#C6.txt: Feb. 11, 2013 Conway's games
#Game is a PAIR [L,R] of sets of simpler games

Help:=proc(): print(` GamesD1(k), GamesD(k) `): 
print(`RandGame(k,m), Age(G) , CanLeftWin(G), CanRightWin(G)  `):
print(`WhatKind(G)`)

end:

with(combinat):

#GamesD1(k): all the games created in day<=k
GamesD1:=proc(k) local L,R,S:
option remember:


if k=0 then
 RETURN({[{},{}] }):
fi:

S:=powerset(GamesD1(k-1)):


{ seq(seq( [ L, R], L in S), R in S) }:

end:


GamesD:=proc(k): GamesD1(k) minus GamesD1(k-1): end:

#RandGame(k,m): a random game created in day <=k
#where L and R are always of size <=m
RandGame:=proc(k,m) local L,R,m1,m2,k1,i:


if k=0 then
 RETURN([{},{}]):
fi:

m1:=rand(0..m)():

m2:=rand(0..m)():

L:={}:

for i from 1 to m1 do
 k1:=rand(0..k-1)(): 
 L:=L union {RandGame(k1,m)}:
od:

R:={}:

for i from 1 to m2 do
 k1:=rand(0..k-1)(): 
 R:=R union {RandGame(k1,m)}:
od:
[L,R]:
end:

#Age(G):the age of G=[{L},{R}]
Age:=proc(G) local L,R:

if G=[{},{}] then
  RETURN(0):
fi:

max(seq(Age(L), L in G[1]), 
seq(Age(R), R in G[2]))+1:

end:




#CanLeftWin(G): Can Left win the game G?
CanLeftWin:=proc(G) local L:
option remember:

#if true in {seq(not CanRightWin(L), L in G[1])} then
 #RETURN(true):
#fi:
#false:
evalb(true in {seq(not CanRightWin(L), L in G[1])}):
end:


#CanRightWin(G): Can Left win the game G?
CanRightWin:=proc(G) local R:
option remember:

#if true in {seq(not CanLeftWin(R), R in G[2])} then
# RETURN(true):
#fi:
#false:

evalb(true in {seq(not CanLeftWin(R), R in G[2])}):

end:

#WhatKind(G): Is the game 
#
WhatKind:=proc(G) local a,b:

a:=CanLeftWin(G):
b:=CanRightWin(G):

if a and b then 
"Fuzzy":
elif a and not b  then
"Positive":
elif not a and b then
 "Negative":
else
 "Zero" :
fi:

end: