فهرس المكتبة على الحاسوب.

With the meaning The library catalog is on the computer, it is a complete sentence in Arabic.

It is a nominal sentence:

• فهرس المكتبة = the subject
• على الحاسوب = the predicate

Arabic often makes full present-tense sentences without any separate word for is. So what looks short to an English speaker can still be a complete sentence.

Out of context, the same words could also appear as a heading or label, but with this meaning, it works as a sentence.

A careful fully vocalized MSA reading is:

فِهْرِسُ الْمَكْتَبَةِ عَلَى الْحَاسُوبِ

A simple transliteration is:

fihrisu al-maktabati ʿalā al-ḥāsūbi

In normal pause, many speakers drop the final case vowels, so you may hear something closer to:

fihris al-maktaba ʿalā al-ḥāsūb

Here it is a noun, meaning catalog or index.

So فهرس المكتبة means the library catalog or literally catalog of the library.

This is a good question because Arabic writing often omits short vowels, and فهرس could be read differently in another context. But in this sentence, with this meaning, it is the noun fihris.

Because فهرس المكتبة is an iḍāfa construction, often called a construct phrase.

In an iḍāfa:

• the first noun usually does not take ال
• the second noun tells you whether the whole phrase is definite or indefinite

So:

• فهرس مكتبة = a library catalog / catalog of a library
• فهرس المكتبة = the library catalog / catalog of the library

Even without ال on فهرس, the whole phrase is definite because المكتبة is definite.

Because Arabic iḍāfa works in the opposite order from many English phrases.

Arabic says:

• فهرس المكتبة
• literally: catalog the-library
• natural English: the library catalog or the catalog of the library

So the thing being possessed or described comes first, and the owner or associated noun comes second.

A similar pattern:

• باب البيت = the door of the house = the house door

In present-tense nominal sentences, Arabic normally leaves out the verb to be.

So:

• فهرس المكتبة على الحاسوب literally looks like:
• the library catalog on the computer

But the intended English meaning is:

• The library catalog is on the computer

If you wanted past or future, Arabic would usually use a verb:

• كان فهرس المكتبة على الحاسوب = The library catalog was on the computer
• سيكون فهرس المكتبة على الحاسوب = The library catalog will be on the computer

Because it is the second part of an iḍāfa construction.

In iḍāfa:

• the first noun takes its case from its role in the sentence
• the second noun is genitive

So in a fully vocalized version:

• فهرسُ = nominative, because it is the subject
• المكتبةِ = genitive, because it is the second term of the iḍāfa

That is why the full form is: فهرسُ المكتبةِ

It is the predicate of the sentence, more specifically a prepositional phrase used as a predicate.

Breakdown:

• على = on
• الحاسوب = the computer

So على الحاسوب tells you where the library catalog is.

In Arabic grammar, a prepositional phrase like this can serve as the predicate of a nominal sentence. You do not need an extra verb like is.

Because على is commonly used in Arabic for things that are:

• on a device
• on a screen
• on a system
• on a platform

So على الحاسوب is a natural way to say on the computer.

A learner may wonder about في الحاسوب. That can exist too, but it often sounds more like in the computer, with a more literal sense of being inside it.
So:

• على الحاسوب = on the computer, using the computer, available via the computer
• في الحاسوب = in the computer, inside the computer

The letter ة is called tāʾ marbūṭa.

Its pronunciation depends on context:

• in pause, it is usually pronounced like -a
• when followed by a grammatical ending in careful MSA, it is pronounced with a t

So:

• in pause: al-maktaba
• in full grammatical reading here: al-maktabati

That is why you may see or hear both types of pronunciation, depending on how carefully the sentence is being read.

In fully vocalized formal MSA, the sentence is:

فِهْرِسُ الْمَكْتَبَةِ عَلَى الْحَاسُوبِ

The endings are:

• فهرسُ: -u because it is the subject of the nominal sentence
• المكتبةِ: -i because it is the second noun of an iḍāfa
• الحاسوبِ: -i because it comes after the preposition على

So the grammatical pattern is:

• subject in the nominative
• second term of iḍāfa in the genitive
• noun after a preposition in the genitive

Yes. Arabic script usually leaves out short vowels, so فهرس can be ambiguous when written by itself.

Depending on context, it could be read in different ways. But in this sentence, if the meaning is The library catalog is on the computer, then the correct reading is the noun فِهرِس.

This is very common in Arabic:

• the writing gives the consonants
• the context tells you the exact reading

That is one reason why learners should pay close attention to sentence meaning and structure, not just the bare spelling.