Type-Directed Program Transformations for the Working Functional Programmer

We present preliminary research on Deuce+, a set of tools integrating plain text editing with structural manipulation that brings the power of expressive and extensible type-directed program transformations to everyday, working programmers without a background in computer science or mathematical theory. Deuce+ comprises three components: (i) a novel set of type-directed program transformations, (ii) support for syntax constraints for specifying "code style sheets" as a means of flexibly ensuring the consistency of both the concrete and abstract syntax of the output of program transformations, and (iii) a domain-specific language for specifying program transformations that can operate at a high level on the abstract (and/or concrete) syntax tree of a program and interface with syntax constraints to expose end-user options and alleviate tedious and potentially mutually inconsistent style choices. Currently, Deuce+ is in the design phase of development, and discovering the right usability choices for the system is of the highest priority

Initial Algebra Semantics for Cyclic Sharing Tree Structures

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural induction and structural recursion. However, for graphs or "tree-like" structures - trees involving cycles and sharing - it remains unclear what kind of inductive structures exists and how we can faithfully assign a term representation of them. In this paper we propose a simple term syntax for cyclic sharing structures that admits structural induction and recursion principles. We show that the obtained syntax is directly usable in the functional language Haskell and the proof assistant Agda, as well as ordinary data structures such as lists and trees. To achieve this goal, we use a categorical approach to initial algebra semantics in a presheaf category. That approach follows the line of Fiore, Plotkin and Turi's models of abstract syntax with variable binding

Structural abstract interpretation, A formal study using Coq

interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory based theorem prover Coq, using inductive types for syntax and structural recursive programming for the abstract interpreter's kernel. The abstract interpreter can then be proved correct with respect to a Hoare logic for the programming language

Information structural notions and the fallacy of invariant correlates

In a first step, definitions of the irreducible information structural categories are given, and in a second step, it is shown that there are no invariant phonological or otherwise grammatical correlates of these categories. In other words, the phonology, syntax or morphology are unable to define information structure. It is a common mistake that information structural categories are expressed by invariant grammatical correlates, be they syntactic, morphological or phonological. It is rather the case that grammatical cues help speaker and hearer to sort out which element carries which information structural role, and only in this sense are the grammatical correlates of information structure important. Languages display variation as to the role of grammar in enhancing categories of information structure, and this variation reflects the variation found in the ‘normal’ syntax and phonology of languages

Dialectal variation in german 3-verb clusters : a surface-oriented optimality theoretic account

We present data from an empirical investigation on the dialectal variation in the syntax of German 3-verb clusters, consisting of a temporal auxiliary, a modal verb, and a predicative verb. The ordering possibilities vary greatly among the dialects. Some of the orders that we found occur only under particular stress assignments. We assume that these orders fulfil an information structural purpose and that the reordering processes are changes only in the linear order of the elements which is represented exclusively at the surface syntactic level, PF (Phonetic Form). Our Optimality theoretic account offers a multifactorial perspective on the phenomenon

The syntax of slavic predicate case

In this article I provide a syntactic framework for case patterns found in Slavic secondary predicates

Distributive Laws for Monotone Specifications

Turi and Plotkin introduced an elegant approach to structural operational semantics based on universal coalgebra, parametric in the type of syntax and the type of behaviour. Their framework includes abstract GSOS, a categorical generalisation of the classical GSOS rule format, as well as its categorical dual, coGSOS. Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence. Unfortunately, the combination of the two formats does not feature these desirable properties. We show that monotone specifications - that disallow negative premises - do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004