Re: letrec/named let

*To*: mathgroup at smc.vnet.net*Subject*: [mg56753] Re: letrec/named let*From*: Daniel Roy <droy at mit.edu>*Date*: Thu, 5 May 2005 06:01:34 -0400 (EDT)*Organization*: MIT*Sender*: owner-wri-mathgroup at wolfram.com

> You always give C as first argument; so it is superflous. > Pleas note, that C is reserved: > "C[i] is the default form for the ith parameter or constant > generated in representing the results of various symbolic > computations." > > CompressNumericalSequence[S_]:= > Module[{fC}, > fC=Function[{R,i}, > If[i<Max[R], > If[Length[Position[R,i]]==0, > fC[(If[#>i,#-1,#])&/@R,i], > fC[R,i+1]],R]]; > fC[S,1]]; > > but this will fail for big numbers unless you set $IterationLimit > appropriate. Hence, I'm not so sure this is true. This function is tail-recursive. Does mathematica handle tail recursion properly? > > CNS[lst_] := lst /. (Thread[#1 -> Ordering[Ordering[#1]]] & )[ > Module[{f}, f[x_] := (f[x] = Sequence[]; x); f /@ lst]]; > > or even better > > CNS[lst_] := Module[{tmp = First /@ Split[Sort[lst]]}, > Flatten[(Position[tmp, #1] & ) /@ lst]] > > would do the task more reliable (and much more faster). Neither of these functions do what CompressNumericalSequence does... And because I'm no mathematica-guru I don't yet quite understand what they do, anyway. Furthermore, they are actually SLOWER than my code (see below on a test of 1,000,000 entries). > > Also, is it possible to do letrec in mathematica? (essentially, i know > > i can do recursive function declarations at the top level... my question > > is whether i can do them at lower levels?)... > Regards, > Peter dan