I am trying to gather the "base" form of verbs across languages. The form that is used to generate all the other various verb forms. But it seems some languages don't have infinitive forms of verbs, such as Classical Tibetan (which only has 4 verb forms, but no infinitive). What I don't understand (not having studied in depth very many languages yet) is how you can associate various verb forms with one "standard" or "base" or "root" form, if there is no standalone verb root or infinitive form. What do languages that don't have infinitive forms do to teach children or newcomers how the verbs work? Like with Latin or Spanish it's clear, you have an infinitive form and then you have variations based on that. But for languages without the infinitive, what do you do to learn the patterns?
The stem of a verb is not, in general, the same as the infinitive, and in many languages, more than one principal part is needed to derive all forms of the verb
This is in fact the case in Latin and Spanish
Spanish comer has the stem com- in all forms, with the infinitive ending -er telling you which set of endings to apply. But when you look at a slightly more complicated verb, like poder, you see that we have the stem pued- in much of the present tense, with pod- in the rest, and pud- in the preterite, meaning we need to know 3 different principle parts to fully capture all verb forms
Likewise, in Latin, whilst in most cases, like portār the stem is port- in all forms with the present active infinitive ending -āre telling you which endings to take (-ō in the 1sg present active indicative, -āre in the present active infinitive, -āvi in the 1sg perfect active indicative, and -ātum in the neuter supine), some verbs cannot be derived in this way, for instance regere which is regō, regere, rēxī, rēctum rather than expected regō, regere, *regī, *rectum
In general the situation is similar to Latin. If you know a specific set of "principal parts" it is possible to derive the entirety of the rest of the inflection. There are generally multiple sets of forms that could work as principal parts, but they are usually chosen to be particularly notable forms (so non-finite forms like infinitives, and participles if they exist are often chosen, along with 1st and 3rd person forms more than 2nd person ones)
The wikipedia page for principal parts has a good summary of what parts are used in different languages. Some points of interest are that Ancient Greek has 6 different principal parts, that all but four English verbs (and their derivatives) can be made regular using 3 principal parts & 3 conjugation classes (weak "regular" verbs with a past in -ed, strong "irregular" verbs with a stem change in the past, and modal/preterite-present verbs with no 3sg -s in the present)
- As you know, not all languages have an infinitive, but many languages have multiple infinitives. Latin, Ancient Greek, Biblical Hebrew, Finnish and many others have more than one. These may be distinguished by tense and voice (like the Latin & Greek infinitives), between a more verb-y and a more noun-y infinitive (like Biblical Hebrew), or purely syntactically without any clear semantic difference at all (like in Finnish)
- Not all languages use an infinitive (if there is one) as their citation form. Latin & Greek use the 1sg present active indicative, & Modern Arabic dictionaries tend to use the 3sg masculine past indicative
Bulgarian has no infinitive and uses 1p. sg. present indicative form (“I do”) for citation purposes:
правя [ˈpravʲə] ‘to do’, but in fact it is “I do / I am doing”
Arabic has no infinitives, either, and they use 3p. sg. masc. past (perfect) indicative for citation purposes:
فَعَلَ /fa.ʕa.la/ ‘to do’, but in fact it is “he did / he has done”
It doesn't actually matter which form of the verb is used for citation purposes, usually the form is chosen which is the most simple and transparent in respect of morphology.
It sounds like what you're looking for isn't an infinitive, but a citation form, or a set of principal parts.
The "citation form" of a lemma is, basically, the form you look up in a dictionary, or the form you use when you want to talk about the lemma itself. In English, that's the same as the infinitive, but in Latin and Greek, it's the first person singular present active indicative: dictionaries will generally list entries for amō and λύω, not for the infinitives amāre and λύειν.
The "principal parts" of a lemma are the minimal set of forms you need to construct all the other forms, assuming the verb is regular. (The definition of "regular" here varies by language and analysis.) For English verbs, it's the infinitive, the preterite/simple past, and the past participle: "break, broke, broken". From those three you can derive everything else.
Latin verbs conventionally have four principal parts, and Greek verbs six, as Tristan mentions. Latin and Greek nouns on the other hand have two, plus the noun's gender. This also varies significantly by language; there's no one-size-fits-all solution.
There are two kinds of answers, a language-learner's answer and a linguist's answer. The classical language-learner approach is based on learning a specific set of "principle parts", which are actual words from which one can form analogical sets, and group words into some number of "paradigms". In Indo-European languages, there are usually a handful of verb sets with only one member, which you just have to entirely memorize (e.g. "be"). The other approach, the linguist's approach, is to construct a single representation, the underlying form which is not a pronounced form, which contains all of the information required to generate the actually-existing words, given the rules of the language. The empirical basis of the two approaches is the same (a minimal subset of forms of the language), the memorized content (one abstract form versus a number of actual words) is different.