cat as banana In AOP

[cutsea110]

Hi,all

I'm studying `Algebra of Programming' written by Prof. Richard Bird.

My question is for section 3.5 "Concatenation and currying > Exponentials".

In page 74, he said

```

cat = (| curry ([outr, cons] . (id+id x apply) . (id+assocr) . distl) |)

```

where (| ... |) means banana operator.

But I guess this left hand side `cat' is typo of `ccat` or `curry cat`?

I think this is reasoned below.

-----------------------------

    cat . (alpha x id) = [outr, cons] . (id + id x cat) . phi   <= page 73 start expr (maybe this is from equation (3.6))

= {- Theorem 3.1 precondition -}

    cat = apply . ( (| curry (h . G apply . phi |) x id)           -----   (A)

= {- on the other hand, exponential's universal property : g = curry f == apply . (g x id) = f -}

   cat = apply . ((curry cat) x id)                                    -----  (B)

= {- from (A) and (B) -}

   (curry cat) = (| curry (h . G apply . phi |)

-----------------------------

This result is

   curry cat = (| curry ( [outr, cons] . (id + id x apply) . (id + assocr) . distl) |)

not cat = rhs(above).

How about this?