make tacit scalar replacement invertible

[tangentstorm]

I request that the idiomatic verb =&m`(,:&n) } for scalar m and n, be invertible. The inverse is =&n`(,:&m) } .

For example:

   in  =. =&'-'`(,:&'_') }
   out =. =&'_'`(,:&'-') }

   io  =. [: ". in :. out

   +:&.io '-1 2 3'
-2 4 6

could be rewritten more succinctly as:

    io =.  [: ". '-'&=`(,:&'_') }
    +:&.io '-1 2 3'
-2 4 6

This one new inverse would suffice for the majority of my use cases, but you may also consider making inverses for the verb's affiliates.

That is, you could create the following mappings (or a subset thereof):

   = &m`(,:&n) } ^:_1  ↔  = &n`(,:&m) }   NB. A
   ~:&m`(n&,:) } ^:_1  ↔  ~:&n`(m&,:) }   NB. B
   m& =`(,:&n) } ^:_1  ↔  n& =`(,:&m) }   NB. C
   m&~:`(n&,:) } ^:_1  ↔  n&~:`(m&,:) }   NB. D

   = &m`(n&,:) } ^:_1  ↔  = &n`(m&,:) }   NB. E
   ~:&m`(,:&n) } ^:_1  ↔  ~:&m`(,:&m) }   NB. F
   m& =`(n&,:) } ^:_1  ↔  n& =`(m&,:) }   NB. G
   m&~:`(,:&n) } ^:_1  ↔  n&~:`(,:&m) }   NB. H

But I'm not convinced these extra inverses provide much value:

• Mappings E-H are going to see less use (it can be useful to say "replace everything that's not a FOO with a BAR, but it's not so useful to invert that function).
• The form m&= is redundant with =&m. It's not so hard to write the latter if you want your function invertible.
• A similar sentiment applies to ~:&m`(n&,:) vs =&m`(,:&n) .

-- Dan Bron <2008-02-01T23:45:30Z>