Find all triangles

triangles.egi

(define $points
  {[3 1] [4 5] [7 7] [8 1] [1 9] [3 8] [3 1]})

(define $on-a-line?
  (match-lambda [[integer integer] [integer integer] [integer integer]]
    {[[[$x1 $y1] [$x2 $y2] [$x3 $y3]]
      (eq? (abs (* (- y2 y1) (- x3 x1)))
           (abs (* (- y3 y1) (- x2 x1))))]}))

; Enumerate triangles
(match-all points (list [integer integer])
  [<join _ <cons $p1
    <join _ <cons $p2
     <join _ <cons (& ^?(on-a-line? p1 p2 $) $p3)
       _>>>>>>
   [p1 p2 p3]])
;=>{[[3 1] [4 5] [7 7]] [[3 1] [4 5] [8 1]] [[3 1] [7 7] [8 1]] [[4 5] [7 7] [8 1]] [[3 1] [7 7] [1 9]] [[3 1] [8 1] [1 9]] [[4 5] [7 7] [1 9]] [[4 5] [8 1] [1 9]] [[7 7] [8 1] [1 9]] [[3 1] [4 5] [3 8]] [[3 1] [7 7] [3 8]] [[3 1] [8 1] [3 8]] [[3 1] [1 9] [3 8]] [[4 5] [7 7] [3 8]] [[4 5] [8 1] [3 8]] [[4 5] [1 9] [3 8]] [[7 7] [8 1] [3 8]] [[7 7] [1 9] [3 8]] [[8 1] [1 9] [3 8]] [[4 5] [7 7] [3 1]] [[4 5] [8 1] [3 1]] [[4 5] [1 9] [3 1]] [[4 5] [3 8] [3 1]] [[7 7] [8 1] [3 1]] [[7 7] [1 9] [3 1]] [[7 7] [3 8] [3 1]] [[8 1] [1 9] [3 1]] [[8 1] [3 8] [3 1]] [[1 9] [3 8] [3 1]]}

; Enumerate tiplets of points on a line
(match-all points (list [integer integer])
  [<join _ <cons $p1
    <join _ <cons $p2
     <join _ <cons (& ?(on-a-line? p1 p2 $) $p3)
       _>>>>>>
   [p1 p2 p3]])
;=>{[[3 1] [4 5] [1 9]] [[3 1] [4 5] [3 1]] [[3 1] [7 7] [3 1]] [[3 1] [8 1] [3 1]] [[3 1] [1 9] [3 1]] [[3 1] [3 8] [3 1]]}