Recursion as a Human Universal and as a Primitive

This contribution asks, in an empirical rather than formal perspective, whether a range of descriptive phenomena in grammar usually characterized in terms of ‘recursion’ actually exhibit recursion. It is concluded that empirical evidence does not support this customary assumption. Language, while formally recursive, need not be recursive in the underlying generative mechanisms of its grammar. Hence, while recursion may well be one of the hallmarks of human nature, grammar may not be the cognitive domain where it is found. Arguments for this claim are briefly exposed and then discussed with respect to a selection of talks from the DGfS workshop on Foundations of Language Comparison: Human Universals as Constraints on Language Diversity that led to this special issue

Semantics and Validation of Shapes Schemas for RDF

We present a formal semantics and proof of soundness for shapes schemas, an expressive schema language for RDF graphs that is the foundation of Shape Expressions Language 2.0. It can be used to describe the vocabulary and the structure of an RDF graph, and to constrain the admissible properties and values for nodes in that graph. The language defines a typing mechanism called shapes against which nodes of the graph can be checked. It includes an algebraic grouping operator, a choice operator and cardinality constraints for the number of allowed occurrences of a property. Shapes can be combined using Boolean operators, and can use possibly recursive references to other shapes. We describe the syntax of the language and define its semantics. The semantics is proven to be well-defined for schemas that satisfy a reasonable syntactic restriction, namely stratified use of negation and recursion. We present two algorithms for the validation of an RDF graph against a shapes schema. The first algorithm is a direct implementation of the semantics, whereas the second is a non-trivial improvement. We also briefly give implementation guidelines

Static Elaboration of Recursion for Concurrent Software

Unlike sequential software, concurrent software needs a structuring mechanism capable of specifying constructs such as pipelines, scatter-gather, and other networks. Concurrent software languages usually provide mechanisms for dynamically creating such structures, but this makes them difficult to analyze statically. In particular, it would be very convenient to be able to put bounds on the resources (memory, processes) required by a particular system. We present a static elaboration technique that can remove bounded recursion from concurrent programs, useful for tools that cannot handle recursion such as those for formal verification and hardware synthesis. We work with SHIM, a concurrent language that provides concurrent, recursive function calls that can be used to elegantly construct concurrent structures such as pipelines and the FFT. Our technique first slices the program from every recursive call to determine which variables control the recursion, then perform a simulation of the program with respect to those variables, performing constant propagation to produce simplified code without recursion. Experimental results suggest our slicing procedure is effective at selecting just those variables that participate in the recursion and that our simulation technique for generating non-recursive code can quickly produce small non-recursive programs, making this technique practical

"Bagatelle in C arranged for VDM SoLo"

This paper sketches a reverse engineering discipline which combines formal and semi-formal methods. Central to the former is denotational semantics, expressed in the ISO/IEC 13817-1 standard specification language (VDM-SL). This is strengthened with algebra of pro- gramming, which is applied in “reverse order” so as to reconstruct formal specifications from legacy code. The latter include code slicing, a “shortcut” which trims down the complexity of handling the formal semantics of all program variables at the same time. A key point of the approach is its constructive style. Reverse calculations go as far as absorbing auxiliary variables, introducing mutual recursion (if applicable) and reversing semantic denota- tions into standard generic programming schemata such as cata/paramorphisms. The approach is illustrated for a small piece of code already studied in the code-slicing literature: Kernighan and Richtie’s word count C programming “bagatelle”.FC

Recursion Aware Modeling and Discovery For Hierarchical Software Event Log Analysis (Extended)

This extended paper presents 1) a novel hierarchy and recursion extension to the process tree model; and 2) the first, recursion aware process model discovery technique that leverages hierarchical information in event logs, typically available for software systems. This technique allows us to analyze the operational processes of software systems under real-life conditions at multiple levels of granularity. The work can be positioned in-between reverse engineering and process mining. An implementation of the proposed approach is available as a ProM plugin. Experimental results based on real-life (software) event logs demonstrate the feasibility and usefulness of the approach and show the huge potential to speed up discovery by exploiting the available hierarchy.Comment: Extended version (14 pages total) of the paper Recursion Aware Modeling and Discovery For Hierarchical Software Event Log Analysis. This Technical Report version includes the guarantee proofs for the proposed discovery algorithm

A Refinement Calculus for Logic Programs

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.Comment: 36 pages, 3 figures. To be published in Theory and Practice of Logic Programming (TPLP

Implicit learning of recursive context-free grammars

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning

Some applications of logic to feasibility in higher types

In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook result on mashine representation of basic feasible functionals. Our proofs are based on essential applications of logic. We introduce a weak fragment of second order arithmetic with second order variables ranging over functions from N into N which suitably characterizes basic feasible functionals, and show that it is a useful tool for investigating the properties of basic feasible functionals. In particular, we provide an example how one can extract feasible "programs" from mathematical proofs which use non-feasible functionals (like second order polynomials)