In Letrec

16 n indicating the number of garbage collections performed during the reduction. Thus-Red runs the program in minimal space and does not improve its performance when supplying more space. In contrast to this, the performance of Lisa critically depends on the available heap-space, with run-times by factor of about three higher than-Red with minimal heap-size, and falling below the run-time of-Red as the heap-size increases. 5 Acknowledgements We are grateful to H.Bll odorn for many valuable discussions about the concept and implementation of Lisa. 15 letrec gen = n: h n:(gen ((+ n) 1) i sel = n::l:if ((eq n) 1) then (hd l) else sel ((? n) 1) (tl l) sieve = l:let p = (hd l), l = (tl l) in letrec filter = l:let e = (hd l); l = (tl l) if eq ((mod e) p) 0 then (filter l) else h e:(filter l) i in h p:(sieve (filter l)) i in (sel 100) (sieve (gen 2)) Figure 4: Prime-sieve of Eratosthenes can use for applicative order reductions essentially the same program except that Consed lists must be replaced by then-else constructs, and head/tail calls must be replaced by applications to the selectors true/false, respectively.-6 1 2 3 heap-size MB] 5 10 15 reduction time sec] minimum memory-size of-Red minimum memory-size of Lisa c c c c c c c c c 7 4 2 1 0 Figure 5: Run-times in relation to provided memory-size of the above example A comparison of the performance gures for this program must take into consideration that Lisa and-Red use diierent heap-management schemes. While Lisa works with a conventional garbage collection scheme,-Red employs reference counting and releases unused heap-space as early as possible. The results are depicted in gure 5 where the symbols represent the values for-Red , and n represent the values for Lisa, with 14 simple y =let A = x::y:(y ((x x) y)) in ((A A) x:x) omega = (x:(x x) x:(x x)) y1 =letrec F = x:(F x)