Other answers relate to the definition of a formal programming language in accordance with Informatics. However, this answer relates to the definition of a formal programming language according to social (wannabe) Science.
According to dictionary.com , one of the definitions for “formal” is being in accordance with the usual requirements, customs, etc.; conventional being in accordance with the usual requirements, customs, etc.; conventional .
A formal programming language is a programming language that is widely used and accepted by the person who talks about it. So this is the domain and the conversation. Perhaps the best way to formulate is “popular,” “traditional,” “core,” or “generally accepted” programming language. For example, in business and industry this applies to SQL , Java , C# , C++ , Python and PHP .
Examples of informal programming languages are SPL (Shakespeare's programming language), FORTRAN and CoffeeScript . More precisely, one language is more conditional and thus formal than another, not to mention that one language is formal and the other unofficial. In the end, Lisp will be a very informal programming language for building a website, but it is a very formal programming language for developing artificial intelligence research.
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