#280 Inconsistencies in noun/verb

[Stavros Macrakis]

-- nounify(diff) displays as derivative when display2d is
true, and diff when display2d is false.

-- In some cases, the noun form is spelled differently
from the verb form. This can be handy, though it is
confusing. For example, "IF" has a convenient noun
form, COND, so you can write COND(a,b,c) without
getting an error ("unable to evaluate predicate").
However, though the noun form of DIFF displays as
DERIVATIVE, when Maxima reads in DERIVATIVE, it in
fact uses the verb form DIFF. Example:

if(1<2,a,b) => a Verb form
nounify("IF") => COND (%cond)
(nounify("IF"))(a,b) Noun form
cond(1<2,a,b) => cond(1<2,a,b) Noun form
part(_,0) => cond Noun form

diff(x^2,x) => 2*x Verb form
nounify('diff) => DERIVATIVE (%derivative)
(nounify('diff))(x^2,x) Noun form
derivative(x^2,x) => 2*x Verb form
part(_,0) => diff Verb form

-- apply_nouns is documented, but nowhere defined

-- Noun/verb behavior of operators like "+" and "IF" is
messed up:

-- ev( (' "+")(x,x), nouns) returns +(x,x) instead of 2*x.
This is because (' "+")(x,y) gives ((&+) x y). It should
give the same thing as (nounify("+"))(x,y), namely ((%
mplus simp) x y).

-- Similarly for "IF".

-- I haven't tested thoroughly, but there seem to be
similar confusions for "DO"/MDO, ":"/SETQ, etc.

[Stavros Macrakis]

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I spoke too soon about the "convenience" of COND.

verbify(COND) and verbify(nounify(COND)) give %COND rather
than MCOND as they should, so COND(a,b,c) doesn't get an
error because it has nothing to do with IF/MCOND.

[Stavros Macrakis]

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The semantics of noun/verb are pretty unclear.

In the case of trig functions, verbs return floating-point
results: (verbify('sin))(0) => 0.0; but not for elementary
arithmetic: (verbify('"+"))(0,4) => 4.

In the case of trig functions, nouns simplify: (nounify('sin))(%
pi) => 0; but not for elementary arithmetic: (nounify('"+"))
(4,5) => PLUS(4,5).

[Stavros Macrakis]

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In general, the noun/verb forms for infix operators are
screwed up:

I was going to write up a detailed analysis, but it is too much
of a mess. Here is a transcript showing some of the peculiar
cases:

(C17) ?print([">",verbify(">"),nounify(">")]);

((MLIST SIMP) &> MGREATERP %GREATERP)
(D17) [>, ">", GREATERP]
(C18) string(%);
(D18) [">",?MGREATERP,GREATERP]
(C19) is(nounify(">")=GREATERP);
(D19) FALSE
(C20) is(nounify(">")=greaterp);
(D20) FALSE
(C21) ?print(["+",verbify("+"),nounify("+")]);

((MLIST SIMP) &+ MPLUS %PLUS)
(D21) [+, "+", PLUS]
(C22) string(%);
(D22) ["+",?MPLUS,PLUS]
(C23) ["+"(a,b),'"+"(a,b),?MPLUS(a,b),PLUS(a,b)];
(D23) [b + a, PLUS(a, b), b + a, PLUS(a, b)]
(C24) map(op,%);
(D24) [+, PLUS, +, PLUS]
(C25) ?print(%);

((MLIST SIMP) &+ %PLUS &+ $PLUS)
(D25) [+, PLUS, +, PLUS]
(C26)

[Robert Dodier]

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Description of "apply_nouns" has been struck from
doc/info/Simplification.texi.