List Commands Library for 50g

[DavidM]

(09-18-2018 03:32 PM)John Keith Wrote:  As an example, this simple program

Code:


\<< LSEQ DUP 2. \->LIST LRPC\->
\>>

returns the first T(n) terms of A002024, where T(n) is the nth triangular number. The above program is similar to the second Haskell program in the OEIS link. It is also quite fast: given an input of 100, it returns the first 5050 terms in less than 700 milliseconds.

Very nice! I had a feeling LRPC→ might be useful for something other than undoing LRPCT, but hadn't yet run into it. Glad to see it put to use!

(09-18-2018 03:32 PM)John Keith Wrote:  A longer (and clunkier) example...

Code:


\<< I\->R { 1 2 } \-> n b
  \<< b 1. n
    START DUP SIZE b OVER 2. / CEIL LMRPT 1. ROT SUB SWAP 2. \->LIST LRPC\->
    NEXT
  \>>
\>>

returns the nth iteration of the Kolakoski sequence. The program is longer and more involved than the Haskell program in the Kolakoski link because the infinite lists and "lazy" evaluation of Haskell make the explicit calculation of list lengths unnecessary.

These programs also demonstrate the similarity of LMRPT and LRPC\-> to the Haskell functions cycle and replicate respectively.

Even after reading the OEIS description, I'm not sure I understand that sequence. It grows rapidly, that's for sure. I believe you should be able to leave out the CEIL function, though, as the result after division by 2 will round up appropriately for LMRPT. This is the same type of handling for counts/indices that most RPL commands apply in similar situations.

These are interesting applications of list processing -- thanks for sharing!