Software that is free is that which, by definition, has its full source code published.
I thought about definitionally, but after looking it up, it doesn't seem to be right.
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Using defined as a verb provides a simple answer to the grammatical issue the question raises. However, the original statement and the suggested revisions of it are untrue. It is not the case that free software is defined as software whose full code is published. Although that is an intrinsic property of free software, it also is a property of freeware. In addition, some proprietary software is distributed as published source code, under restrictions like copyrights and non-disclosure agreements. Refer to wikipedia's article about Free Software for a better definition (eg, “Free software is computer software that is distributed along with its source code, and is released under terms that guarantee users the freedom to study, adapt/modify, and distribute the software”) and for further distinguishing characteristics.
To connect “Free Software” and “published source code” with by definition, is defined as, or definitionally is wrong. Instead say that having published code is an intrinsic, innate, or inherent property of Free Software.
These two sentences are not equivalent:
By definition, free software has its full source code published.
Free software is defined as software that has its full source code published.
The first one states a property of free software, which can be read directly from the definition, but there may be more to it. The second is saying what the definition is, and therefore would need to include the entire definition in order to be correct.
So, given the definition of free software from the referenced wikipedia article, one could say:
By definition, free software provides the freedom to run the software for any purpose.
Free software is defined as software one may run for any purpose.
because there is software that may be run for any purpose which is not technically free software.
So, assuming you rearrange the sentence a bit, there are some words you could use instead of the phrase 'by definition', such as 'always', 'obviously', 'clearly', 'inherently' and so on, but I don't know of any that also communicate the key piece of information that 'by definition' expresses. Namely, that you can glean this information directly from the definition without additional reasoning.