Annotated Type System Research Articles

Typing Context-Dependent Behavioural Variation

Context Oriented Programming (COP) concerns the ability of programs to adapt to changes in their running environment. A number of programming languages endowed with COP constructs and features have been developed. However, some foundational issues remain unclear. This paper proposes adopting static analysis techniques to reason on and predict how programs adapt their behaviour. We introduce a core functional language, ContextML, equipped with COP primitives for manipulating contexts and for programming behavioural variations. In particular, we specify the dispatching mechanism, used to select the program fragments to be executed in the current active context. Besides the dynamic semantics we present an annotated type system. It guarantees that the well-typed programs adapt to any context, i.e. the dispatching mechanism always succeeds at run-time.

Syntactic control of concurrency

We consider a finitary procedural programming language (finite data-types, no recursion) extended with parallel composition and binary semaphores. Having first shown that may-equivalence of second-order open terms is undecidable we set out to find a framework in which decidability can be regained with minimum loss of expressivity. To that end we define an annotated type system that controls the number of concurrent threads created by terms and give a fully abstract game semantics for the notion of equivalence induced by typable terms and contexts. Finally, we show that the semantics of all typable terms, at any order and in the presence of iteration, has a regular-language representation and thus the restricted observational equivalence is decidable.

Inferring annotated types for inter-procedural register allocation with constructor flattening

We introduce an annotated type system for a compiler intermediate language. The type system is designed to support inter-procedural register allocation and the representation of tuples and variants directly in the register file. We present an algorithm that generates constraints for assigning annotations, and prove its soundness with respect to the type system.

Strictness and totality analysis

We define a novel inference system for strictness and totality analysis for the simply-typed lazy lambda-calculus with constants and fixpoints. Strictness information identifies those terms that definitely denote bottom (i.e. do not evaluate to WHNF) whereas totality information identifies those terms that definitely do not denote bottom (i.e. do evaluate to WHNF). The analysis is presented as an annotated type system allowing conjunctions at “top-level” only. We give examples of its use and prove the correctness with respect to a natural-style operational semantics.

A type-based escape analysis for functional languages

An important issue faced by implementors of higher-order functional programming languages is the allocation and deallocation of storage for variables. The possibility of variables escaping their scope during runtime makes traditional stack allocation inadequate. We consider the problem of detecting when variables in such languages do not escape their scope, and thus can have their bindings allocated in an efficient manner. We use an annotated type system to infer information about the use of variables in a higher-order, strict functional language and combine this system with a translation to an annotated language which explicitly indicates which variables do not escape. The type system uses a notion of annotated types which extends the traditional simple type system with information about the extent of variables. To illustrate the use of this information we define an operational semantics for the annotated language which supports both stack and environment allocation of variable bindings. Only the stack allocated bindings need follow the protocol for stacks: their extent may not exceed their scope. Environment allocated bindings can have any extent, and their allocation has no impact on the stack allocated ones. We prove the analysis and translation correct with respect to this operational semantics by adapting a traditional type consistency proof to our setting. We have encoded the proof into the Elf programming language and typechecked it, providing a partially machine-checked proof.

Behaviour Analysis and Safety Conditions: a Case Study in CML

We describe a case study where novel program analysis technology has been used to pinpoint a subtle bug in a formally developed control program for an embedded system. The main technology amounts to first defining a process algebra (called behaviours) suited to the programming language used (in our case CML) and secondly to devise an annotated type and effect system for extracting behaviours from programs in a such a manner that an automatic inference algorithm can be developed. The case study is a control program developed for the "Karlsruhe Production Cell" and our analysis of the behaviours shows that one of the safety conditions fails to hold.

Polymorphic Subtyping for Effect Analysis: The Semantics

We study an annotated type and effect system that integrates <kbd>let</kbd>-polymorphism, effects, and subtyping into an annotated type and effect system for a fragment of Concurrent ML. First a small step operational semantics is defined for concurrent ML and next the annotated type and effect system is proved semantically sound. This provides insights into the rule for generalisation in the annotated type and effect system.

Polymorphic Subtyping for Effect Analysis: the Algroithm

We study an annotated type and effect system that integrates <kbd>let</kbd>-polymorphism, effects, and sybtyping into an annotated type and effect system for a fragment of Concurrent ML. First a type inference algorithm and a procedure for constraint normalisation and simplification are defined, and next they are proved syntactically sound with respect to the annotated type and effect system.

Polymorphic Subtyping for Effect Analysis: The Integration

The integration of polymorphism (in style of the ML <kbd>let</kbd>-construct), subtyping, and effects (modelling assignment or communication) into one common type system has proved remarkably difficult. One line of research has succeeded in integrating polymorphism and subtyping; adding effects in a straightforward way results in a semantically unsound system. Another line of research has succeeded in integrating polymorphism, effects, and subeffecting; adding sybtyping in a straightforward way invalidaters the construction of the inference algorithm. This paper integrates all op polymorphism, effects, and sybtyping into an annotated type and effect system for Concurrent ML and shows that the resulting system is a conservative extension of the ML type system.

Annotated Type Systems for Program Analysis

<p>In this Ph.D. thesis, we study four program analyses. Three of them are specified by annotated type systems and the last one by abstract interpretation.</p><p>We present a combined strictness and totality analysis. We are specifying the analysis as an annotated type system. The type system allows conjunctions of annotated types, but only at the top-level. The analysis is somewhat more powerful than the strictness analysis by Kuo and Mishra due to the conjunctions and in that we also consider totality. The analysis is shown sound with respect to a natural-style operational semantics. The analysis is not immediately extendable to full conjunction.</p><p>The second analysis is also a combined strictness and totality analysis, however with ``full´´ conjunction. Soundness of the analysis is shown with respect to a denotational semantics. The analysis is more powerful than the strictness analyses by Jensen and Benton in that it in addition to strictness considers totality. So far we have only specified the analyses, however in order for the analyses to be practically useful we need an algorithm for inferring the annotated types. We construct an algorithm for the second analysis using the lazy type approach by Hankin and Le Métayer. The reason for choosing the second analysis from the thesis is that the approach is not applicable to the first analysis.</p><p>The third analysis we study is a binding time analysis. We take the analysis specified by Nielson and Nielson and we construct a more efficient algorithm than the one proposed by Nielson and Nielson. The algorithm collects constraints in a structural manner like the type inference algorithm by Damas. Afterwards the minimal solution to the set of constraints is found.</p><p>The last analysis in the thesis is specified by abstract interpretation. Hunt shows that projection based analyses are subsumed by PER (partial equivalence relation) based analyses using abstract interpretation. The PERs used by Hunt are strict, i.e. bottom is related to bottom. Here we lift this restriction by requiring the PERs to be uniform, in the sense that they treat all the integers equally. By allowing non-strict PERs we get three properties on the integers, corresponding to the three annotations used in the first and second analysis in the thesis.</p>

Strictness and Totality Analysis

We define a novel inference system for strictness and totality analysis for the simply-typed lazy lambda-calculus with constants and fixpoints. Strictness information identifies those terms that definitely denote bottom (i.e. do not evaluate to WHNF) whereas totality information identifies those terms that definitely do not denote bottom (i.e. do evaluate to WHNF). The analysis is presented as an annotated type system allowing conjunctions only at ``top level´´. We give examples of its use and prove the correctness with respect to a natural-style operational semantics.