The term "'adl" literally means "moderation" and refraining from going to extremes. If the preposition "'an" (عن) is added to it, then it means to relinquish or give up doing something.  This word has also been used to means "like" "equal" and such likes. Sometimes, it has been used to mean substitute or compensation.[1] However, when it comes to theology and ideology etc. it is discussed with a view to the following meanings:
1. 'Adl means to behave in a balanced way or to act equitably without discrimination when all deserve equally.
2. 'Adl means to stay away from major sins and not to be known for a committing a sin. Of course, 'adl is used in this sense in jurisprudence.  However, in theology, 'adl is applied or used in imamate and guardianship of the jurist.
3. In a moral sense, 'adl means to respect others' rights, as opposed to violating them.
4. The term 'adl has a social meaning which is to distribute equally the social privileges and to be able to benefit equally from educational, cultural, scientific, economic and other privileges.
5. 'Adl in the sense of being moderate and harmonious denotes placing things in their rightful place in the sense that those things create, as a result of interaction with other things, a good system and steer the world towards a specific goal. This meaning, which has a view towards the entire universe, is considered a philosophical concept.
6. Justice means to observe what is due in matters appertained to legislation, judgment, accountability, giving rewards or imposing punishment as opposed to injustice or oppression which means giving less to someone who deserve or impose more punishment that he deserves. In other words, the rewards and punishments are disproportionate.
The term 'adl has also been used in its various literal and technical meanings in the Holy Quran[2] but in most cases, the term has been used to negate injustice on the part of Allah in this world and in the hereafter when He bestows rewards or inflicts punishments on His creatures.
In other cases, justice and equity have been considered to be important goals of prophethood. Thus, the prophets and other people have been commanded not only to establish and uphold justice and respect one another's rights but also to respect others' rights or pass just, fair and equitable judgments.  In addition, Allah, the Glorified, describes the creation of the universe, the earth and humans as moderate and balanced.
Among the foregoing meanings, divine justice in terms of giving reward and inflicting punishment is more prominent and has been subject to debate and contention. The Ash'arites (followers of Abul Hasan Ash'ari) maintain that nothing is necessary or obligatory on Allah.  Believing in something being necessary upon Allah means that we are imposing something on Allah and deciding what Allah should do, whereas in fact, no servant has the right to decide what Allah should do because it limits His power, intention and the sphere of His activity. Therefore, no one can say that "it is necessary upon Allah to do justice and to avoid what is evil such as injustice".  Rather, whatever Allah does is pure justice, even if He may be taking all believers to Hell and all unbelievers to Paradise. That is not impossible.
The root cause of this misgiving is the way the Mu'azilites (Mu'azilah) have described divine justice. The Mu'atazilites who are the followers of Wasil bin 'Ataa believe in rational and inherent good and evil and based on this belief, they deem it necessary for Allah to do justice in both this world and the next. The way they describe divine justice somehow projects a kind of limitation of divine authority and determination of divine duty!
Meanwhile, the Imamiyah Shia (followers of the twelve infallible imams) believe that in view of inherent and rational good and evil and essential requirements of Allah, as a perfect and necessary being,  it is not possible for Allah to do evil acts such as breaking one's promise, telling lies and doing injustice.  When it is not possible for Allah to commit evil acts, whatever Allah, therefore, does would be good and just. Hence, given the promises which Allah has given in the Holy Quran and in view of the fact that breach of promise is impossible on His part, the infidels, hypocrites and pagans will not possibly go to Paradise. Similarly, God will not take the prophets and believers to Hell.
To put it more clearly, doing justice or what is right, and respecting covenants are essential on the part of Allah and it is not becoming of Allah to commit evil. That does not mean it is wajib (obligatory) on Allah to do justice and it is haram (forbidden) for him to commit evil. Essentiality here has been used in the sense of philosophy necessity as opposed to philosophical impossibility; it has not been used in the rational or legal necessity which means imposing a duty on Allah and holding him responsible for it. Therefore, the role of human intellect is to discover and explore the actuality, not to issue a ruling. The intellect distinguishes that Allah is definitely Just and He does not and will not do injustice to anyone in this world and hereafter. But it can never make Allah duty-bound or impose an obligation on Allah. In the wake of this contention, Imamiyah and Mu'atazilah were later known as 'adliyah (proponents of justice) and the two schools added "justice" to the principles of the religion. On the other hand, the Ash'arites still considered monotheism, prophecy and resurrection as the only principles of faith. Of course, it should be noted that there is a difference between Mu'atazilah's notion of justice and that of Imamiyah. The Shia view of justice is free of both extremes.
It is necessary to mention that justice in this sense has its implications and connotations which have been used and studied in jurisprudence and theology. They are:
A) Justice in creation:
Every creature has been created in a balanced and moderate fashion with all parts and components put together in such a way as to help it achieve perfection. On the other hand, he has given every creature a special role to play so that the entire universe may, in a coherent and consistent manner, move on towards realizing a predetermined goal.
B) Justice in legislation:
Legal justice has two implications:

C) Justice on the Day of Resurrection:
God, the Glorified, will do justice on the Day of Judgment in view of the foregoing details.
D) Justice in enforcing laws:
God, the Glorified, will also treat with justice when it comes to implementing divine commands; He will give rewards to the good doers and inflict punishment on the evil-doers.  It goes without saying that in the supplications which are attributed to the Infallible Imams (AS), the Imams seek refuge to Allah from His justice. The secret is that obeying Allah in such a way as being worthy of Him and thanking Him in a worthy manner for His bounties and blessing to make up for His gifts and blessings is not within anyone's capacity and ability. Because the very success that Allah bestows upon His creature and then thanking Him are yet another gift from Allah requiring another thanksgiving.
On the other hand, obedience and thanksgiving are for the blessings which Allah has bestowed upon us. Therefore, the divine reward which Allah is going to give us in the next world is an extra grace and blessing. That is to say, since Allah's blessing precedes his wrath and Allah, the Glorified, has made it incumbent upon himself to be merciful[6], it is the divine sunnah (practice) to give rewards once again for the obedience and gratefulness of His servants. For this reason, Allah grants the believer many times the size of their good deeds.  He also decreases from their punishments in one way or the other, protecting them from worldly calamities, and decreasing the pain of death and graves and not punishing them to the extent they deserve.
Therefore, when it comes to gracious conduct, Allah is Merciful, Compassionate and All-Forgiving.  He repays an act of kindness manifold and those who are just, kind and gracious are superior in the eye of Allah than others. As a result, He is above justice because He is the ruler, the absolute master and pure good and pure mercy.
It is noteworthy that belief in divine justice in all its forms has a lot of scientific, ideological and practical benefits and aftermaths. This belief is used along with the arguments concerning imamate, prophethood, resurrection and so forth. It also plays a tremendous role in deciphering and deducing Islamic laws.  With hope in divine justice on Judgment Day, patience and forbearance against oppression and tyranny (in case one is unable to defend himself against injustice) will become easier and believers are encouraged to excel one another in doing good, establishing justice and equity in society and respecting one another's rights.
Sources and references:
1. Subhani, Ja'far, al-Ilahyat, vol.1-3, International Center for Islamic Studies, second edition, 1409 A.H, p. 290 -273 and p. 301 -310.
2. Subhani, Ja'far Buhuth fi al-Melal wa al-Nehal, vol.2, Hawzah Management Center, second edition, Qom, 1366, p. 329 -334.
3. Shahristani, Abdul Karim, al-Melal wa al-Nehal, vol.1-2, Al-Anjelu, Egypt, second edition, 1375 A.H., Egypt, p. 47 and 48.
4. Halabi, Abi al-Salah, Taqrib al-Ma'aref, Islamic Propagations Office, 1363, Qom, p. 88-92, and 71.
5. Alam al-Huda, Sayyid Murteza, al-Zakhirah, Islamic Propagations Office, 1411, A.H. p. 211 – 255.
6. Mutahhari, Murteza, Divine Justice, tenth edition, year, 57, p. 59 – 66.
7. Tusi, Khawja Nasiruddin Kashf al-Murad, Shakuri, fourth edition, year 73 (1994), Qom, p. 356 -367.
8. Mesbah Yazi, Muhammad Taqi, Ideological Instruction, vol.1-2, Islamic Propagations ffice, 12^th edition, year 76 (1997), Qom p. 190 -199, (Lesson 20).
9. Mesbah Yazi, Muhammad Taqi, Morality in the Quran, vol.1, Imam Khomeini (ra) Educational and Research Institute, Qom, p. 72.
10. Sa'eidi Mehr, Muhammad, Islamic Theological Instruction, vol.1, p. second edition, 81, Qom, 313 -325.

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