˝
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˝ y
ory ≡ F˝ F y
holds; - 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˝ y
ory ≡ x F˝ x F y
holds; - 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˝ y
orx ≡ (x F˝ y) F y
holds; - 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/˝ y
holds; - 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⍨˝ y
ory ≡ F⍨˝ F⍨ y
holds; - 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/˝ y
holds.