Binding-time analysis determines when variables and expressions in a program can be bound to their values, distinguishing between early (compile-time) and late (run-time) binding. Binding-time information can be used by compilers to produce more efficient target programs by partially evaluating programs at compile-time. Binding-time analysis has been formulated in abstract interpretation contexts and more recently in a type-theoretic setting. In a type-theoretic setting binding-time analysis is a type inference problem: the problem of inferring a completion of a λ-term e with binding-time annotations such that e satisfies the typing rules. Nielson and Nielson and Schmidt have shown that every simply typed λ-term has a unique completion ê that minimizes late binding in TML, a monomorphic type system with explicit binding-time annotations, and they present exponential time algorithms for computing such minimal completions. 1 Gomard proves the same results for a variant of his two-level λ-calculus without a so-called “lifting ” rule. He presents another algorithm for inferring completions in this somewhat restricted type system and states that it can be implemented in time O(n 3). He conjectures that the completions computed are minimal.

peteOCAELN.engin.UMich.EDU We have developed a new style of semantic definition called high-level semantics. In constrast to traditional de-notational semantics, high-level semantics is suitable for both defining the functional meaning of programming lan-guages, as well as describing realistic compiler implcmen-tations. Moreover, high-level specifications are consid-erably more descriptive and intelligible than traditional specifications. This paper describer the compiler generator MESS, which embodies the principles of high-level semantics. MESS has been used to generate compilers for nontrivial languages. The compilers are efficient, and produce ob-ject programs that are competitive with those generated by hand-written compilers. 1

The objective of this thesis is to explore the connections between abstract interpretation and attribute grammars as frameworks in program analysis. Abstract interpretation is a semantics-based program analysis method. A large class of data flow analysis problems can be expressed as non-standard semantics where the “meaning ” contains information about the runtime behaviour of programs. In an abstract interpretation the analysis is proved correct by relating it to the usual semantics for the language. Attribute grammars provide a method and notation to specify code generation and program analysis directly from the syntax of the programming language. They are especially used for describing compilation of programming languages and very efficient evaluators have been developed for subclasses of attribute grammars. By relating abstract interpretation and attribute grammars we obtain a closer connection between the specification and implementation of abstract interpretations which at the same time facilitates the correctness proofs of interpretations. Implementation and specification of abstract interpretations using circular attribute grammars is realised with an evaluator system for a class of domain theoretic attribute grammars. In this system thecircularity of attribute grammars is resolved by fixpoint iteration. The use of finite lattices in abstract interpretations requires automatic generation of specialised fixpoint iterators. This is done using a technique called lazy fixpoint iteration which is presented in the thesis. Methods from abstract interpretation can also be used in correctness proofs of attribute grammars. This proof technique introduces a new class of attribute grammars based on domain theory. This method is illustrated with examples. i ii SUMMARY

An object-oriented formal specification workbench is proposed for defining the syntax and semantics of programming languages, using which the formal properties of different languages can be elaborated and analyzed. Our specification approach is an object-oriented representation structured around a denotational semantics methodology, which abstracts out various common details so that formal syntax and semantics can be defined elegantly. Specific details can be inherited and specialized in defining the semantics of various programming languages, and the reusability and modifiability of many programming languages features can be manifested across language paradigms. Furthermore, prototype implementations for these languages may be automatically developed from the formal specifications, providing a mechanism for compiler/interpreter reuse at the specification level.