A. Bond or Curry

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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

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