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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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