_i $h_i) _> _>
                  ...>
            rest)>)))