Andrew K. Wright

A Syntactic Approach to Type Soundness

We present a new approach to proving type soundness for Hindley/Milner-style polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations.

Simple imperative polymorphism

This paper describes a simple extension of the Hindley-Milner polymorphic type discipline to call-by-value languages that incorporate imperative features like references, exceptions, and continuations. This extension sacrifices the ability to type every purely functional expression that is typable in the Hindley-Milner system. In return, it assigns the same type to functional and imperative implementations of the same abstraction. Hence with a module system that separates specifications from implementations, imperative features can be freely used to implement polymorphic specifications. A study of a number of ML programs shows that the inability to type all Hindley-Milner typable expressions seldom impacts realistic programs. Furthermore, most programs that are rendered untypable by the new system can be easily repaired.

A practical soft type system for Scheme

Soft typing is a generalization of static type checking that accommodates both dynamic typing and static typing in one framework. A soft type checker infers types for identifiers and inserts explicit run-time checks to transform untypable programs into typable form. Soft Scheme is a practical soft type system for R4RS Scheme. The type checker uses a representation for types that is expressive, easy to interpret, and supports efficient type inference. Soft Scheme supports all of R4RS Scheme, including uncurried procedures of fixed and variable arity, assignment, and continuations.

Polymorphic splitting: an effective polyvariant flow analysis

This article describes a general-purpose program analysis that computes global control-flow and data-flow information for higher-order, call-by-value languages. The analysis employs a novel form of polyvariance called polymorhic splitting that uses let-expressions as syntactic clues to gain precision. The information derived from the analysis is used both to eliminate run-time checksand to inline procedure. The analysis and optimizations have been applied to a suite of Scheme programs. Experimental results obtained from the prototype implementation indicate that the analysis is extremely precise and has reasonable cost. Compared to monovariantflow analyses such as 0CFA, or analyses based on type inference such as soft typing, the analysis eliminates significantly more run-time checks. Run-time check elimination and inlining together typically yield a 20 to 40% performance improvement for the benchmark suite, with some programs running four times as fast.

Effective Flow Analysis for Avoiding Run-Time Checks

This paper describes a general purpose program analysis that computes global control-flow and data-flow information for higher-order, call-by-value programs. This information can be used to drive global program optimizations such as inlining and run-time check elimination, as well as optimizations like constant folding and loop invariant code motion that are typically based on special-purpose local analyses.

Single and loving it: must-alias analysis for higher-order languages

In standard control-flow analyses for higher-order languages, a single abstract binding for a variable represents a set of exact bindings, and a single abstract reference cell represents a set of exact reference cells. While such analyses provide useful may-alias information, they are unable to answer mustalias questions about variables and cells, as these questions ask about equality of specific bindings and references.In this paper, we present a novel program analysis for higher-order languages that answers must-alias questions. At every program point, the analysis associates with each variable and abstract cell a cardinality, which is either single or multiple. If variable x is single at program point p, then all bindings for x in the heap reachable from the environment at p hold the same value. If abstract cell r is single at p, then at most one exact cell corresponding to r is reachable from the environment at p.Must-alias information facilitates various program optimizations such as lightweight closure conversion [19]. In addition, must-alias information permits analyses to perform strong updates [3] on abstract reference cells known to be single. Strong updates improve analysis precision for programs that make significant use of state.A prototype implementation of our analysis yields encouraging results. Over a range of benchmarks, our analysis classifies a large majority of the variables as single.

Flow-directed inlining

A flow-directed inlining strategy uses information derived from control-flow analysis to specialize and inline procedures for functional and object-oriented languages. Since it uses control-flow analysis to identify candidate call sites, flow-directed inlining can inline procedures whose relationships to their call sites are not apparent. For instance, procedures defined in other modules, passed as arguments, returned as values, or extracted from data structures can all be inlined. Flow-directed inlining specializes procedures for particular call sites, and can selectively inline a particular procedure at some call sites but not at others. Finally, flow-directed inlining encourages modular implementations: control-flow analysis, inlining, and post-inlining optimizations are all orthogonal components. Results from a prototype implementation indicate that this strategy effectively reduces procedure call overhead and leads to significant reduction in execution time.

Typing references by effect inference

Hindley/Milner-style polymorphism is a simple, natural, and flexible type discipline for functional languages, but incorporating imperative extensions is difficult. We present a new technique for typing references in the presence of polymorphism by inferring a concise summary of each expressions allocation behavior—a type effect. A simple technique for proving soundness with respect to a reduction semantics demonstrates that the type system prevents type errors. By establishing that the system corresponds to an alternate system better suited to implementation, we obtain an algorithm to perform type and effect inference.

Type-Directed Flow Analysis for Typed Intermediate Languages

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 SRTrespects types: whenever it assigns abstract value \(\hat \upsilon\)to a variable and the type system assigns type σ to the same variable, then \(\left[ {\hat \upsilon } \right] \subseteq \left[ \sigma \right]\), where [ · ] denotes a set of values. SRT does not terminate 1569 1655 V 3 for some programs. We present several variants of SRT that are better suited to practical use.

Type-dependent parameter inference

An algorithm is presented to infer the type and operation parameters of polymorphic functions. Operation parameters are named and typed at the function definition, but are selected from the set of overloaded definitions available wherever the function is used. These parameters are always implicit, implying that the complexity of using a function does not increase with the generality of its type.