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I'm writing a computer science paper, and need to give a formal definition of many-sorted term algebras (which correspond to the abstract syntax of programming languages). I'm having trouble finding a standard development of the theory to use.

So far, I've been giving my own notation for use in the rest of the paper, using the definitions from the book Term Rewriting and All That as a starting point and doing the straightforward generalization to the many-sorted case. However, I suspect I've used a name incorrectly at some point, and really would like to have an existing set of definitions to work with. Anyone know one?

James Koppel
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    In the answer to this question there is a link to a paper which presents an introduction to the topic focusing on the differences between one-sorted and many-sorted algebraic treatment. Maybe that paper and its references could be helpful to you too. – amrsa Jun 16 '18 at 09:43
  • Skimming through now.

    "as A (many-sorted) signature is a pair Σ = S, Ω, where: • S is a set (of sort names); and • Ω is an (S ∗ × S )-sorted set (of operation names)"

    Already much clearer than my exposition. Thank you!

     – James Koppel Jun 16 '18 at 16:52

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