An applicative computing language

Closed applicative languages (CALs) are a highly parallel and semantically appealing models of computation, but they do not address process and resource related issues in computing; i.e.:- they do not express histories of computation.- they cannot describe interprocess communication.This dissertation defines a new model, CFFP, derived from a CAL, FFP, which addresses these issues. In CFFP, the semantics of FFP are relaxed to allow a computation to persist over a series of actions, and explicit cycles are added to allow bidirectional communication between loci of computation. CFFP retains the appealing characteristics of CALs, and addresses process and resource related computing issues

A Rational Deconstruction of Landin's SECD Machine with the J Operator

Landin's SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin's J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continu-ation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke's double-barrelled continuations and to Felleisen's encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. These reduction semantics mechanically correspond to the modernized versions of the SECD machine and to the best of our knowledge, they provide the first syntactic theories of applicative expressions with the J operator

Parallelism in declarative languages

Imperative programming languages were initially built for uniprocessor systems that evolved out of the Von Neumann machine model. This model of storage oriented computation blocks parallelism and increases the cost of parallel program development and porting. Declarative languages based on mathematical models of computation, seem more suitable for the development of parallel programs. In the first part of this thesis we examine different language families under the declarative paradigm: functional, logic, and constraint languages. Functional languages are based on the abstract model of functions and (lamda)-calculus. They were initially developed for symbolic computation, but today they are commonly used in numerical analysis and many other application areas. Pure lisp is a widely known member of this class. Logic languages are based on first order predicate calculus. Although they were initially developed for theorem proving, fifth generation operating systems are written in them. Most logic languages are descendants or distant relatives of Prolog. Constraint languages are related to logic languages. In a constraint language you define a program object by placing constraints on its structure and its behavior. They were initially used in graphics applications, but today researchers work on using them in parallel computation. Here we will compare and contrast the language classes above, locate advantages and deficiencies, and explain different choices made by language implementors. In the second part of thesis we describe a front end for the CONSUL, a prototype constraint language for programming multiprocessors. The most important features of the front end are compact representation of constraints, type definitions, functional use of relations, and the ability to split programs into multiple files

Fexprs as the basis of Lisp function application; or, $vau: the ultimate abstraction

Abstraction creates custom programming languages that facilitate programming for specific problem domains. It is traditionally partitioned according to a two-phase model of program evaluation, into syntactic abstraction enacted at translation time, and semantic abstraction enacted at run time. Abstractions pigeon-holed into one phase cannot interact freely with those in the other, since they are required to occur at logically distinct times. Fexprs are a Lisp device that subsumes the capabilities of syntactic abstraction, but is enacted at run-time, thus eliminating the phase barrier between abstractions. Lisps of recent decades have avoided fexprs because of semantic ill-behavedness that accompanied fexprs in the dynamically scoped Lisps of the 1960s and 70s. This dissertation contends that the severe difficulties attendant on fexprs in the past are not essential, and can be overcome by judicious coordination with other elements of language design. In particular, fexprs can form the basis for a simple, well-behaved Scheme-like language, subsuming traditional abstractions without a multi-phase model of evaluation. The thesis is supported by a new Scheme-like language called Kernel, created for this work, in which each Scheme-style procedure consists of a wrapper that induces evaluation of operands, around a fexpr that acts on the resulting arguments. This arrangement enables Kernel to use a simple direct style of selectively evaluating subexpressions, in place of most Lisps\u27 indirect quasiquotation style of selectively suppressing subexpression evaluation. The semantics of Kernel are treated through a new family of formal calculi, introduced here, called vau calculi. Vau calculi use direct subexpression-evaluation style to extend lambda calculus, eliminating a long-standing incompatibility between lambda calculus and fexprs that would otherwise trivialize their equational theories. The impure vau calculi introduce non-functional binding constructs and unconventional forms of substitution. This strategy avoids a difficulty of Felleisen\u27s lambda-v-CS calculus, which modeled impure control and state using a partially non-compatible reduction relation, and therefore only approximated the Church-Rosser and Plotkin\u27s Correspondence Theorems. The strategy here is supported by an abstract class of Regular Substitutive Reduction Systems, generalizing Klop\u27s Regular Combinatory Reduction Systems

Definitional interpreters for higher-order programming languages

Abstract. Higher-order programming languages (i.e., languages in which procedures or labels can occur as values) are usually defined by interpreters that are themselves written in a programming language based on the lambda calculus (i.e., an applicative language such as pure LISP). Examples include McCarthy’s definition of LISP, Landin’s SECD machine, the Vienna definition of PL/I, Reynolds ’ definitions of GEDANKEN, and recent unpublished work by L. Morris and C. Wadsworth. Such definitions can be classified according to whether the interpreter contains higher-order functions, and whether the order of application (i.e., call by value versus call by name) in the defined language depends upon the order of application in the defining language. As an example, we consider the definition of a simple applicative programming language by means of an interpreter written in a similar language. Definitions in each of the above classifications are derived from one another by informal but constructive methods. The treatment of imperative features such as jumps and assignment is also discussed

Computing with Capsules

Capsules provide a clean algebraic representation of the state of a computation in higher-order functional and imperative languages. They play the same role as closures or heap- or stack-allocated environments but are much simpler. A capsule is essentially a finite coalgebraic representation of a regular closed lambda-coterm. One can give an operational semantics based on capsules for a higher-order programming language with functional and imperative features, including mutable bindings. Lexical scoping is captured purely algebraically without stacks, heaps, or closures. All operations of interest are typable with simple types, yet the language is Turing complete. Recursive functions are represented directly as capsules without the need for unnatural and untypable fixpoint combinators

Efficient execution in an automated reasoning environment

We describe a method that permits the user of a mechanized mathematical logic to write elegant logical definitions while allowing sound and efficient execution. In particular, the features supporting this method allow the user to install, in a logically sound way, alternative executable counterparts for logically defined functions. These alternatives are often much more efficient than the logically equivalent terms they replace. These features have been implemented in the ACL2 theorem prover, and we discuss several applications of the features in ACL2.Ministerio de Educación y Ciencia TIN2004–0388