## Church-Rosser Theorem

<*theory*>

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.

Last updated: 1995-01-25

### Nearby terms:

Church integer ♦ Church of the SubGenius ♦ **Church-Rosser Theorem** ♦ ci ♦ CI$

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