Left factorials: Difference between revisions

{{incorrect|Lambdatalk| <br><br> The first range of left factorials should start with 0 (zero), not 2. <br><br>

<center>Hi Rosetta, I fixed the code. Thanks for the warning, it gave me a chance to improve it. At least that's what I think.</center>

}}

The code can be tested in this wiki page: http://lambdaway.free.fr/lambdawalks/?view=left_factorial

{def !n // the main function's name

{def !n.mem {A.new 0 1 2}} // initializing a global array

// memorizing the computed values of !n

{def !n.set // computing and storing the values

{A.set! :n // assign at n

{long_mult :n {A.get {- :n 1} {!n.mem}} } // product of n and computed value at n-1

{!n.mem}}}} // in the global array

{def !n.get // getting a value

{lambda {:n}

{A.get :n {if {W.equal? {A.get :n {!n.mem}} undefined} // if it doesn't exist

then {!n.set :n} // then compute it

else {!n.mem}}}}} // else get it from the global array

{lambda {:n} // the main function's body

{if {< :n 2} // if n=0 and n=1

then :n // then return 0 or 1

else {S.reduce long_add // apply add_long to

1 {S.map !n.get {S.serie 1 {- :n 1}}}}}}} // the sequence of computed values

{S.serie 0 10}}

!n(0) = 0

!n(1) = 1