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      4th.CoSy

      On those weekends I have stolen time to work on 4th.CoSy , I have made progress only possible in FORTH . I have never worked in a non-interpretive language since FORTRAN days ( before meeting APL around `75 ) and cannot imagine working in a traditional compiling environment . Building structures directly in the machine's static address space with FORTH is clumsy enough .

      It's very hard to get across why language creation is so foundational a pursuit . I have not been very successful at conveying an understanding of most of the consequential things I've done in my life , especially before the fact . That's a reason why I have on a couple of occasions done things whose geometric purity is self evident .

      The nature of 4th.CoSy .
      My description below reflects the current state of 4th.CoSy . Some details , like the structure of the header of objects , may change .

      The implementation of 4th.CoSy is as minimalistic as I can conceive . I believe that simplicity of rules comes from simplicity of code , so 4th.CoSy "theory" comes naturally from its implementation as opposed to the APL tradition of forcing grand notions into reality .

      All counting starts with 0 because 0 is the 1st number . I will generally follow the convention of using ordinals 1st , 2nd ... corresponding to
       " 1 take " ... . This is a constant conundrum tho .
      A good image for the structure is perhaps a tree or a bush , each branch having any number of branches , leaves , flowers , or other things on it . More formally , everything is a list of 0 or more items which may themselves be lists or something else . If it is a 4th.CoSy list , its 1st cell ( 32 bit word ) is a 0 . That "something else" is essentially open-ended and what exactly the object may be is given by it's type which is stored in that 1st cell . Generic 4th.CoSy objects have a header , currently of 4 cells as shown below .
          t y p e     count ( # of items ) bits % item | reference count meta   <---   body of object   --->  
      Note that all objects created so far have a count so are set up to be lists themselves which most of the items created so far are - lists of integers , strings of text , symbols - which are just specialized strings .
      All objects in 4th.CoSy are dynamically created in virtual memory ( allocated ) and destroyed
      ( freed ) as needed . That reference count keeps track of whether anything is using the object .


      As I said , everything in 4th.CoSy is a tree or a leaf . The language itself , the dictionary , is a tree . It's a tree with currently 2 branches ; the first is a list of words ( symbols ) in the vocabulary and the second , a matching list of the values ( definitions ) of those words . Following Charles Moore's brilliant use of whitespace ( blanks ) as the prime delimiter , words can be any non-blank string of characters as in FORTH . The values can be any 4th.CoSy object , including , of course , 4th.CoSy lists . [ 20070930 | have added a third "attibute" column ala K ala some Lisps | 20071101 | poor notion . will replace with cell in header ]

      VOCABULARY
      The power of APLs comes from their vocabulary to apply functions ( verbs ) to lists . Many of the earliest words I have created in FORTH , even to implement the parsing and interpreter yet to come are "APL" words . Much of this discussion will resonate more with APLers than "outsiders" . Note the examples are FORTH "parse a word , do it" syntax because they are in fact at this point in time all executing in FORTH .

      An example of how transparent to the machine 4th.CoSy is is given by the definition of @ which is machine code :
        : @ inline{ 8b 00 } ;inline  ( a -- n ) 
      | get the contents n of cell at address a
      see @
      005FCECB 8B 00 mov eax,[eax]
      005FCECD C3 ret

    • i# The number of items in an object is , as shown above , stored the 2nd cell of the header so the FORTH is simply
        : i# cell + @ ;   name changed to avoid conflict with FORTH # ) .

    • i@ and i! Index fetch and store . All indexing is is modulo . That is , indexing wraps around so that
        Obj i# i@   grabs the same item as   Obj 0 i@   , and   Obj -1 i@   grabs the last item ,   Obj i# 1- i@   .

    • each in various forms and across . ( At this level in FORTH , there isn't the generic covering of functions specific to each data type like byte or integer so multiple forms are needed . ) These "operators" ( adverbs ) can be implemented , tho in a primitive form , in FORTH because FORTH's ' function returns the address of a word making it easy to pass that pointer to a function which then calls execute to actually execute it . I plan to retain this style of passing the pointers to words , generally their symbolic names , to functions which may take functions as arguments . Thus , APLs distinctions between functions ( verbs ) and operators ( adverbs ) and possibly higher order constructs becomes rather open , arbitrary , and extensible .

    • take , APL's "rho" . Consistent with the modulo indexing ,   List n take   replicates the items of List cyclically to length n .

    • & Arthur Whitney's "where" function . For each item of its integer argument , return n replications of corresponding index . This is one of those APLish definitions which seem terminally inscrutable , but the normal use is just to extract the indices of 1s in boolean lists of 0s and 1s . It's just that the more general definition is just about as easy to write , and does have some very subtle uses .

    • _ Arthur Whitney's "cut" function . Splits or partitions a list into sublists at a set of indices . If there is just one index , it's the same as APL's "drop" .

    • ? A generalization of Whitney's "find" and APL's dyadic "iota" which return the index of the first item in the left argument matching the right argument . ? in CoSy is an operator , list fn ? item which returns the first index in list where { fn item } is true . If not found , returns nil .

    • general function application Generally , arguments are "taken" to the length of the longer for application of "atomic" functions . This is a generalization of APL's "scalar" extension .

       
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    Contact : Bob Armstrong ; About this page : Feedback ; 719-337-2733
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