Explicit Negation

Negation is a very important part of logic and it must be considered into a declarative language.
In functional programming negation just moves true into false and vice versa.
PROLOG uses the negation as failure rule what it is very interesting but usually has an incomplete implementation.
In many cases, the problem states when some things are not true in the model of computation. => Explicit negation.
Functional logic languages: predicates as boolean functions that can return the value false.
Explicit negation comes, in some sense, closer to logical negation than in PROLOG.

Syntactic sugar:

p t1 . . . tN = false.           ~p (t1, . . ., tN).
p t1 . . . tN = C => false.      ~p (t1, . . ., tN) :- C.

Expressivity of Explicit Negation

Problem: The Alpine Club puzzle

Tony, Mike, and John belong to the Alpine Club. Every member of the Alpine Club is either a skier or a mountain climber or both. No mountain climber likes rain, and all skiers like snow. Mike dislikes whatever Tony likes and likes wathever Tony dislikes. Tony likes rain and snow. Is there a member of the Alpine Club who is a mountain climber, but not a skier?.

Try to solve it in your favourite language before you check the solution in a functional logic language

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