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:
“The obese is ... in a total delirium. For he is not only large, of a size opposed to normal morphology: he is larger than large. He no longer makes sense in some distinctive opposition, but in his excess, his redundancy.”
—Jean Baudrillard (b. 1929)
“The sun, that brave man,
Comes through boughs that lie in wait,
That brave man.
Green and gloomy eyes
In dark forms of the grass
Run away.”
—Wallace Stevens (1879–1955)