Halliday & Matthiessen (1999: 30-4):
We noted above that the semantics/lexicogrammar of natural language is itself a 'realisation' (an abstract construction) of daily experience. Likewise, the system we use to explore the semantics/lexicogrammar — our theory of semantics and our grammatics — is a 'realisation' of that part of daily experience that is constituted by semantics and lexicogrammar; that is, it is an abstract construction of language. This system is itself a semiotic one — a metalanguage; in Firth's more everyday terms, it is language turned back on itself (cf. Matthiessen & Nesbitt, 1996). So whereas a language is (from an ideational point of view) a resource for construing our experience of the world, a metalanguage is a resource for construing our experience of language.
Metalanguage has the same basic properties as any semiotic system. This means that it is stratified. It construes language in abstract theoretical terms; but this construal is in turn realised as some form of representation — either language itself, in discursive constructions of theory, or some form of designed semiotic (system networks, constituency rules, conceptual networks, logical formulae, and so on). In the environment of computational work, this level is in turn realised in some form of implementation (stated in a programming language1 such as LISP, Prolog or C). We could summarise as follows (see Figure 1-7):
- metalanguage construes language at various strata (theoretical construal, representation, and implementation)
- metalanguage construes language in terms of resources (the circles) and processes using the resources (the arrows), where processes include description, deduction and compilation.
- the relationship between theoretical construal and representation should preferably be a natural one (note the 'should be'!), while the relationship between representation and implementation is likely to be more arbitrary (for instance, it should not matter whether LISP, Prolog or C is used).
- the range of phenomena accounted for in metalanguage tends to decrease at lower levels. (A primary goal of research is always to expand it.)
If we recognise stratification as an aspect of the design of metalanguage, we are in a position to locate aspects of the overall construal of meaning at the appropriate stratum. …
Thus any account of [language] has to be metalinguistically stratified. It has to be constructed as a theoretical model out of the resources the theory provides and according to the constraints imposed by these resources. …
As we have already noted, the representational semiotic may also be language itself — the theory may be represented discursively in the registers) of linguistics. In this case, the relationship between theory and language is similar to the relationship between 'theme' and 'language' in Hasan's (1985/9) theory of verbal art — a relationship where theory might be construed as a connotative semiotic (in Hjelmslev's, 1943, conception: a semiotic system whose expression plane is a semiotic system) …
Finally, the representational semiotic may also be a diagrammatic one — e.g. network graphs, tree diagrams, our circle diagrams. With such graphic representation, it is important to ask (i) if the information represented graphically can be restated in some other form of representation and (ii) if its realisational relationship with respect to theory is clear.