Curry-Howard Exercise
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// (A => B and not B) => not A | |
Not<A> ModusTollens<A, B>( | |
Func<A, B> A_implies_B, | |
Not<B> not_B) | |
{ | |
Absurd A_to_Absurd(A a) | |
{ | |
return not_B.Apply(A_implies_B(a)); | |
} | |
return new Not<A>(A_to_Absurd); | |
} |
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// (A => B and B => C) => A => C | |
Func<A, C> Syllogism<A, B, C>( | |
Func<A, B> A_implies_B, | |
Func<B, C> B_implies_C) | |
{ | |
C Composed(A a) | |
{ | |
return B_implies_C(A_implies_B(a)); | |
} | |
return Composed; | |
} |
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