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A term model for CCS
 9 th Symposium on Mathematical Foundations of Computer Science
, 1980
"... In a series of papers [Hen2, Mill, Mi147] Milner and his colleagues have studied a model of parallelism in which concurrent systems communicate by sending and receiving values along lines. Communication is synchronised in that the exchange of values takes place only when the sender and receiver are ..."
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Cited by 21 (3 self)
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In a series of papers [Hen2, Mill, Mi147] Milner and his colleagues have studied a model of parallelism in which concurrent systems communicate by sending and receiving values along lines. Communication is synchronised in that the exchange of values takes place only when the sender and receiver are both ready, and the exchange
Universally programmable intelligent matter summary
 in IEEE Nano 2002. IEEE Press
, 2002
"... Abstract — We explain how a small set of molecular building blocks will allow the implementation of “universally programmable intelligent matter, ” that is, matter whose structure, properties, and behavior can be programmed, quite literally, at the molecular level. I. DEFINITIONS Intelligent matter ..."
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Cited by 7 (3 self)
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Abstract — We explain how a small set of molecular building blocks will allow the implementation of “universally programmable intelligent matter, ” that is, matter whose structure, properties, and behavior can be programmed, quite literally, at the molecular level. I. DEFINITIONS Intelligent matter is any material in which individual molecules or supramolecular clusters function as agents to accomplish some purpose. Intelligent matter may be solid, liquid, or gaseous, although liquids and membranes are perhaps most typical. Universally programmable intelligent matter (UPIM) is made from a small set of molecular building blocks that are universal in the sense that they can be rearranged to accomplish any purpose that can be described by a computer program. In effect, a computer program controls the behavior of the material at the molecular level. In some applications the molecules selfassemble a desired nanostructure by “computing ” the structure and then becoming inactive. In other applications the material remains active so that it can respond, at the molecular level, to its environment or to other external conditions. An extreme case is when programmable supramolecular clusters act as autonomous agents to achieve some end. Although materials may be engineered for specific purposes, we will get much greater technological leverage by designing a “universal material ” which, like a generalpurpose computer, can be “programmed ” for a wide range of applications. To accomplish this, we must identify a set of molecular primitives that can be combined for widely varying purposes. The existence of such universal molecular operations might seem highly unlikely, but there is suggestive evidence that it may be possible to discover or synthesize them. II. APPROACH Accomplishing the goals of UPIM will require the identification of a small set of molecular building blocks that is
A proof of the churchrosser theorem for the lambda calculus in higher order logic
 TPHOLs’01: Supplemental Proceedings
, 2001
"... Abstract. This paper describes a proof of the ChurchRosser theorem within the Higher Order Logic (HOL) theorem prover. This follows the proof by Tait/MartinLöf, preserving the elegance of the classic presentation by Barendregt. We model the lambda calculus with a namecarrying syntax, as in practi ..."
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Cited by 6 (0 self)
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Abstract. This paper describes a proof of the ChurchRosser theorem within the Higher Order Logic (HOL) theorem prover. This follows the proof by Tait/MartinLöf, preserving the elegance of the classic presentation by Barendregt. We model the lambda calculus with a namecarrying syntax, as in practical languages. The proof is simplified by forming a quotient of the namecarrying syntax by the αequivalence relation, thus separating the concerns of αequivalence and βreduction. 1
Normal Forms in Combinatory Logic
 Wesleyan University
, 1992
"... Abstract Let R be a convergent term rewriting system, and let CRequality on (simply typed) combinatory logic terms be the equality induced by βηRequality on terms of the (simply typed) lambda calculus under any of the standard translations between these two frameworks for higherorder reasoning. We ..."
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Abstract Let R be a convergent term rewriting system, and let CRequality on (simply typed) combinatory logic terms be the equality induced by βηRequality on terms of the (simply typed) lambda calculus under any of the standard translations between these two frameworks for higherorder reasoning. We generalize the classical notion of strong reduction to a reduction relation which generates CRequality and whose irreducibles are exactly the translates of long βRnormal forms. The classical notion of strong normal form in combinatory logic is also generalized, yielding yet another description of these translates. Their resulting tripartite characterization extends to the combined firstorder algebraic and higherorder setting the classical combinatory logic descriptions of the translates of long βnormal forms in the lambda calculus. As a consequence, the translates of long βRnormal forms are easily seen to serve as canonical representatives for CRequivalence classes of combinatory logic terms for nonempty, as well as for empty, R. 573
Classical combinatory logic
, 2009
"... Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written ..."
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Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written in a system “à la Hilbert”. We present in this paper a combinatory logic which corresponds to propositional classical logic. This system is equivalent to the system
Universally Programmable Intelligent Matter
, 2002
"... Intelligent matter is any material in which individual molecules or supramolecular clusters function as agents to accomplish some purpose. Intelligent matter may be solid, liquid or gaseous, although liquids and membranes are perhaps most typical. Universally programmable intelligent matter (UPIM) ..."
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Intelligent matter is any material in which individual molecules or supramolecular clusters function as agents to accomplish some purpose. Intelligent matter may be solid, liquid or gaseous, although liquids and membranes are perhaps most typical. Universally programmable intelligent matter (UPIM) is made from a small set of molecular building blocks that are universal in the sense that they can be rearranged to accomplish any purpose that can be described by a computer program. In effect, a computer program controls the behavior of the material at the molecular level. In some applications the molecules selfassemble a desired nanostructure by “computing ” the structure and then becoming inactive. In other applications the material remains active so that it can respond, at the molecular level, to its environment or to other external conditions. An extreme case is when programmable supramolecular clusters act as autonomous agents to achieve some end. This report outlines a oneyear exploratory research project to investigate the feasibility of UPIM. 1 Project Summary
A Systematic Approach to Nanotechnology Based on a Small Set of Molecular Building Blocks
"... Abstract — A small set of molecular building blocks will allow the implementation of “universally programmable intelligent matter,” that is, matter whose structure, properties, and behavior can be programmed, quite literally, at the molecular level. The approach is based on combinatory logic, a term ..."
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Abstract — A small set of molecular building blocks will allow the implementation of “universally programmable intelligent matter,” that is, matter whose structure, properties, and behavior can be programmed, quite literally, at the molecular level. The approach is based on combinatory logic, a termrewriting or graphsubstitution system, which can be interpreted as an abstract model of molecular processes. In such systems there are small sets of substitution operations (reactions) that are universal in the sense that they can be used to program any Turingcomputable function. Although these operations provide the building blocks for univerally programmable intelligent matter, there are many issues that arise in the context of molecular computation, which we address. Index Terms — adaptive matter, combinatory logic, DNA computing, functional programming, intelligent matter, molecular computing, nanocomputation, nanotechnology, programmable matter, termrewriting systems. I.
Under consideration for publication in Math. Struct. in Comp. Science Reversible Combinatory Logic
, 2006
"... The λcalculus is destructive: its main computational mechanism – beta reduction – destroys the redex and makes it thus impossible to replay the computational steps. Combinatory logic is a variant of the λcalculus which maintains irreversibility. Recently, reversible computational models have been ..."
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The λcalculus is destructive: its main computational mechanism – beta reduction – destroys the redex and makes it thus impossible to replay the computational steps. Combinatory logic is a variant of the λcalculus which maintains irreversibility. Recently, reversible computational models have been studied mainly in the context of quantum computation, as (without measurements) quantum physics is inherently reversible. However, reversibility also changes fundamentally the semantical framework in which classical computation has to be investigated. We describe an implementation of classical combinatory logic into a reversible calculus for which we present an algebraic model based on a generalisation of the notion of group. 1.
Classical Combinatory Logic
"... Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written ..."
Abstract
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Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written in a system “à la Hilbert”. We present in this paper a combinatory logic which corresponds to propositional classical logic. This system is equivalent to the system of Barbanera and Berardi. λ Sym P rop