Is it valid to define functions in JSON results?

No.

JSON is purely meant to be a data description language. As noted on http://www.json.org, it is a "lightweight data-interchange format." - not a programming language.

Per http://en.wikipedia.org/wiki/JSON, the "basic types" supported are:

• Number (integer, real, or floating point)
• String (double-quoted Unicode with backslash escaping)
• Boolean (true and false)
• Array (an ordered sequence of values, comma-separated and enclosed in square brackets)
• Object (collection of key:value pairs, comma-separated and enclosed in curly braces)
• null

The problem is that JSON as a data definition language evolved out of JSON as a JavaScript Object Notation. Since Javascript supports eval on JSON, it is legitimate to put JSON code inside JSON (in that use-case). If you're using JSON to pass data remotely, then I would say it is bad practice to put methods in the JSON because you may not have modeled your client-server interaction well. And, further, when wishing to use JSON as a data description language I would say you could get yourself into trouble by embedding methods because some JSON parsers were written with only data description in mind and may not support method definitions in the structure.

Wikipedia JSON entry makes a good case for not including methods in JSON, citing security concerns:

Unless you absolutely trust the source of the text, and you have a need to parse and accept text that is not strictly JSON compliant, you should avoid eval() and use JSON.parse() or another JSON specific parser instead. A JSON parser will recognize only JSON text and will reject other text, which could contain malevolent JavaScript. In browsers that provide native JSON support, JSON parsers are also much faster than eval. It is expected that native JSON support will be included in the next ECMAScript standard.

Let's quote one of the spec's - https://www.rfc-editor.org/rfc/rfc7159#section-12

The The JavaScript Object Notation (JSON) Data Interchange Format Specification states:

JSON is a subset of JavaScript but excludes assignment and invocation.

Since JSON's syntax is borrowed from JavaScript, it is possible to use that language's "eval()" function to parse JSON texts. This generally constitutes an unacceptable security risk, since the text
could contain executable code along with data declarations. The same consideration applies to the use of eval()-like functions in any other programming language in which JSON texts conform to that
language's syntax.

So all answers which state, that functions are not part of the JSON standard are correct.

The official answer is: No, it is not valid to define functions in JSON results!

The answer could be yes, because "code is data" and "data is code". Even if JSON is used as a language independent data serialization format, a tunneling of "code" through other types will work.

A JSON string might be used to pass a JS function to the client-side browser for execution.

[{"data":[["1","2"],["3","4"]],"aFunction":"function(){return \"foo bar\";}"}]

This leads to question's like: How to "https://stackoverflow.com/questions/939326/execute-javascript-code-stored-as-a-string".

Be prepared, to raise your "eval() is evil" flag and stick your "do not tunnel functions through JSON" flag next to it.

It is not standard as far as I know. A quick look at http://json.org/ confirms this.