Defining sharp primitives (#> and <#) using Joy

icpdesign — 2005-09-23 12:45:16

#

# since Joy does not have the sharp integers data type, we use

# strings in the format "#nnnn" to represent a sharp integer

#

DEFINE

issharp == [string]

[uncons swap ['# =] [swap cons true] [swap cons false]

ifte]

[false]

ifte;

dig == [] swap 1 - [cons] times # pop nth element and push on top

dip;

peek == [] swap 1 - [cons] times # read nth element and push

swap dup [swap] dip swap dip; # on top

sdig == [issharp] [uncons swap pop 0 strtol dig] [] ifte;

speek == [issharp] [uncons swap pop 0 strtol peek] [] ifte;

END.



where the previously defined #> is named to sdig, and <# is named

speek.



First example:

10 20 30 [1 "#2" "#3" ["#2"] 2] [sdig] map

==> 10 20 30 [1 20 10 ["#2"] 2]



Second example: lets compute a*a + b*b + c*c :

3 4 5 ["#3" "#3" * "#2" "#2" * "#1" "#1" * + +] [speek] map i

==> 3 4 5 50



note that the elements 2 and 3 were not popped from the stack

because the map operator restore the old stack below the result,

but fortunately equal sharp integers are replaced by the same

stack element. Note that speek and sdig used with map returns

the same result!



Other examples:

dup == "#1" speek

swap == "#2" sdig

rollup == "#3" sdig "#3" sdig    // X Y Z -> Z X Y 

rolldown ==  "#3" sdig  // X Y Z -> Y Z X 

rotate ==  "#2" sdig "#3" sdig  // X Y Z -> Z Y X 

popd ==  "#2" sdig pop // Y Z -> Z 

dupd == "#2" speek swap // Y Z -> Y Y Z 

     == "#2" speek "#2" sdig pop

swapd == "#2" sdig "#3" sdig "#3" sdig //  X Y Z -> Y X Z 

It would be interesting to add destructive and non destructive

versions of sbury, where the non-destructive version leaves the

buried element on top of the stack.



Why a sharp integer data type is needed?



look at the first and second examples, if we did not have the

sharp integers we will not be able to know where to apply sdig or 

speek,

since they are selective in the sense they do something only if the 

top 

element of the stack is a sharp number; this needed if we want to use

sdig and speek with map operator as in the shown examples.



In summary, we saw that the sharp primitives can be defined using

Joy, and we just need to add sharp integer data type to Joy.



Taoufik Dachraoui