Typed Generic Traversal With Term Rewriting Strategies

A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by designated generic strategy types gamma. We consider two generic strategy types, namely the types of type-preserving and type-unifying strategies. S'_{gamma} offers traversal combinators to construct traversals or schemes thereof from many-sorted and generic strategies. The traversal combinators model different forms of one-step traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a many-sorted strategy $s$ to a generic type gamma. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be type-dependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program transformation and program analysis.Comment: 85 pages, submitted for publication to the Journal of Logic and Algebraic Programmin

A Study In Monads

This thesis investigates both theory and applications of the monad in a functional setting. Monads are constructs simulating different types of computations, such as indeterminism, exception handling, stateful computations, IO, and much more, all in the functional paradigm. The thesis starts by defining the monad, and builds up the theory around it. Three large implementaional examples using monads are presented: One implementation of a small interpreter for lambda calculus with graph sharing, one framework for writing symmetric cryptographic algorithms, and one more theoretical construction of a catamorphism and comprehension based monadic query language. All of these examples uses combinations of several monads to form complex computations with a high level of expressiveness. Other related constructs are discussed, as well as a presentation of the foundation for monads in category theory. A new monad is also introduced, the Pair monad. This monad is a generalisation of the list monad, and simulates substitution in tree-like structures, such as lambda terms. Furthermore, the thesis makes an investigation into the Curry-Howard Correspondence with a first order lambda calculus extended with monads, called computational lambda calculus. This results in a sublogic of constructive S4 modal logic. The thesis also uses the Kripke semantic for this logic to deduce a Kripke semantic for type setting lambda terms in computational lambda calculus

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Embedding programming languages: Prolog in Haskell

This thesis focuses on combining the two most important and wide spread declarative programming paradigms, functional and logic programming. The proposed approach aims at adding logic programming features which are native to Prolog onto Haskell. We develop extensions which replicate the target language by utilizing advanced features of the host language for an efficient implementation. The thesis aims to provide insights into merging two declarative languages namely, Haskell and Prolog by embedding the latter into the former and analyzing the results of doing so as the two languages have conflicting characteristics. The finished products will be something similar to a haskellised Prolog which has logic programming-like capabilities. --Leaf ii.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b214135

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

The design and implementation of a relational programming system.

The declarative class of computer languages consists mainly of two paradigms - the logic and the functional. Much research has been devoted in recent years to the integration of the two with the aim of securing the advantages of both without retaining their disadvantages. To date this research has, arguably, been less fruitful than initially hoped. A large number of composite functional/logical languages have been proposed but have generally been marred by the lack of a firm, cohesive, mathematical basis. More recently new declarative paradigms, equational and constraint languages, have been advocated. These however do not fully encompass those features we perceive as being central to functional and logic languages. The crucial functional features are higher-order definitions, static polymorphic typing, applicative expressions and laziness. The crucial logic features are ability to reason about both functional and non-functional relationships and to handle computations involving search. This thesis advocates a new declarative paradigm which lies midway between functional and logic languages - the so-called relational paradigm. In a relationallanguage program and data alike are denoted by relations. All expressions are relations constructed from simpler expressions using operators which form a relational algebra. The impetus for use of relations in a declarative language comes from observations concerning their connection to functional and logic programming. Relations are mathematically more general than functions modelling non-functional as well as functional relationships. They also form the basis of many logic languages, for example, Prolog. This thesis proposes a new relational language based entirely on binary relations, named Drusilla. We demonstrate the functional and logic aspects of Drusilla. It retains the higher-order objects and polymorphism found in modern functional languages but handles non-determinism and models relationships between objects in the manner of a logic language with notion of algorithm being composed of logic and control elements. Different programming styles - functional, logic and relational- are illustrated. However, such expressive power does not come for free; it has associated with it a high cost of implementation. Two main techniques are used in the necessarily complex language interpreter. A type inference system checks programs to ensure they are meaningful and simultaneously performs automatic representation selection for relations. A symbolic manipulation system transforms programs to improve. efficiency of expressions and to increase the number of possible representations for relations while preserving program meaning