-- vectorized boolean operations defined in terms of step or cond import Numeric.LinearAlgebra infix 4 .==., ./=., .<., .<=., .>=., .>. infixr 3 .&&. infixr 2 .||. a .<. b = step (b-a) a .<=. b = cond a b 1 1 0 a .==. b = cond a b 0 1 0 a ./=. b = cond a b 1 0 1 a .>=. b = cond a b 0 1 1 a .>. b = step (a-b) a .&&. b = step (a*b) a .||. b = step (a+b) no a = 1-a xor a b = a ./=. b equiv a b = a .==. b imp a b = no a .||. b taut x = minElement x == 1 -- examples clip a b x = cond y b y y b where y = cond x a a x x disp = putStr . dispf 3 eye n = ident n :: Matrix Double row = asRow . fromList :: [Double] -> Matrix Double col = asColumn . fromList :: [Double] -> Matrix Double m = (3><4) [1..] :: Matrix Double p = row [0,0,1,1] q = row [0,1,0,1] main = do print \$ find (>6) m disp \$ assoc (6,8) 7 \$ zip (find (/=0) (eye 5)) [10..] disp \$ accum (eye 5) (+) [((0,2),3), ((3,1),7), ((1,1),1)] disp \$ m .>=. 10 .||. m .<. 4 (disp . fromColumns . map flatten) [p, q, p.&&.q, p .||.q, p `xor` q, p `equiv` q, p `imp` q] print \$ taut \$ (p `imp` q ) `equiv` (no q `imp` no p) print \$ taut \$ (xor p q) `equiv` (p .&&. no q .||. no p .&&. q) disp \$ clip 3 8 m disp \$ col [1..7] .<=. row [1..5] disp \$ cond (col [1..3]) (row [1..4]) m 50 (3*m)