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Why "and" on an empty list returns true, does it imply that an empty list holds True? Sorry but I cannot read and comprehend this correctly, so please correct me. Thanks.
Prelude> and []
True
Prelude> or []
False
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One way to think about
TrueandFalseis as elements of the lattice ordered byFalse < True.&&and||can be viewed as the binary "meet" (greatest lower bound) and "join" (least upper bound) operations for this lattice. Similarly,andandorare general finite meet and finite join operations. What isand []? It's the greatest lower bound of[]. ButTrueis (vacuously) less than or equal to every element of[], so it's a lower bound of[], and (of course) it's greater than any other lower bound (the other beingFalse), soand [] = True. The algebraic view (thinking about monoids and such) turns out to be entirely equivalent to the order-theoretic view, but I think the order-theoretic one offers more visual intuition.