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Functional dependencies are a popular and useful extension to Haskell style type classes. We give a reformulation of functional dependencies in terms of Constraint Handling Rules (CHRs). In previous work, CHRs have been employed for describing user-programmable type extensions in the context of Haskell style type classes. Here, we make use of CHRs to provide for the first time a concise result that under some sufficient conditions, functional dependencies allow for sound, complete and decidable type inference. The sufficient conditions imposed on functional dependencies can be very limiting. We show how to safely relax these conditions and suggest several sound extensions of functional dependencies. Our results allow for a better understanding of functional dependencies and open up the opportunity for new applications.

Bibliography 241 Index 243

3.1 Errors 193.2 Variables, Constructors, Operators, and Literals 203.3 Curried Applications and Lambda Abstractions 213.4 Operator Applications 213.5 Sections 223.6 Conditionals 233.7 Lists 233.8 Tuples 243.9 Unit Expressions and Parenthesized Expessions 253.10 Arithmetic Sequences 253.11 List Comprehensions 253.12 Let Expressions 273.13 Case Expressions 273.14 Do Expressions 293.15 Datatypes with Field Labels 293.16 Expression Type Signatures 323.17 Pattern Matching 32

5.1 Module Structure 685.2 Export Lists 695.3 Import Declarations 715.4 Importing and Exporting Instance Declarations 745.5 Name Clashes and Closure 745.6 Standard Prelude 775.7 Separate Compilation 785.8 Abstract Datatypes 78

In the end, research on functional languages does little good unless they are used to write something other than compilers for functional languages. However, if one scans a typical functional programming conference or journal, one mainly sees papers on twists in language design, speed-ups in compiled code, clever new analyses, or refinements to semantic models. It much less common to see a paper that considers a functional language as a tool to some other practical end. We would like to see this change.The Journal of Functional Programming carries, and will continue to carry, articles on all aspects of functional programming from lambda calculus theory to language design to implementation. But we have specially sought, and will continue to seek, papers on functional programming practice and experience.Research and papers on practice and experience sometimes receive less attention because they are perceived as possessing less academic content. So we want to remind potential authors that we have published a number of papers on this topic in the past, and to spell out the criteria we apply to such papers.

25.1 Library Locale 231

Contents i Preface vii1.1 Program Structure 31.2 The Haskell Kernel 41.3 Values and Types 41.4 Namespaces 5