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Unformatted text preview: tion of equivalence between Haskell functions: • (re²exivity) ∀ f . f = f ; • (symmetry) ∀ f 1 , f 2 . f 1 = f 2 ⇒ f 2 = f 1 ; • (transitivity) ∀ f 1 , f 2 , f 3 . f 1 = f 2 ∧ f 2 = f 3 ⇒ f 1 = f 3 . We give universal de±nitions for the properties just described. A relation may or may not satisfy such properties. D EFINITION 3.11 Let R be a binary relation on A . Then 1. R is refexive if and only if ∀ x ∈ A. x R x ; 2. R is symmetric if and only if ∀ x, y ∈ A. x R y ⇔ y R x ; 3. R is transitive if and only if ∀ x, y, z ∈ A. x R y ∧ y R z ⇒ x R z . 24...
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This note was uploaded on 01/02/2010 for the course MATH Math2009 taught by Professor Koskesh during the Spring '09 term at SUNY Empire State.
 Spring '09
 Koskesh
 Math

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