Primitive Functions

Note

The examples of primitives come from the ELI Primer which is available at ELI Document

Symbol Table

Name Symbol Name Symbol
jot .    
dot :    
each “    
unique/equal =    
minus(negate/substract) -    
at(pi/circle) @ del @.
epsilon(member) ? random ?.
star(signum/multiply) * natural log/power *.
percent(reciprocal/div) % log %.
bar(absolute/residue) | gamma(factorial/binom) |.
rho(shape/reshape) # domino #.
turn(reverse/rotate) $ reverse/roate(1st axis) $.
left(grade_up/less) < pack(enclose/encode) <.
right(grade_down/greater) > unpack(grouping/decode) >.
iota(interval/index_of) ! execute/drop !.
count/and ^ first/take ^.
or & flip(transpose) &.
plus(conjugate/add) + format +.
high_minus _ lower(floor/minimum) _.
not ~ upper(ceiling/maximum) ~.
slash(reduce/compress) / slashdot(reduct1/compre1) /.
back slash(scan/expand) \ back slash(scan1/expand1) \.
catenate , raze/catenate(1st axis) ,.
    assign <-
    branch ->
    nand ~^
    nor ~&
    not equal ~=
    less or equal <=
    greater or equal >=
    comment //
    quad []
    bare quad [)

Monadic

A monadic function only takes one argument. For example, f x where f is the monadic function and x is the only argument the function takes. Usually, the function f has different behaviors based on different types of input data.

Unique (=)

  • Domain of the parameter x

    Boolean ✓ Month ✓ List ✗
    Integer ✓ Date ✓ Enumeration ✗
    Float ✓ Datetime ✓ Dictionary ✗
    Char ✓ Minute ✓ Keyed table ✗
    Complex ✓ Second ✓ Table ✗
    Symbol ✓ Time ✓    

  • Code examples

          V
86 25 55 48 78 95 36 36 14 65
      =V
86 25 55 48 78 95 36 14 65
      V=36
0 0 0 0 0 0 1 1 0 0

Negate (-)

  • Domain of the parameter x

    Boolean ✓ Month ✗ List ✗
    Integer ✓ Date ✗ Enumeration ✗
    Float ✓ Datetime ✗ Dictionary ✗
    Char ✓ Minute ✗ Keyed table ✗
    Complex ✓ Second ✗ Table ✗
    Symbol ✗ Time ✗    

  • Code examples

          V
86 25 55 48 78 95 36 36 14 65
      -V
_86 _25 _55 _48 _78 _95 _36 _36 _14 _65

Pi (@)

  • Domain of the parameter x (The same as negate)

  • Code examples

          @0 1 2 3
0 3.141592654 6.283185307 9.424777961

Signum (*)

  • Domain of the parameter x (The same as negate)

  • Code examples

        V
86 25 55 48 78 95 36 36 14 65
    P
17.3 22.3 24.3 17.5 21.4 18.4 17.2 15 20.8 21.8
    *P-P0<-20
_1 1 1 _1 1 _1 _1 _1 1 1
    V**P-P0
_86 25 55 _48 78 _95 _36 _36 14 65

Reciprocal (%)

  • Domain of the parameter x (The same as negate)

  • Code examples

          %0
Error: domain error
      %0
      ^
      %1 2 4 8
1 0.5 0.25 0.125

Absolute (|)

  • Domain of the parameter x (The same as negate)

  • Code examples

          | _1 2 _3.2 5 0 _10
1 2 3.2 5 0 10

Shape (#)

  • Domain of the parameter x

    Boolean ✓ Month ✓ List ✓
    Integer ✓ Date ✓ Enumeration ✓
    Float ✓ Datetime ✓ Dictionary ✓
    Char ✓ Minute ✓ Keyed table ✓
    Complex ✓ Second ✓ Table ✓
    Symbol ✓ Time ✓    

  • Code examples

          a<-2 3#9 2 3 4 5 6
      a
9 2 3
4 5 6
      #a
2 3
      #empv<-0#a
0
      #empm<-0 10#'A'
0 10

Reverse ($)

  • Domain of the parameter x

    Boolean ✓ Month ✓ List ✓
    Integer ✓ Date ✓ Enumeration ✓
    Float ✓ Datetime ✓ Dictionary ✗
    Char ✓ Minute ✓ Keyed table ✗
    Complex ✓ Second ✓ Table ✗
    Symbol ✓ Time ✓    

  • Code examples

          V
86 25 55 48 78 95 36 36 14 65
      $V
65 14 36 36 95 78 48 55 25 86

Grade Up (<)

  • Domain of the parameter x

    Boolean ✓ Month ✓ List ✗
    Integer ✓ Date ✓ Enumeration ✗
    Float ✓ Datetime ✓ Dictionary ✗
    Char ✓ Minute ✓ Keyed table ✗
    Complex ✓ Second ✓ Table ✗
    Symbol ✓ Time ✓    

  • Code examples

          V
86 25 55 48 78 95 36 36 14 65
      <V
9 2 7 8 4 3 10 5 1 6
      V[<V]
14 25 36 36 48 55 65 78 86 95

Grade Down (>)

  • Domain of the parameter x (The same as grade up)

  • Code examples

          V
86 25 55 48 78 95 36 36 14 65
      >V
6 1 5 10 3 4 7 8 2 9
      V[>V]
95 86 78 65 55 48 36 36 25 14

Interval (!)

  • Domain of the parameter x (The same as not)

  • Code examples

        !5
1 2 3 4 5
    !2.3
Error: domain error
    !2.3
    ^

    The generated interval is influenced by the system variable []IO.

          []IO<-0
0
      !12
0 1 2 3 4 5 6 7 8 9 10 11

Count (^)

  • Domain of the parameter x (The same as shape)

  • Code examples

        ^`abc
1
    s3<-`abc `ddl `comp
    ^s3
4

Conjugate (+)

  • Domain of the parameter x (The same as negate)

  • Code examples

          +_1 2 _3.2 5 0 _10
_1 2 _3.2 5 0 _10
      +1j2 2.3j_3
1j_2 2.3j3

High_minus (_)

  • Domain of the parameter x (The same as negate)

  • Code examples

          _1 2 3
_1 2 3

Not (~)

  • Domain of the parameter x

    Boolean ✓ Month ✗ List ✗
    Integer ✓ Date ✗ Enumeration ✗
    Float ✗ Datetime ✗ Dictionary ✗
    Char ✗ Minute ✗ Keyed table ✗
    Complex ✗ Second ✗ Table ✗
    Symbol ✗ Time ✗    

  • Code examples

          ~0 1 1 0
1 0 0 1

Natural logarithm (*.)

  • Domain of the parameter x (The same as negate)

  • Code examples

          e<-*.1
      e
2.7182818
      *. _1 0 1 2 3
0.36787944 1 2.7182818 7.3890561 20.085537
      e*. _1 0 1 2 3
0.36787944 1 2.7182818 7.3890561 20.085537

Factorial (|.)

  • Domain of the parameter x (The same as negate)

  • Code examples

          |.1 2 3 4 5
1 2 6 24 120

  • Note: non-negative integer is required.

Domino (#.)

Reverse on 1st axis ($.)

Enclose (<.)

Grouping (>.)

Execute (!.)

First (^.)

Floor (_.)

  • Domain of the parameter x (The same as negate)

  • Code examples

          _. 0.5 _1.2 0 3 _5
0 _2 0 3 _5

  • Note: similar to the function floor in C

Ceiling (~.)

  • Domain of the parameter x (The same as negate)

  • Code examples

          ~. 0.5 _1.2 0 3 _5
1 _1 0 3 _5

  • Note: similar to the function ceil in C

Raze (,.)

  • Domain of the parameter x

    Boolean ✓ Month ✓ List ✓
    Integer ✓ Date ✓ Enumeration ✗
    Float ✓ Datetime ✓ Dictionary ✗
    Char ✓ Minute ✓ Keyed table ✗
    Complex ✓ Second ✓ Table ✗
    Symbol ✓ Time ✓    

  • Code examples

          ,(1 2;3 4)
<1 2
<3 4
      ,.(1 2;3 4)
1 2 3 4

  • Note: currently designed for flattening lists

Dyadic

A dyadic function only takes two arguments. For example, y f x where f is the monadic function and x and y are the two arguments the function takes. Usually, the function f has different behaviors based on different kinds of input data.

Equal (=)

Substract (-)

Circle (@)

Member (?)

Multiply (*)

      2j5 * 3j2.5
_6.5j20

Divide (%)

      (!6)%2
0.5 1 1.5 2 2.5 3
      24%!6
24 12 8 6 4.8 4

A special monadic form:

      %!6
1 0.5 0.33333333 0.25 0.2 0.16666667

Now to take the cubic root of numbers or various roots of a number, we do

      1 2 8 1000 81 125 *.%3
1 1.259921 2 10 4.3267487 5
      1024*.%1 2 3 5 10
1024 32 10.079368 4 2

Residue (|)

      2|!12
1 0 1 0 1 0 1 0 1 0 1 0
      2 3 4.5|9
1 0 0
      3.2|3 6.4 7
3 0 0.6

Reshape (#)

      a<-2 3#9 2 3 4 5 6
      a
9 2 3
4 5 6
      #a
2 3

Rotate ($)

Less (<)

Greater (>)

Index Of (!)

    5 1 7 9 3 7 ! 5
1
    5 1 7 9 3 7 ! 7
3

And (^)

      1 1 0 1 0 0 ^ 0 1 0 0 1 0
0 1 0 0 0 0

Or (&)

      1 1 0 1 0 0 & 0 1 0 0 1 0
1 1 0 1 1 0

Add (+)

      1+A<-10
11
      n+1
Error: value error
      n+1
       ^
      2j5+3j2.5
5j7.5

Power (*.)

      2 _3 10 0.5 25 *. 2
4 9 100 0.25 625
      10 *. _1 0 1 2 3
0.1 1 10 100 1000
      2*.!10
2 4 8 16 32 64 128 256 512 1024
      4 9 100 0.25 625 *.0.5
2 3 10 0.5 25
      _1 *. 0.5
0j1

Catenate (,)

      0,!10
0 1 2 3 4 5 6 7 8 9 10
       (!10),_1
1 2 3 4 5 6 7 8 9 10 _1
      'WATCH OUT','!'
WATCH OUT!
      'WATCH OUT',' GUYS!'
WATCH OUT GUYS!
      100 200,2 3 5
100 200 2 3 5

Binom (|.)

Rotate on 1st axis ($.)

Encode (<.)

Decode (>.)

Drop (!.)

Take (^.)

Minimum (_.)

Maximum (~.)

Catenate (,)

Mixed

Each (”)

      *"(_2 3;4 _5 6)
<_1 1
<1 _1 1
      *"_2 3
_1 1
  • Apply a monadic operator to a list or a simple array

Jot (.)

Dot (:)

Reduce (/)

Scan ()

Compress (/)

Expand (\)

Del (@.)

Random (?.)

Log (%.)

      10%. 1 10 100 1000 10000
0 1 2 2 3 4
      10%. 1 10 100 1000 10000 100000
0 1 2 3 4 5
      2%. 0.5 1 2 4 8 16
_1 0 1 2 3 4
      2 3 10%. 4 9 100
2 2 2
      e<-*.1
      e
2.718282
      %.1 10 100 1000 10000 100000
0 2.302585 4.60517 6.907755 9.21034 11.512925
      e%.1 10 100 1000 10000 100000
0 2.302585 4.60517 6.907755 9.21034 11.512925

Transpose (&.)

Format (+.)

Reduct on 1st axis (/.)

Compre on 1st axis (/.)

Scan on 1st axis (\.)

Expand on 1st axis (\.)

Assign (<-)

      A<-'BC'
      ch<-'abcde''1234'
      ch
abcde'1234
      A
BC

Branch (->)

Nand (~^)

Nor (~&)

Not equal (~=)

Less than equal (<=)

Greater than equal (>=)

Comment (//)

Quad ([])

Bare quad ([)

The End.