Pipe-calculus: Difference between revisions

{{Note}} Pipe-calculus is work in progress. This wiki page serves as an informal introduction, and details may change by time.

Development of pipe-calculus stemmed from the author's conviction that syntax should be a first class element of programming languages the same way as formation rules are integral part of logical systems. A language that complies with this principle is able to recognize the syntax of input data without using a parser library. Pipe-calculus is a very minimal language with this capability.

The first attempt to implement this idea resulted in a logical system which is referred to as ''well-typed parsing''. The author's interest in process calculus led him to the realization that well-typed parsing can be translated to a calculus that uses combinators and rewriting rules instead of inference rules.

Pipe-calculus is inspired by logical programming, substructural logic, process calculus, formal grammars, automata theory, type theory (up to the lambda-cube) and the study of algebraic effects. Its early version was considered a process calculus. However it has since diverged in subtle details, it is still very close to process calculi and its presentation style maintains that heritage.

Pipe-calculus is meant to be an extensible framework. Extensions add various features to the basic calculus. One such important feature is the inclusion of variables. Variants without variables and any kind of scoped construction are called '''zero-order'''.

Somewhat surprisingly, even the zero-order calculus has a limited computational power. On the other end of the scale there are '''higher-order''' variants where variables can bind arbitrary terms. Intermediate variants can be constructed by extending the basic calculus with recursion and with a stack.