Normal Forms and Confluence
For the untyped lambda calculus, β-reduction as a rewriting rule is neither strongly normalising nor weakly normalising.
However, it can be shown that β-reduction is confluent. (Of course, we are working up to α-conversion, i.e. we consider two normal forms to be equal, if it is possible to α-convert one into the other.)
Therefore, both strongly normalising terms and weakly normalising terms have a unique normal form. For strongly normalising terms, any reduction strategy is guaranteed to yield the normal form, whereas for weakly normalising terms, some reduction strategies may fail to find it.
Read more about this topic: Lambda Calculus
Famous quotes containing the words normal and/or forms:
“We have been weakened in our resistance to the professional anti-Communists because we know in our hearts that our so-called democracy has excluded millions of citizens from a normal life and the normal American privileges of health, housing and education.”
—Agnes E. Meyer (1887–1970)
“The atmosphere of orthodoxy is always damaging to prose, and above all it is completely ruinous to the novel, the most anarchical of all forms of literature.”
—George Orwell (1903–1950)