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Joined 2026-09-21 Message
Incoming links: Type synonym
Use coordinates with row and column in :
type Place = (Int,Int)
type Places = [Place]
type Board = (Places,Places,Places)
data Player = O | X deriving (Eq,Ord,Show)The components of
Board record the positions occupied by O, occupied by X, and still empty, respectively. On a nonterminal legal board, equal occupied counts mean O moves next; one extra O means X moves next.The type synonym does not enforce the representation invariant: coordinates are in range; each component has no duplicates; the three represented sets form a set partition of the nine positions; and the occupied counts differ as just described. Both players cannot have won. A winning
O board has one extra O, and a winning X board has equal counts. More fundamentally, a legal tic-tac-toe state has a legal alternating history that stops at the first win: satisfying a type alone never licenses continuing an already completed game.Use arbitrary-precision integers for positions, avoiding overflow on infinite sequences:The type synonym
type Seq a = a -> [Integer]
rep :: Eq a => [a] -> Seq a
rep xs v = [i | (i,x) <- zip [0..] xs, x == v]Seq a needs no equality constraint; the equality test is required specifically by rep. The list comprehension visits input positions in increasing order, so the output is an increasing list of precisely the matching positions. For finite inputs this includes a terminating empty list when the value is absent. Infinite inputs require the additional productivity distinctions discussed below. This is an occurrence-position representation of a sequence.