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Summary: Delta-Rules
A set of rules of the form c t1 . . . tn r
with c C, t1, . . . , tn, r is a set of Delta-rules iff
· t1, . . . , tn, r are closed lambda-terms
· all ti are in -normal form and
they do not contain the left-hand side of a rule from
· does not contain rules c t1 . . . tn r and c t1 . . . tm r
with m n
-Reduction
· l r, if l r
· t1 t2 implies (t1 r) (t2 r), (r t1) (r t2), y.t1 y.t2
We define = .
Non-Terminating Reductions
· Even -reduction does not terminate:
(x.x x) (x.x x) (x.x x) (x.x x) . . .
· In general, termination depends on the reduction strategy.
Leftmost outermost reduction:
(x.y)((x.x x) (x.x x)) y,
Leftmost innermost reduction:
(x.y)((x.x x) (x.x x)) (x.y)((x.x x) (x.x x)) . . .
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