This peculiar behavior is about to be tested in court. Three groups have brought a lawsuit seeking to force Mr. Trump and his advisers to follow the laws that govern presidential and federal agency records. So far, they allege, the president has failed to do so.

At issue are the Presidential Records Act, which covers Mr. Trump’s activities, and the Federal Records Act, which covers agencies such as the State Department. In normal procedure, State provides interpreters for such meetings. The presidential records law was passed by Congress in 1978, after Richard M. Nixon’s resignation, to prevent Nixon from destroying or otherwise disposing of his records and secretly recorded White House conversations. The law established that records of the presidency relating to duties of the office are the property of the American people, and it ended the previous tradition of presidential records belonging to former presidents. Importantly, the law also demands that the president take care to ensure his activities are documented and preserved for eventual access by the public — a vital form of accountability. Likewise, the Federal Records Act requires government officials to document their activities and preserve their history.

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The three organizations questioning Mr. Trump’s adherence to the law are Citizens for Responsibility and Ethics in Washington, a nonprofit government accountability group; the National Security Archive, a leading nonprofit research group at George Washington University that uses the Freedom of Information Act extensively; and the Society for Historians of American Foreign Relations, which represents scholars seeking to document U.S. diplomacy. In addition to Mr. Trump’s meetings with Mr. Putin, the groups question in their lawsuit whether an adequate record exists of the president’s conversations with North Korean leader Kim Jong Un in Hanoi, or of senior White House aide Jared Kushner’s meetings with Saudi Arabia’s Crown Prince Mohammed bin Salman.

The failure to document these meetings is not only about compliance with the law. Mr. Trump’s secrecy deprives his own advisers of knowledge about what is going on and thus harms their ability to give him good advice. It will blast a huge crater in the work of historians who attempt to piece together what transpired in Mr. Trump’s presidency. It also deprives the American people of a basic method of holding Mr. Trump accountable for his performance. No doubt he likes it that way. But the courts must insist that no president is above the law, including the law for keeping honest and full records of the presidency.