Church-Rosser theorem

Church-Rosser theorem [¦chərch ¦rȯs·ər ¦thir·əm]

(mathematics)

If for a lambda expression there is a terminating reduction sequence yielding a reduced formB, then the leftmost reduction sequence will yield a reduced form that is equivalent toBup to renaming.

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(theory)

Church-Rosser Theorem - A property of a reduction system that states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced. This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition. It does not imply that a normal form is reachable, only that if reduction terminates it will reach a unique normal form.