From Operational Semantics to Abstract Machines: Preliminary Results

The operational semantics of functional programming languages is frequently presented using inference rules within simple meta-logics. Such presentations of semantics can be high-level and perspicuous since meta-logics often handle numerous syntactic details in a declarative fashion. This is particularly true of the meta-logic we consider here, which includes simply typed λ-terms, quantification at higher types, and β-conversion. Evaluation of functional programming languages is also often presented using low-level descriptions based on abstract machines: simple term rewriting systems in which few high-level features are present. In this paper, we illustrate how a high-level description of evaluation using inference rules can be systematically transformed into a low-level abstract machine by removing dependencies on high-level features of the meta-logic until the resulting inference rules are so simple that they can be immediately identified as specifying an abstract machine. In particular, we present in detail the transformation of two inference rules specifying call-by-name evaluation of the untyped λ-calculus into the Krivine machine, a stack-based abstract machine that implements such evaluation. The initial specification uses the meta-logic\u27s β-conversion to perform substitutions. The resulting machine uses de Bruijn numerals and closures instead of formal substitution. We also comment on a similar construction of a simplified SECD machine implementing call-by-value evaluation. This approach to abstract machine construction provides a semantics directed method for motivating, proving correct, and extending such abstract machines

Proof-Theoretic Methods for Analysis of Functional Programs

We investigate how, in a natural deduction setting, we can specify concisely a wide variety of tasks that manipulate programs as data objects. This study will provide us with a better understanding of various kinds of manipulations of programs and also an operational understanding of numerous features and properties of a rich functional programming language. We present a technique, inspired by structural operational semantics and natural semantics, for specifying properties of, or operations on, programs. Specifications of this sort are presented as sets of inference rules and are encoded as clauses in a higher-order, intuitionistic meta-logic. Program properties are then proved by constructing proofs in this meta-logic. We argue the following points regarding these specifications and their proofs: (i) the specifications are clear and concise and they provide intuitive descriptions of the properties being described; (ii) a wide variety of program analysis tools can be specified in a single unified framework, and thus we can investigate and understand the relationship between various tools; (iii) proof theory provides a well-established and formal setting in which to examine meta-theoretic properties of these specifications; and (iv) the meta-logic we use can be implemented naturally in an extended logic programming language and thus we can produce experimental implementations of the specifications. We expect that our efforts will provide new perspectives and insights for many program manipulation tasks

Strong types for relational databases: functional pearl

Haskell's type system with multi-parameter constructor classes and functional dependencies allows static (compile-time) computations to be expressed by logic programming on the level of types. This emergent capability has been exploited for instance to model arbitrary-length tuples (heterogeneous lists), extensible records, functions with variable length argument lists, and (homogenous) lists of statically fixed length (vectors).We explain how type-level programming can be exploited to define a strongly-typed model of relational databases and operations on them. In particular, we present a strongly typed embedding of a significant subset of SQL in Haskell. In this model, meta-data is represented by type-level entities that guard the semantic correctness of database operations at compile time.Apart from the standard relational database operations, such as selection and join, we model functional dependencies (among table attributes), normal forms, and operations for database transformation. We show how functional dependency information can be represented at the type level, and can be transported through operations. This means that type inference statically computes functional dependencies on the result from those on the arguments.Our model shows that Haskell can be used to design and prototype typed languages for designing, programming, and transforming relational databasesFundação para a Ciência e a Tecnologia (FCT) - POSI/ICHS/44304/2002; SFRH/BPD/11609/2002