1: //Declare some types
  2: type Country = 
  3:     |Germany    |Italy      |England    |Spain
  4:     |France     |Portugal   |Turkey     |Scotland
  5:     |Ukraine
  6: 
  7: type Group = |A|B|C|D|E|F|G|H
  8: 
  9: type Place = |First |Second
 10: 
 11: type Team = {
 12:     name : string;
 13:     country : Country;
 14:     group : Group;
 15:     place: Place;
 16: }
 17: 
 18: //Declare all teams
 19: let PSG = {name ="Paris Saint-Germain"; country=France; group=A;place=First}
 20: let Porto = {name ="FC Porto"; country=Portugal; group=A; place=Second}
 21: 
 22: let Schalke = {name ="FC Schalke 04"; country=Germany; group=B;place=First}
 23: let Arsenal = {name ="Arcenal FC"; country=England; group=B; place=Second}
 24: 
 25: let Malaga = {name ="Malaga CF"; country=Spain; group=C;place=First}
 26: let Milan = {name ="AC Miland"; country=Italy; group=C; place=Second}
 27: 
 28: let Dortmund = {name ="Borussia Dortmund"; country=Germany; group=D;place=First}
 29: let Real = {name ="Real Madrid CF"; country=Spain; group=D; place=Second}
 30: 
 31: let Juventus  = {name ="Juventus"; country=Italy; group=E;place=First}
 32: let Shakhtar = {name ="FC Shakhtar Donetsk"; country=Ukraine; group=E; place=Second}
 33: 
 34: let Bayern  = {name ="FC Bayern München"; country=Germany; group=F;place=First}
 35: let Valencia = {name ="Valemcia CF"; country=Spain; group=F; place=Second}
 36: 
 37: let Barcelona  = {name ="FC Barcelona"; country=Spain; group=G;place=First}
 38: let Celtic = {name ="Celtic FC"; country=Scotland; group=G; place=Second}
 39: 
 40: let ManchesterU  = {name ="Manchester United FC"; country=England; group=H;place=First}
 41: let Galatasaray = {name ="Galatasaray AŞ"; country=Turkey; group=H; place=Second}
 42: 
 43: //And put them in a list
 44: let allTeams = [PSG; Porto; Schalke; Arsenal; Malaga; Milan; Dortmund; Real; Juventus;
 45:     Shakhtar; Bayern; Valencia; Barcelona;Celtic;ManchesterU; Galatasaray;]
 46: //Partition the list in group winners and runner ups
 47: let groupWinners, runnerUps = 
 48:     let isGroupWinner team  = (team.place = First)
 49:     List.partition isGroupWinner allTeams;
 50: //I stole this function from stack overflow to generate all permutaions of a list
 51: let rec perms = 
 52:     let distrib e L =
 53:         let rec aux pre post = 
 54:             seq {
 55:                 match post with
 56:                 | [] -> yield (L @ [e])
 57:                 | h::t -> yield (List.rev pre @ [e] @ post)
 58:                           yield! aux (h::pre) t 
 59:             }
 60:         aux [] L
 61:     function 
 62:     | [] -> Seq.singleton []
 63:     | h::t -> Seq.collect (distrib h) (perms t)
 64: 
 65: //Create all draws by using all permutations of the runner ups and pairing
 66: //them with an unchanged list of gruop winners
 67: let getDraws runnerUps  groupWinners = 
 68:     [for perm in (perms runnerUps) do
 69:         yield List.zip perm groupWinners
 70:     ]
 71: 
 72: let draws = getDraws runnerUps  groupWinners
 73: 
 74: //fnction to check if a match is valid
 75: let isValidMatch (footballMatch: Team*Team) = 
 76:     match footballMatch with
 77:     |(teamA,teamB) when teamA.group = teamB.group -> false
 78:     |(teamA,teamB) when teamA.country = teamB.country  ->false
 79:     |_ -> true
 80: //checks if all matches in a draw are valid
 81: let isValidDraw (draw: (Team*Team) list)  = 
 82:     draw
 83:     |>List.map isValidMatch 
 84:     |>List.fold (&&) true
 85: //filter the draws so we only keep the valid ones
 86: let validDraws = List.filter isValidDraw draws
 87: //Calculates the probability of a match by looking how many of the draws
 88: //contain the match and dividing by the total amount of matches
 89: let matchProbability (footballMatch:Team*Team) =  
 90:     let occurences = 
 91:         validDraws 
 92:         |> List.filter (List.exists (fun (x:Team*Team) -> x= footballMatch)) 
 93:         |> List.length
 94: 
 95:     (float occurences)*100.0/(float <| List.length validDraws)
 96: //Gets a list of tupples where each tuple consist of the match and it respective probability           
 97: let getProbabilities runnerUps groupWinners = 
 98:     [for runnerUp in runnerUps do
 99:         for adversary in groupWinners do
100:         let footbalMatch = (runnerUp,adversary)
101:         yield (footbalMatch, matchProbability footbalMatch)
102:     ]
103: 
104: let probabilities = getProbabilities runnerUps groupWinners
105: 
106: //a function to print a probability
107: let printProbability probabilities = 
108:     match probabilities with
109:     |((teamA,teamB),probability) -> printfn "%s  \t  %s   \t  %F%% " teamA.name teamB.name probability
110: //print all probabilities
111: List.iter printProbability probabilities