When deconstructing a composed EO word, we split the word into its elements, then put them back together as if some of them were operators and/or functions. It reminds me of constructions we use in programming languages, so I came to wonder which operators we can define in EO, and what is their precedence?

Take for instance malsanulejo: mal-san-ul-ej-o
The steps to parse it are:
san
malsan
malsanul
malsanulej
malsanulejo

It evaluates mostly from left to right, except for the first step. I could write it like this:
o(ej(ul(mal(san)))), or o(mal(san) + ul + ej) if '+' means concatenation (kunmetaĵo?)

mal has a high priority and is evaluated first. Grammatical markers like -o, -a, -e etc. have very low priority and are evaluated at the end. -j and -n have even lower priority

What prompted me to think about this was the word for invisible: nevidebla. Invisible being the opposite of visible, my instincts told me to expect a mal-, but then I realized that malvidebla is actually a(mal(vid)+ebl), meaning "possible to unsee"? So we use ne-, which turns the meaning around just like mal-, but has lower priority.
nevidebla = ne-vid-ebl-a = a(ne(vid+ebl))

Would you agree with this list of operators ordered by precedence from highest priority to lowest priority, and which others do I miss on the list?

* "mal-"
* "sen-"
* "+" kunmetaĵo
* "ne-"
* "-a" "-e" "-o" "-u" "-i" "-as" "-is" "-os" "-us" vortklasaj finaĵoj
* "-j" plural
* "-n" object marker

Should the standard suffixes like "-ul" and "-ej" have an operator class of their own?

Esperanto is not always consistent in its compounds in the way the components operate.

A ĉirkaŭbrako is not a brako, and a triangulo is not an angulo.

On the other hand kantobirdo (song bird) is definitely a bird.

I seem to recall that Zamenhof said that the ĉefa vorto staras ĉe la fino but at the same time he thought of the finaĵoj as vortoj.

In general all attempts to impose an all-inclusive formal systematicity on the language are likely to be an uncomfortable straitjacket inhibiting oportunaj formoj for compound words.

I'm not looking for an algorithm to derive the meaning of compound words, but only the order in which these operations apply. For instance, ĉirkaŭbrako is still ĉirkaŭ-brak-o, and the order is:
1) join ĉirkaŭ with brak
2) apply -o to mark it as a noun

It still fits the model. If there is no system that can be applied without exceptions, that is still an interesting answer for me. EO is one of the languages where I would expect to most likely encounter such a system, so it's worth trying to find it. However, if there are such rules, I'm interested in the priority of the different operations, similar to programming languages or mathematics, where a+b*c will evaluate b*c first because multiplication has a higher priority than addition.

For people not interested in formal languages, I'd formulate a different type of questions:
Is it true that in mal-radiko1-radiko2 the mal- prefix modifies only the first radiko? and:
Is it true that in ne-radiko1-radiko2 the ne- prefix modifies the compound word radiko1-radiko2?

Again, the meaning of the compound word is not important, it doesn't even need to have a meaning.

What prompted me to think about this was the word for invisible: nevidebla. Invisible being the opposite of visible, my instincts told me to expect a mal-, but then I realized that malvidebla is actually a(mal(vid)+ebl), meaning "possible to unsee"? So we use ne-, which turns the meaning around just like mal-, but has lower priority.
nevidebla = ne-vid-ebl-a = a(ne(vid+ebl))

I would say that nevidebla and malvidebla are synonyms because both ne(videbla) and mal(videbla) are opposite to videbla. These words are mostly used interchangeably.
It's not so obvious to detemine priority of affixes, suffixes and roots. For example:

1.
san
malsan
malsanul
malsanulej
malsanulejo

2.
san
sanul
malsanul
malsanulej
malsanulejo

3.
san
sanul
sanulej
malsanulej
malsanulejo

I think that at least 2 of these priorities are possible. Maybe even all three because I'm not certain if the opposite of "a place of healthy people" is "hospital".

Duko:What prompted me to think about this was the word for invisible: nevidebla. Invisible being the opposite of visible, my instincts told me to expect a mal-, but then I realized that malvidebla is actually a(mal(vid)+ebl), meaning "possible to unsee"? So we use ne-, which turns the meaning around just like mal-, but has lower priority.
nevidebla = ne-vid-ebl-a = a(ne(vid+ebl))

It doesn't make sense to me at all. What is expressed by "possible to un-see" is not the same thing as "invisible". Almost all objects are possible to unsee. You just close your eyes or turn your head, then you do not see them any longer. Then you un-see them. Or?
Only about an extremely intensive light or a hallucination we ca say that they are not possible to un-see. So, I mean ne- and mal- should be analysed the same way, with the same priority. The difference is that ne- expresses a contradiction (everything that is not videbla is ne-videbla) while mal- leaves space for something which is between the two extremes.

First: The prefixes ne- and mal- are not the same. ne- creates the counter-part, while mal- mirrors the thing it refers to; e.g.: malgranda is small and negranda is anything but not big — maybe medium size.

Second: I encountered the problem too not long ago I found that it's quite hard to find a good example where both variants are equally plausible. Additionally i think mal- should only be applicated to raw attributes, not verbs or subjects. Still it's possible to get ambiguities, e.g.: malliberigenda (must get cought (and imprisoned) vs. must not be freed).

I guess for being clear one should split up such words.

Duko:Again, the meaning of the compound word is not important, it doesn't even need to have a meaning.

Sorry, but every linguistic sign consists of form and meaning, you can't do serious linguistics without one of them - especially with compounds, which are situated at the intersection of lexicon, morphology, and syntax.

But even if you neglect the meaning, a problem with Esperanto word formation is the fact, that different morphological processes can result in similar surface structures, e.g. antaŭ-X-o:
[[antaŭ X-o]-a]-o : antaŭtagmezo 'forenoon'
[antaŭ X-o]-o : antaŭbrako 'forearm'
[antaŭ-X-i]-o : antaŭpreparo 'preparation'

Rugxdoma:It doesn't make sense to me at all. What is expressed by "possible to un-see" is not the same thing as "invisible". Almost all objects are possible to unsee. You just close your eyes or turn your head, then you do not see them any longer. Then you un-see them. Or?
Only about an extremely intensive light or a hallucination we ca say that they are not possible to un-see. So, I mean ne- and mal- should be analysed the same way, with the same priority. The difference is that ne- expresses a contradiction (everything that is not videbla is ne-videbla) while mal- leaves space for something which is between the two extremes.

It doesn't make sense, that's why I wouldn't use "malvidebla". The lernu dictionary translates for me "nevidebla" as "invisible", whereas for "malvidebla" there's no direct translation.

In your last two sentences, you disagree with my priority list by saying that ne- and mal- should have the same priority. But at the same time, indirectly support it by giving evidence for it, I mean this part: "(everything that is not videbla is ne-videbla)". What you did there is to first combine "vid" with "ebl" (OK, with "-a" too), and only after this did you apply ne- to make a negation. So, in your way to parse nevidebla, "ne-" had a low priority.

I'm not sure that I make much sense for people who are not into programming, sorry 'bout that.

Fenris_kcf:First: The prefixes ne- and mal- are not the same. ne- creates the counter-part, while mal- mirrors the thing it refers to; e.g.: malgranda is small and negranda is anything but not big — maybe medium size.

Second: I encountered the problem too not long ago I found that it's quite hard to find a good example where both variants are equally plausible. Additionally i think mal- should only be applicated to raw attributes, not verbs or subjects. Still it's possible to get ambiguities, e.g.: malliberigenda (must get cought (and imprisoned) vs. must not be freed).

I guess for being clear one should split up such words.

Beautiful example of a word Exactly what I'm looking for, not mal-something, but mal-something-something-something.

mal- is used to build antonyms. It's easy when mal is followed by a single radiko, grand=big => malgrand=small. But what happens when you string several radikoj after mal- ?
Do we create the antonym of "liber", or do we create the antonym of "liberigenda" (which must be freed)? I support the first variant, that mal- is applied to "liber", and the other components are applied in later steps.

malliberigenda = a(end(ig(mal(liber))))

Steps:
liber = free, freedom
malliber = captive, imprisonment
malliberig = make captive, imprison
malliberigend = must imprison
malliberigenda = adjective to describe someone who must be imprisoned

How about these translations?
liberigenda = which must be set free
malliberigenda = which must me imprisoned
neliberigenda = which doesn't have to be set free

Interesting topic. My feeling is that there is no precedence that is always true. You have to use context to guess the meaning. After all, L. L. Zamenhof never described the language accurately.

I wonder, if the Plena Manlibro de Esperanta Gramatiko touches this subject. Do somebody know?