Types of Affix Grammars
In the simplest type of affix grammar, affixes can only take values from a finite domain, and affix values can only be related through agreement, as in the example. Applied in this way, affixes increase compactness of grammars, but do not add expressive power.
Another approach is to allow affixes to take arbitrary strings as values and allow concatenations of affixes to be used in rules. The ranges of allowable values for affixes can be described with context-free grammar rules. This produces the formalism of two-level grammars, also known as Van Wijngaarden grammars or 2VW grammars. These have been successfully used to describe complicated languages, in particular, the syntax of the Algol 68 programming language. However, it turns out that, even though affix values can only be manipulated with string concatenation, this formalism is Turing complete; hence, even the most basic questions about the language described by an arbitrary 2VW grammar are undecidable in general.
Extended Affix Grammars, developed in the 1980s, are a more restricted version of the same idea. They were mainly applied to describe the grammar of natural language, e.g. English.
Another possibility is to allow the values of affixes to be computed by code written in some programming language. Two basic approaches have been used:
- In attribute grammars, the affixes (called attributes) can take values from arbitrary domains (e.g. integer or real numbers, complex data structures) and arbitrary functions can be specified, written in a language of choice, to describe how affix values in rules are derived from each other.
- In CDL (the Compiler Description Language) and its successor CDL2, developed in the 1970s, fragments of source code (usually in assembly language) can be used in rules instead of normal right-hand sides, allowing primitives for input scanning and affix value computations to be expressed directly. Designed as a basis for practical compiler construction, this approach was used to write compilers, and other software, e.g. a text editor.
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