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-- 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 $ 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)
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