3 Languages

▼ |  | Redex: Practical Semantics Engineering

1 | Patterns
2 | Terms
3 | Languages
4 | Reduction Relations
5 | Metafunctions and Relations
6 | Testing
7 | GUI
8 | Typesetting
| Index

On this page:

define-language
define-extended-language
language-nts
compiled-lang?

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### 3`` Languages

All of the exports in this section are provided both by redex/reduction-semantics (which includes all non-GUI portions of Redex) and also exported by redex (which includes all of Redex).

( define-language lang-name
(non-terminal-spec pattern ...)
...)

non-terminal-spec |  | = |  | symbol
|  | | |  | (symbol ...)

This form defines the grammar of a language. It allows the definition of recursive patterns, much like a BNF, but for regular-tree grammars. It goes beyond their expressive power, however, because repeated name patterns and side-conditions can restrict matches in a context-sensitive way.

The non-terminal-spec can either by a symbol, indicating a single name for this non-terminal, or a sequence of symbols, indicating that all of the symbols refer to these productions.

As a simple example of a grammar, this is the lambda calculus:

( define-language lc-lang
(e (e e ...)
x
v)
(c (v ... c e ...)
hole)
(v ( lambda (x ...) e))
(x variable-not-otherwise-mentioned))

with non-terminals e for the expression language, x for variables, c for the evaluation contexts and v for values.

( define-extended-language language language
(non-terminal pattern ...)
...)

This form extends a language with some new, replaced, or extended non-terminals. For example, this language:

( define-extended-language lc-num-lang
lc-lang
(v .... ; extend the previous `v' non-terminal
+
number)
(x (variable-except lambda +)))

extends lc-lang with two new alternatives for the v non-terminal, carries forward the e and c non-terminals, and replaces the x non-terminal with a new one (which happens to be equivalent to the one that would have been inherited).

The four-period ellipses indicates that the new language’s non-terminal has all of the alternatives from the original language’s non-terminal, as well as any new ones. If a non-terminal occurs in both the base language and the extension, the extension’s non-terminal replaces the originals. If a non-terminal only occurs in either the base language, then it is carried forward into the extension. And, of course, extend-language lets you add new non-terminals to the language.

If a language is has a group of multiple non-terminals defined together, extending any one of those non-terminals extends all of them.

( language-nts lang) → ( listof symbol?)
lang : compiled-lang?

Returns the list of non-terminals (as symbols) that are defined by this language.

( compiled-lang? l) → boolean?
l : any/c

Returns #t if its argument was produced by language, #f otherwise.
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