Lambda Calculus Primes - Sieve of Eratosthenese.

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Note the use of "infinite" lists (e.g. from 2) in the functional-programming Sieve of Eratosthenese algorithm.

let rec
   first = lambda n. lambda l.
      if n=0 then nil
      else (hd l)::(first (n-1) tl l),

   from = lambda n. n::(from (n+1))

in let rec
   filter = lambda f. lambda l. { remove multiples of f from l }
      if null l then nil
      else if hd l/f*f = hd l then filter f  tl l
      else hd l :: filter f  tl l,

   sieve = lambda l.
      if null l then nil
      else let p = hd l { prime }
           in p :: sieve (filter  p  tl l)

in first 10 ( sieve (from 2) )

{\fB Sieve of Eratosthenes. \fP}


Coding Ockham's Razor, L. Allison, Springer

A Practical Introduction to Denotational Semantics, L. Allison, CUP

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λ ...
:: list cons
nil the [ ] list
null  predicate
hd head (1st)
tl tail (rest)

© L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated),
Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University,
was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.)
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