Linear type systems permit programmers to deallocate or explicitly recycle memory, but they are severly restricted by the fact that they admit no aliasing. This paper describes a pseudo-linear type system that allows a degree of aliasing and memory reuse as well as the ability to define complex recursive data structures. Our type system can encode conventional linear data structures such as linear lists and trees as well as more sophisticated data structures including cyclic and doubly-linked lists and trees. In the latter cases, our type system is expressive enough to represent pointer aliasing and yet safely permit destructive operations such as object deallocation. We demonstrate the flexibility of our type system by encoding two common compiler optimizations: destination-passing style and Deutsch-Schorr-Waite or "link-reversal" traversal algorithms.

Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, unfortunately, are very hard to represent and manipulate efficiently; a naive implementation can easily add exponential overhead to the compilation and execution of a program. This paper describes our experience with implementing the FLINT typed intermediate language in the SML/NJ production compiler. We observe that a type-preserving compiler will not scale to handle large types unless all of its type-preserving stages preserve the asymptotic time and space usage in representing and manipulating types. We present a series of novel techniques for achieving this property and give empirical evidence of their effectiveness.

Proof-carrying code (PCC) is a framework for mechanically verifying the safety of machine language programs. A program that is successfully verified by a PCC system is guaranteed to be safe to execute, but this safety guarantee is contingent upon the correctness of various trusted components. For instance, in traditional PCC systems the trusted computing base includes a large set of low-level typing rules. Foundational PCC systems seek to minimize the size of the trusted computing base. In particular, they eliminate the need to trust complex, low-level type systems by providing machine-checkable proofs of type soundness for real machine languages. In this thesis, I demonstrate the use of logical relations for proving the soundness of type systems for mutable state. Specifically, I focus on type systems that ensure the safe allocation, update, and reuse of memory. For each type in the language, I define logical relations that explain the meaning of the type in terms of the oper-ational semantics of the language. Using this model of types, I prove each typing rule as a lemma. The major contribution is a model of System F with general references — that is, mutable cells that can hold values of any closed type including other references, functions, recursive types, and impredicative quantified types. The model is based on ideas from both possible worlds and the indexed model of Appel and McAllester. I show how the model of mutable references is encoded in higher-order logic. I also show how to construct an indexed possible-worlds model for a von Neumann machine. The latter is used in the Princeton Foundational PCC system to prove type safety for a full-fledged low-level typed assembly language. Finally, I present a semantic model for a region calculus that supports type-invariant references as well as memory reuse. iii

We present # CIL , a typed #-calculus which serves as the foundation for a typed intermediate language for optimizing compilers for higher-order polymorphic programming languages. The key innovation of # CIL is a novel formulation of intersection and union types and flow labels on both terms and types. These flow types can encode polyvariant control and data flow information within a polymorphically typed program representation. Flow types can guide a compiler in generating customized data representations in a strongly typed setting. Since # CIL enjoys confluence, standardization, and subject reduction properties, it is a valuable tool for reasoning about programs and program transformations.

We present a typed intermediate language # CIL for optimizing compilers for function-oriented and polymorphically typed programming languages (e.g., ML). The language # CIL is a typed lambda calculus with product, sum, intersection, and union types as well as function types annotated with flow labels. A novel formulation of intersection and union types supports encoding flow information in the typed program representation. This flow information can direct optimization.

I present a type-preserving translation that eliminates subtyping and bounded quantification without introducing any run-time costs. This translation is based on Mitchell and Pierce's encoding of bounded quantification using intersection types. I show that, previous negative observations notwithstanding, the encoding is adequate given a sufficiently rich target type theory. The necessary target type theory is made easily typecheckable by including a collection of explicit coercion combinators, which are already desired for eliminating subtyping. However, no form of coercion abstraction is necessary (even to support bounded quantification) , leading to a simple target language. 1 Introduction Type-preserving compilers, those that utilize strongly typed intermediate languages, offer several compelling advantages over untyped compilers. A typed compiler can utilize type information to enable optimizations that would otherwise be prohibitively difficult or impossible. Internal type check...

. Flow analysis is especially valuable for optimizing functional languages because control-flow information is not syntactically apparent in higher-order programs. Flow analyses typically operate on untyped languages. However, recent compilers for typed functional languages such as ML and Haskell use a typed intermediate language to expose data representations for optimization. This paper presents a polyvariant flow analysis framework for the predicative subset of system F , a common basis for typed intermediate languages. Analyses in this framework can take advantage of types to analyze programs more precisely. We study a specific analysis called SRT that uses types to control polyvariance. We prove that SRT respects types: whenever it assigns abstract value v to a variable and the type system assigns type oe to the same variable, then [[v]] ` [[oe]], where [[ \Delta ]] denotes a set of values. SRT does not terminate for some programs. We present several variants of SRT that are bett...

Recent work h& s h wn equivalences between various type systems and flow logics. Ideally, th translations upon wh= h such equivalences are basedshd&@ be faithful in th sense the information is not lost in round-trip translations from flows to types and back or from types to flows and back. Building on t h work of Nielson Nielson and of Palsberg Pavlopoulou, we present t h firstfaithT# translations between a class of finitary polyvariant flow analyses and a type system supporting polymorph@@ in th form of intersection and union types. Additionally, our flow/type correspondence solves several open problems posed by Palsberg Pavlopoulou: (1) it expresses call-string based polyvariance (such as k-CFA) as well as argument based polyvariance; (2) it enjoys a subject reduction property for flows as well as for types; and (3) it supports a flow-oriented perspectiverath# thh a type-oriented one. 1

The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying out compositional type inference. The fundamental idea of expansion is to be able to calculate the effect on the final judgement of a typing derivation of inserting a use of the intersection-introduction typing rule at some (possibly deeply nested) position, without actually needing to build the new derivation.

Cloning is a transformation where several copies are made of some functions in a program in order to improve the effectiveness of optimizations of these functions. Cloning may thus lead to a reduction in the number of executed instructions, but it does in general also lead to an increase in the size of the executable program. Depending on the characteristics of the memory hierarchy of the target machine, this may increase the instruction cache miss rate enough that the cloned program executes slower than the original. In this paper we try to quantify both the benefits and costs of cloning in the context of an optimizing compiler for a simple lazy functional language. We will also evaluate a few techniques for reducing the number of instruction cache misses. 1 Introduction Cloning is a program transformation where functions called from multiple call sites are duplicated. In general, this increases the effectiveness of optimizations which depend on properties which may hold at some, b...