A free morpheme is one that can act as a stand alone word.
A compound word hard to detect because it is a semantic, not a syntactic phenomena. You can observe someone utter blackboard, but you can’t easily tell if in their skulls they’re processing it as a board that is black, or a specific type of board that is black, namely one for writing on with chalk and might not even be black! I suppose you could ask enough fluent speakers, but this isn’t really an available option with artificial langauges.
Toki pona has only free mophemes, except for possibly the “la”, “li”, “e” and maybe “ni”. (If those were used as free mophemes, it would be peculiar cases not representative of typcial speech)
Free morphemes will combine with other free morphemes to form new lexemes.
These multi-stem lexemes typically require memorization, but not always. If they are somewhat obvious on first read then they are transparent. Multi-stem lexemes are interpreted by their narrow meaning first and by their generic meaning as an after thought. In a language like toki pona which has accent on first syllable, the second free morpheme may have weakened or lost accent. Punctuation and spelling tend to be of no help in identifying compound word, for example in English they may have no space, hyphens or a space between the stems. Real spoken language tends to have no pauses between words, so that won’t help either.
Productive word creation through free morphemes is common to many languages. Some languages like to include preposition-like particles, e.g. French chemin-de-fer some don’t, English iron lung.
The toki pona multistem lexeme has this official form
[head noun] – [any number of modifiers] pi [new head noun]- [any number of modifiers] pi [etc]
The resulting multi-stem lexeme can be plugged into anywhere that a bare head noun is permissible. AFAIK, the “chemin-de-fer”/”man-of-war” style lexeme is illegal, that is, you can’t use kepeken, tawa, lon, or other prepositions to build up a mulit-stem lexeme, but it appears that the “pi” particle can act as a neutral proposition that means “some relationship, including ‘of’, ‘in’, ‘by’, ‘for’, ‘with’” Collapsing all relationships into “pi” actually leads to a loss of information. A possible improvement would be
[head noun] – [any number of modifiers] pi [preposition] [new head noun]- [any number of modifiers] pi [etc]
The verb has the same potentialities as the noun.
[head verb] – [any number of modifiers] pi [new head verb? noun?]- [any number of modifiers] pi [etc]
What these mean are considerable more difficult to say. That all human verb patterns can be squished into categories of mood, tense, voice, etc. make me think that either these are linguistic universals or these are just the salient factors of moving and being that makes up reality. You have to have the machinery to describe reality to say something interesting.
See Part 2… it’s somewhere, someday.