We describe a new compiler for Standard ML called TIL, that is based on four technologies: intensional polymorphism, tag-free garbage collection, conventional functional language optimization, and loop optimization. We use intensional polymorphism and tag-free garbage collection to provide specialized representations, even though SML is a polymorphic language. We use conventional functional language optimization to reduce the cost of intensional polymorphism, and loop optimization to generate good code for recursive functions. We present an example of TIL compiling an SML function to machine code, and compare the performance of TIL code against that of a widely used compiler, Standard ML of New Jersey.

We present an internal language with equivalent expressive power to Standard ML, and discuss its formalization in LF and the machine-checked verification of its type safety in Twelf. The internal language is intended to serve as the target of elaboration in an elaborative semantics for Standard ML in the style of Harper and Stone. Therefore, it includes all the programming mechanisms necessary to implement Standard ML, including translucent modules, abstraction, polymorphism, higher kinds, references, exceptions, recursive types, and recursive functions. Our successful formalization of the proof involved a careful interplay between the precise formulations of the various mechanisms, and required the invention of new representation and proof techniques of general interest.

9706572, and the US Air Force under grant F19628-95-C-0050 and a generous fellowship. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.

We study the λΠΣS ≤ calculus, which contains singleton types S(M) classifying terms of base type provably equivalent to the term M. The system includes dependent types for pairs and functions (Σ and Π) and a subtyping relation induced by regarding singletons as subtypes of the base type. The decidability of type checking for this language is non-obvious, since to type check we must be able to determine equivalence of well-formed terms. But in the presence of singleton types, the provability of an equivalence judgment Γ ⊢ M1 ≡ M2: A can depend both on the typing context Γ and on the particular type A at which M1 and M2 are compared. We show how to prove decidability of term equivalence, hence of type checking, in λΠΣS ≤ by exhibiting a type-directed algorithm for directly computing normal forms. The correctness of normalization is shown using an unusual variant of Kripke logical relations organized around sets; rather than defining a logical equivalence relation, we work directly with (subsets of) the corresponding equivalence classes. We then provide a more efficient algorithm for checking type equivalence without constructing normal forms. We also show that type checking, subtyping, and all other judgments of the system are decidable.

Module systems for languages with complex type systems, such as Standard ML, often lack the ability to express mutually recursive type and function dependencies across module boundaries. Previous work by Crary, Harper and Puri [5] set out a type-theoretic foundation for recursive modules in the context of a phase-distinction calculus for higher-order modules. Two constructs were introduced for encoding recursive modules: a fixed-point module and a recursively dependent signature. Unfortunately, the implementations of both constructs involve the use of equi-recursive type constructors at higher-order kinds, the equivalence of which is not known to be decidable. In this paper, we show that the practicality of recursive modules is not contingent upon that of equi-recursive constructors. We begin with the theoretical infrastructure described above and study precisely how equi-recursiveness is used in the recursive module constructs, resulting in a clarification and generalization of the underlying ideas. We then examine in depth how the recursive module constructs in the revised type system can serve as the target of elaboration for a recursive module extension to Standard ML. This research was sponsored by the Advanced Research Projects Agency CSTO under the title "The Fox Project: Advanced Languages for Systems Software", ARPA Order No. C533, issued by ESC/ENS under Contract No. F19628-95-C-0050. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing o#cial policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the U.S. Government. Keywords: Type systems, module systems, functional programming, phase splitting. 1

Standard ML employs an opaque (or generative) semantics of datatypes, in which every datatype declaration produces a new type that is different from any other type, including other identically defined datatypes. A natural way of accounting for this is to consider datatypes to be abstract. When this interpretation is applied to type-preserving compilation, however, it has the unfortunate consequence that datatype constructors cannot be inlined, substantially increasing the run-time cost of constructor invocation compared to a traditional compiler. In this paper we examine two approaches to eliminating function call overhead from datatype constructors. First, we consider a transparent interpretation of datatypes that does away with generativity, altering the semantics of SML; and second, we propose an interpretation of datatype constructors as coercions, which have no run-time effect or cost and faithfully implement SML semantics.

or implied, of any sponsoring institution, the U.S. government or any other entity.

The TILT compiler for Standard ML is type-directed and type-preserving, that is, it makes use of and translates type information during the phases of compilation. Unfortunately, such use of type data incurs a significant overhead. This paper explores methods for abstractly, conveniently, and efficiently storing and manipulating type information in TILT. In the end, we discover that doing more work to reduce overhead is a bad strategy for this situation. This material is based on work supported in part by ARPA grant F-19628-95-C-0050 and NSF grant CCR-9984812. Any opinions, findings, and conclusions or recommendations in this publication are those of the authors and do not reflect the views of these agencies. Keywords: types, typed intermediate languages, type representations, Standard ML, hash consing, de Bruijn indices, views1 The Wizard of TILT TILT is a certifying compiler for Standard ML [1]. Its major distinguishing feature is the use of Typed Intermediate Languages throughout the phases of compilation. Because each of the code transformations that the compiler performs also transforms the types, we preserve type information that is normally discarded after typechecking the source language in traditional compilers. This allows us to typecheck the results of these transformations (catching compiler

Run-time type analysis is an increasingly important linguistic mechanism in modern programming languages. Language runtime systems use it to implement services such as accurate garbage collection, serialization, cloning and structural equality. Component frameworks rely on it to provide reflection mechanisms so they may discover and interact with program interfaces dynamically. Run-time type analysis is also crucial for large, distributed systems that must be dynamically extended, because it allows those systems to check program invariants when new code and new forms of data are added. Finally, many generic user-level algorithms for iteration, pattern matching, and unification can be defined through type analysis mechanisms. However, existing frameworks for run-time type analysis were designed for simple type systems. They do not scale well to the sophisticated type systems of modern and next-generation programming languages that include complex constructs such as first-class abstract types, recursive types, objects, and type parameterization. In addition, facilities to support type analysis often require complicated

Explicit or implicit, enforced or not, safety policies are ubiquitous in software systems. In the many settings where third-party software is executed in the context of a larger client program, the supervisor usually enforces a safety policy that prevents the foreign code from behaving in ways that would disrupt the client, corrupt data or destabilize the system. Certified code provides a static means for controlling the behavior of untrusted programs or components by bringing the power of type systems and formal logic to bear on the problem. Code certification systems that prevent bad memory accesses and enforce the abstractions provided by libraries and runtime system interfaces have been well studied. This thesis presents a system for certifying conformance to timing requirements. The approach is simple, comprising an incremental change to an existing type system for assembly language, but flexible in the set of policies it can enforce. Moreover, in principle, it can be extended to support arbitrarily complex coding idioms. Focusing on a particular timing policy of interest, I describe a compiler that produces certifiably compliant programs with no help from the programmer and only a small impact on runtime performance. Later, I discuss the applicability of both the type