A monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library's interface is similar to those of many other parser combinator libraries, with two important differences: one is that the interface clearly specifies which parts of the constructed parsers may be infinite, and which parts have to be finite, using dependent types and a combination of induction and coinduction; and the other is that the parser type is unusually informative.The library comes with a formal semantics, using which it is proved that the parser combinators are as expressive as possible. The implementation is supported by a machine-checked correctness proof.

http://www.cse.chalmers.se/~nad/publications/danielsson-parser-combinators.pdf

Total parser combinators

We propose a novel context-free grammar representation for parsing libraries in a pure programming language. Our representation explicitizes the recursion in the grammar, thus avoiding fundamental limitations of the grammar model currently employed by parser combinator libraries. Additionally, we decouple the grammar from its semantic actions using techniques from the Multirec generic programming library. The look and feel of the grammar and semantic actions remain close to traditional EBNF and syntax-directed definitions respectively.

Explicitly Recursive Grammar Combinators

We propose a novel context-free grammar representation for parsing libraries in a pure programming language. Our representation explicitizes the recursion in the grammar, thus avoiding fundamental limitations of the grammar model currently employed by parser combinator libraries. Additionally, we decouple the grammar from its semantic actions using techniques from the Multirec generic programming library. The look and feel of the grammar and semantic actions remain close to traditional EBNF and syntax-directed definitions respectively.

In an accompanying technical report, we demonstrate that our representation supports more declarative implementations of grammar transformations than other work. The ideas described in this paper form the basis for our freely available grammar-combinators parsing library.

https://lirias.kuleuven.be/bitstream/123456789/295467/1/tekst.pdf

Explicitly recursive grammar combinators: a better model for shallow parser DSLs

We define a finally tagless, shallow embedding of a typed grammar language. In order to avoid the limitations of traditional parser combinator libraries (no bottom-up parsing, no full grammar analysis or transformation), we require object-language recursion to be observable in the meta-language. Since existing proposals for recursive constructs are not fully satisfactory, we propose new finally tagless primitive recursive constructs to solve the problem. To do this in a well-typed way, we require considerable infrastructure, for which we reuse techniques from the multirec generic programming library. Our infrastructure allows a precise model of the complex interaction between a grammar, a parsing algorithm and a set of semantic actions. On the flip side, our approach requires the grammar author to provide a type-and value-level encoding of the grammar's domain and we can provide only a limited form of constructs like many. We demonstrate five meta-language grammar algorithms exploiting our model, including a grammar pretty-printer, a reachability analysis, a translation of quantified recursive constructs to the standard one and an implementation of the left-corner grammar transform. The work we present forms the basis of the grammar-combinators parsing library 1 , which is the first to work with a precise, shallow model of abstract context-free grammars in a classical (not dependently typed) functional language and which supports a wide range of grammar manipulation primitives. From a more general point of view, our work shows a solution to the well-studied problem of observable sharing in shallowly embedded domain-specific languages and specifically in finally tagless domain-specific languages.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0956796812000226

Finally tagless observable recursion for an abstract grammar model

Ideally complexity is managed by composing a system out of quite a few, more or less independent, and much smaller descriptions of various aspects of the overall artefact. When describing (extensible) programming languages, attribute grammars have turned out to be an excellent tool for modular definition and integration of their different aspects. In this paper we show how to construct a programming language implementation by composing a collection of separately compiled attribute grammar fragments, each describing a separate aspect of the language.More specifically we describe how to use a coherent set of libraries and tools which together makes it possible to express this directly in Haskell, where the correctness of the composition is enforced through the Haskell type system's ability to represent attribute grammars as plain Haskell values and their interfaces as Haskell types makes this possible.Semantic objects thus constructed can be combined with parsers which are constructed on the fly out of a collection of grammar fragments, which are also represented by typed Haskell values. Again the type checker prevents unsound compositions.Using a very small example language and some simple extensions, we show how our techniques fit together towards the construction of extensible compilers out of a collection of pre-compiled, statically type-checked "language definition fragments".

/pdf/first-class-syntax-semantics-and-their-composition-536ldpaowj.pdf

First Class Syntax, Semantics, and Their Composition

Parser combinators are a popular tool for designing parsers in functional programming languages. If such combinators generate an abstract representation of the grammar as an intermediate step, it becomes easier to perform analyses and transformations that can improve the behaviour of the resulting parser. Grammar transformations must satisfy a number of invariants. In particular, they have to preserve the semantics associated with the grammar. Using conventional type systems, these constraints cannot be expressed satisfactorily, but as we show in this article, dependent types are a natural fit. We present a framework for grammars and grammar transformations using Agda. We implement the left-corner transformation for left-recursion removal and prove a language-inclusion property as use cases.

Kasper Brink

Papers

Dependently typed grammars