˝ Inverse r←[x](F˝)y
r is the result of calling the inverse of F on [x and] y. Each function can have up to six inverses:
- an un-inverse, which is the monadic inverse, accessed by
F˝ y; usually at least one ofy ≡ F F˝ yory ≡ F˝ F yholds; - an anti-inverse, which is the inverse formed after binding the left argument, accessed by
x F˝ y; usually at least one ofy ≡ x F x F˝ yory ≡ x F˝ x F yholds; - a contra-inverse, which is the inverse formed after binding the right argument, accessed by
x F⍨˝⍨ y; usually at least one ofx ≡ (x F y) F⍨˝⍨ yorx ≡ (x F⍨˝⍨ y) F yholds; - a dis-inverse, which is the full dyadic inverse, accessed by
Fᑒ/˝ y(or, when the two results are shape-compatible, byF/˝ y); usuallyy ≡ Fᑒ/ Fᑒ/˝ yholds; - a bi-inverse, which is the dyadic inverse where the two arguments are the same, accessed by
F⍨˝; usually at least one ofy ≡ F⍨ F⍨˝ yory ≡ F⍨˝ F⍨ yholds; - an ana-inverse, which is the inverse of folding, accessed by
x Fᑒ/˝y(or, when all the results are shape-compatible, byx F/˝ y); usuallyy ≡ x Fᑒ/ x Fᑒ/˝ yholds.