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2A. Bond or Curry
Fixing an argument of a verb produces a monad. Some verbs so produced are sufficiently important to justify being denoted by a primitive symbol, and the following table often shows the corresponding primitive together with the English definition. The conjunction & (often called with) is used to bond an argument to a verb.
| m0 =: 1&+ | Increment >: |
| m1 =: +&1 | " |
| m2 =: _1&+ | Decrement <: |
| m3 =: -&1 | " |
| m4 =: 1&- | Not -. (logical and probability complement) |
| m5 =: 1&~: | " |
| m6 =: 0&= | " |
| m7 =: 0&- | Negate - (arithmetic) |
| m8 =: _1&* | " |
| m9 =: *&_1 | " |
| m10=: 2&* | Double +: |
| m11=: *&2 | " |
| m12=: 3&* | Triple |
| m13=: *&3 | " |
| m14=: 0j1&* | j. (Multiply by √-1) |
| m15=: ^@j. | r. (Complex # on unit circle at y radians) |
| m16=: 1p1&* | π times |
| m17=: 0.5&* | Halve -: |
| m18=: *&0.5 | " |
| m19=: %&2 | " |
| m20=: 1&% | Reciprocal % |
| m21=: ^&_1 | " |
| m22=: ^&2 | Square *: |
| m23=: ^&3 | Cube |
| m24=: ^&0.5 | Square root %: |
| m25=: ^&1r2 | " |
| m26=: 2&%: | " |
| m27=: ^&(%3) | Cube root |
| m28=: ^&1r3 | " |
| m29=: 3&%: | " |
| m30=: (^1)&^ | Exponential ^ |
| m31=: 1x1&^ | " |
| m32=: 1x1&^. | Natural log ^. |
| m33=: 10&^ | Antilog |
| m34=: 10&^. | Base-10 log |
| m35=: >:@<.@(10&^.)@(1&>.) | # of digits needed to represent integer y |
| m36=: #@(10&#.^:_1)"0 | " |
| m37=: >:@<.@( 2&^.)@(1&>.) | # of bits needed to represent integer y |
| m38=: #@( 2&#.^:_1)"0 | " |
| m39=: 0&{ | Head (first) {. |
| m40=: _1&{ | Tail (last) {: |
| m41=: 1&}. | Behead }. |
| m42=: _1&}. | Curtail }: |
| m43=: 0&< | Positive test |
| m44=: 0&> | Negative test |
| m45=: 0&>. | Max (0,y) |
| m46=: 0&<. | Min (0,y) |
| m47=: (0&=)@(2&|) | Even test |
| m48=: (1&=)@(2&|) | Odd test |
| m49=: _1&A. | Reverse |. |
| m50=: (<0 _1)&C. | Interchange first and last items |
| m51=: <.@(0.5&+) | Round |
| m52=: ,~ $ 1: , ] $ 0: | Identity matrix of order y |
| m53=: -.@(' '&E.) # ] | Remove multiple blanks |
| m54=: BC=: i.@>: ! ] | Binomial coefficients of order y |
| m55=: (0&,+,&0)^:([ `1:) | " (recursive) |
| m56=: BCT=:i. !/ i. | BC table of orders to y-1 |
| m57=: PAT=: |:@BCT | Pascal’s triangle |
| m58=: (0&,+,&0)^:(i.`1:) | " (recursive) |
| m59=: IX=: a.&i. | Index in ASCII alphabet |
| m60=: Lt=:(1&e.)@(e.&a.)@, | Literal test |
| m61=: 1&#. | Sum over lists (last axis) +/"1 |
| m62=: 1&, | Preface a row of 1’s |
| m63=: ,&1 | Append a row of 1’s |
| m64=: 1&,. | Preface a column of 1’s |
| m65=: ,.&1 | Append a column of 1’s |
| m66=: 1&,@$ $ , | Itemize (append leading 1 to shape) ,: |
| m67=: sin=: 1&o. | Sin |
| m68=: asin=: _1&o. | Arcsin |
| m69=: cos=: 2&o. | Cos |
| m70=: acos=: _2&o. | Arccos |
| m71=: tan=: 3&o. | Tan |
| m72=: atan=: _3&o. | Arctan |
| m73=: sinh=: 5&o. | Sinh |
| m74=: asinh=: _5&o. | Arcsinh |
| m75=: cosh=: 6&o. | Cosh |
| m76=: acosh=: _6&o. | Arccosh |
| m77=: tanh=: 7&o. | Tanh |
| m78=: atanh=: _7&o. | Arctanh |