Inter-deriving semantic artifacts for object-oriented programming

We present a new abstract machine for Abadi and Cardelli's untyped non-imperative calculus of objects. This abstract machine mechanically corresponds to both the reduction semantics (i.e., small-step operational semantics) and the natural semantics (i.e., big-step operational semantics) specified in Abadi and Cardelli's monograph. To move closer to actual implementations, which use environments rather than actual substitutions, we then represent methods as closures and we present three new semantic artifacts for a version of Abadi and Cardelli's calculus with explicit substitutions: a reduction semantics, an environment-based abstract machine, and a natural semantics (i.e., an interpreter) with environments. These three new semantic artifacts mechanically correspond to each other, and the two abstract machines are bisimilar. Their significance lies in the fact that they have not been designed from scratch and then proved correct; instead, they have been inter-derived.To illustrate the inter-derivation and to make this article stand-alone, we also comprehensively treat the example of negational normalization over Boolean formulas, in appendix.     

Polymorphic type inference and containment

Type expressions may be used to describe the functional behavior of untyped lambda terms. We present a general semantics of polymorphic type expressions over models of untyped lambda calculus and give complete rules for inferring types for terms. Some simplified typing theories are studied in more detail, and containments between types are investigated.     

Two-level languages for program optimization

Two-level languages incorporate binding time information inside types, that is, whether a piece of code is completely known at compile-time, or needs some more inputs and can be evaluated only at run-time. We consider the use of 2-level languages in the framework of partial evaluation, and use a 2-level version of the simply typed lambda calculus with recursion. We give an operational semantics, an equational theory and a denotational semantics, that give an account of the distinction between compilation and execution phases. An adequacy theorem is given to relate the two semantics, showing in particular how they agree on non-termination at compile time. We finally give a more refined model using functor categories.     

A Polymorphic Environment Calculus and its Type-Inference Algorithm

The polymorphic environment calculus is a polymorphic lambda calculus which enables us to treat environments as first-class citizens. In the calculus, environments are formalized as explicit substitutions, and the substitutions are included in the set of terms of the calculus. First, we introduce an untyped environment calculus, and we present a semantics of the calculus as a translation into the lambda calculus. Second, we propose a polymorphic type system for the environment calculus based on Damas-Milner's ML-polymorphic type system. In ML, polymorphism is allowed only in let-expressions; in the polymorphic environment calculus, polymorphism is provided with environment compositions. We prove a subject-reduction theorem for the type system. Third, a type-inference algorithm is given to the polymorphic environment calculus, and we establish its soundness, termination, and principal-typing theorem.     

Syntactic Type Soundness Results for the Region Calculus

The region calculus of Tofte and Talpin is a polymorphically typed lambda calculus with annotations that make memory allocation and deallocation explicit. It is intended as an intermediate language for implementing Hindley-Milner typed functional languages such as ML without traditional trace-based garbage collection. Static region and effect inference can be used to annotate a statically typed ML program with memory management primitives. Soundness of the calculus with respect to the region and effect system is crucial to guarantee safe deallocation of regions, i.e., deallocation should only take place for objects which are provably dead. The original soundness proof by Tofte and Talpin requires a complex co-inductive safety relation. In this paper, we present two small-step operational semantics for the region calculus and prove their type soundness with respect to the region and effect system. Following the standard syntactic approach of Wright, Felleisen, and Harper, we obtain simple inductive proofs. The first semantics is store-less. It is simple and elegant and gives rise to perspicuous proofs. The second semantics provides a store-based model for the region calculus. Albeit slightly more complicated, its additional expressiveness allows us to model operations on references with destructive update. A pure fragment of both small-step semantics is then proven equivalent to the original big-step operational approach of Tofte and Talpin. This leads to an alternative soundness proof for their evaluation-style formulation.     

On generic context lemmas for higher-order calculi with sharing

This paper proves several generic variants of context lemmas and thus contributes to improving the tools for observational semantics of deterministic and non-deterministic higher-order calculi that use a small-step reduction semantics. The generic (sharing) context lemmas are provided for may- as well as two variants of must-convergence, which hold in a broad class of extended process- and extended lambda calculi, if the calculi satisfy certain natural conditions. As a guide-line, the proofs of the context lemmas are valid in call-by-need calculi, in call-by-value calculi if substitution is restricted to variable-by-variable and in process calculi like variants of the $\pi$-calculus. For calculi employing beta-reduction using a call-by-name or call-by-value strategy or similar reduction rules, some iu-variants of ciu-theorems are obtained from our context lemmas. Our results reestablish several context lemmas already proved in the literature, and also provide some new context lemmas as well as some new variants of the ciu-theorem. To make the results widely applicable, we use a higher-order abstract syntax that allows untyped calculi as well as certain simple typing schemes. The approach may lead to a unifying view of higher-order calculi, reduction, and observational equality.     

Alias types for “environment-aware” computations

In previous work with Bono we introduced a calculus for modelling “environment-aware” computations, that is computations that adapt their behavior according to the capabilities of the environment. The calculus is an imperative, object-based language (with extensible objects and primitives for discriminating the presence or absence of attributes of objects) equipped with a small-step operational semantics.In this paper we define a type and effect system for the calculus. The typing judgements specify, via constraints, the shape of environments which guarantees the correct execution of expressions and the typing rules track the effect of expression evaluation on the environment. The type and effect system is sound w.r.t. the operational semantics of the language.     

A Monadic Semantics for Core Curry

We give a deterministic, big-step operational semantics for the essential core of the Curry language, including higher-order functions, call-by-need evaluation, non-determinism, narrowing, and residuation. The semantics is structured in modular monadic style, and is presented in the form of an executable interpreter written in Haskell. It uses monadic formulations of state, non-determinism, and resumption-based concurrency.     

A Calculus for Reconfiguration: (Extended abstract)

We present a simple calculus, called R-calculus (for “reconfiguration”), intended to provide a kernel model for a computational paradigm in which standard execution (that is, execution of a single computation described by a fragment of code) can be interleaved with operations at the meta-level which can manipulate in various ways the context in which this computation takes place. Formally, this is achieved by introducing as basic terms of the calculus configurations, which are, roughly speaking, pairs consisting of an (open, mutually recursive) collection of named components and a term representing a program running in the context of these components. The R-calculus has been originally developed as a formal model for programming-in-the large, where computations correspond to applications running in some context of software components, and operations at the meta-level correspond to the possibility of dynamically loading, updating or in general manipulat- ing these software components without stopping the application. However, the calculus can also encode programming-in-the-small issues, because configurations combine the features of lambda- abstractions (first-class functions), records, environments with mutually recursive definitions, and modules. We state confluence of the calculus and define a call-by-need strategy which leads to a generalization, including reconfiguration features, of call-by-need lambda-calculi.     

Evolvable concurrent processes

This paper presents a formal model of concurrent processes whose functions can be modified from the environments during execution. In many applications, it takes too much cost to stop the whole of the concurrent system working in distributed environments to update its components. Features of dynamic evolution that make it possible to modify functions of processes without termination are important. In this paper, a formal model of evolvable concurrent processes is presented using logical formulas of linear logic. The operational semantics is defined using a formal proof in a fragment of the sequent calculus of linear logic. A method for replacing the continuations of working processes by applications of inference rules of linear logic is presented.     

Eliminating Proofs from Programs

This paper presents a step in the development of an operational approach to program extraction in type theory. In order to get a program from a lambda term, the logical parts need to be removed. This is done by a reduction relation →_ε. We study the combination of β-reduction and ε-reduction, both in the setting of simply typed lambda calculus and for pure type systems. In the general setting the properties confluence, subject reduction, and strong normalization are studied.     

Algebraic Correctness Proofs for Compiling Recursive Function Definitions with Strictness Information

Adding appropriate strictness information to recursive function definitions we achieve a uniform treatment of lazy and eager evaluation strategies. By restriction to first-order functions over basic types we develop a pure stack implementation that avoids a heap even for lazy arguments. We present algebraic definitions of denotational, operational, and stack-machine semantics and prove their equivalence by means of structural induction.     

A pure labeled transition semantics for the applied pi calculus

The applied pi calculus proposed by Abadi and Fournet is successful in the analysis of security protocols. Its semantics mainly depends on several structural rules. Structural rules are convenient for specification, but inefficient for implementation. In this paper, we establish a new semantics for applied pi calculus based upon pure labeled transition system and propose a new formulation of labeled bisimulation. We prove that the new labeled bisimularity coincides with observational equivalence. A zero-knowledge protocol is given as an example to illustrate the effectiveness of this new semantics.     

Directly reflective meta-programming

Existing meta-programming languages operate on encodings of programs as data. This paper presents a new meta-programming language, based on an untyped lambda calculus, in which structurally reflective programming is supported directly, without any encoding. The language features call-by-value and call-by-name lambda abstractions, as well as novel reflective features enabling the intensional manipulation of arbitrary program terms. The language is scope safe, in the sense that variables can neither be captured nor escape their scopes. The expressiveness of the language is demonstrated by showing how to implement quotation and evaluation operations, as proposed by Wand. The language’s utility for meta-programming is further demonstrated through additional representative examples. A prototype implementation is described and evaluated.     

LETOS – a lightweight execution tool for operational semantics

A lightweight tool is proposed to aid in the development of operational semantics. To use LETOS an operational semantics must be expressed in its meta‐language, which itself is a superset of Miranda. The LETOS compiler is smaller than comparable tools, yet LETOS is powerful enough to support publication quality rendering using LaTeX, fast enough to provide competitive execution using Haskell, and versatile enough to support browsing of execution traces using Netscape. LETOS can be characterised as an experiment in ‘creative laziness’, showing how far one can get by gluing existing components together. The major specifications built using LETOS to‐date are a smart card version of the Java Virtual Machine, a deterministic version of the π‐calculus, and an electronic payment protocol. In addition, we have specified the semantics of many small programming languages and systems, totaling over 9000 lines of formal text. LETOS is unique in that it helps to check that a specification is operationally conservative. Copyright © 1999 John Wiley & Sons, Ltd.     

Comparing two functional programming systems

A technique is presented for comparing the performance of functional languages with different evaluation strategies running on different machines. A set of small benchmarks is used, and th execution times of these programs running in the functional language and in the implementation language of the functional system are compared. The ratio of these execution times measured how well the functional system used the resources of the underlying hardware and implementation language. Also two functional programming systems are described. One system is a graph reduction interpreter for lambda calculus. The other is a DEL-style intermediate instruction set architecture for FP. The benchmarks in FP and the performances of the two systems on these benchmarks are presented     

Building Interpreters with Rewriting Strategies

Programming language semantics based on pure rewrite rules suffers from the gap between the rewriting strategy implemented in rewriting engines and the intended evaluation strategy. This paper shows how programmable rewriting strategies can be used to implement interpreters for programming languages based on rewrite rules. The advantage of this approach is that reduction rules are first class entities that can be reused in different strategies, even in other kinds of program transformations such as optimizers. The approach is illustrated with several interpreters for the lambda calculus based on implicit and explicit (parallel) substitution, different strategies including normalization, eager evaluation, lazy evaluation, and lazy evaluation with updates. An extension with pattern matching and choice shows that such interpreters can easily be extended.     

Executable structural operational semantics in Maude

This paper describes in detail how to bridge the gap between theory and practice when implementing in Maude structural operational semantics described in rewriting logic, where transitions become rewrites and inference rules become conditional rewrite rules with rewrites in the conditions, as made possible by the new features in Maude 2. We validate this technique using it in several case studies: a functional language Fpl (evaluation and computation semantics), an imperative language WhileL (evaluation and computation semantics), Kahn’s functional language Mini-ML (evaluation or natural semantics), Milner’s CCS (with strong and weak transitions), and Full LOTOS (including ACT ONE data type specifications). In addition, on top of CCS we develop an implementation of the Hennessy–Milner modal logic for describing local capabilities of processes, and for LOTOS we build an entire tool where Full LOTOS specifications can be entered and executed (without user knowledge of the underlying implementation of the semantics). We also compare this method based on transitions as rewrites with another one based on transitions as judgements.     

The logic of message-passing

Message-passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message-passing. In order to achieve this we introduce the categorical notion of a linear actegory and the related polycategorical notion of a poly-actegory. Not surprisingly the notation used for the term calculus borrows heavily from the (synchronous) π-calculus. The cut-elimination procedure for the system provides an operational semantics.