scholarly journals On the subject reduction property for algebraic type systems

Author(s):  
G. Barthe ◽  
P. -A. Mellies
2001 ◽  
Vol 11 (1) ◽  
pp. 3-19 ◽  
Author(s):  
ROEL BLOO

We define an extension of pure type systems with explicit substitution. We show that the type systems with explicit substitution are strongly normalizing iff their ordinary counterparts are. Subject reduction is shown to fail in general but a weaker, though still useful, subject reduction property is established. A more complicated extension is proposed for which subject reduction does hold in general.


2007 ◽  
Vol 17 (4) ◽  
pp. 587-645 ◽  
Author(s):  
PABLO GARRALDA ◽  
EDUARDO BONELLI ◽  
ADRIANA COMPAGNONI ◽  
MARIANGIOLA DEZANI-CIANCAGLINI

We define BACI(Boxed Ambients with Communication Interfaces), an ambient calculus with a flexible communication policy. Traditionally, typed ambient calculi have a fixed communication policy determining the kind of information that can be exchanged with a parent ambient, even though mobility changes the parent. BACI lifts that restriction, allowing different communication policies with different parents during computation. Furthermore, BACI separates communication and mobility by making the channels of communication between ambients explicit. In contrast with other typed ambient calculi where communication policies are global, each ambient in BACI is equipped with a description of the communication policies ruling its information exchange with parent and child ambients. The communication policies of ambients increase when they move: more precisely, when an ambient enters another ambient, the entering ambient and the host ambient can exchange their communication ports and agree on the kind of information to be exchanged. This information is recorded locally in both ambients.We show the type-soundness of BACI, proving that it satisfies the subject reduction property, and we study its behavioural semantics by means of a labelled transition system.


1997 ◽  
Vol 7 (6) ◽  
pp. 557-591 ◽  
Author(s):  
P. ØRBÆK ◽  
J. PALSBERG

This paper introduces trust analysis for higher-order languages. Trust analysis encourages the programmer to make explicit the trustworthiness of data, and in return it can guarantee that no mistakes with respect to trust will be made at run-time. We present a confluent λ-calculus with explicit trust operations, and we equip it with a trust-type system which has the subject reduction property. Trust information is presented as annotations of the underlying Curry types, and type inference is computable in O(n3) time.


Author(s):  
Georgе B. Kleiner

The article discusses the ways of creating unified economic theory describing the functioning and interaction of significant units of the national economy and the economy as a whole. The general construction of a unified economic theory, its connection with the system economic theory and its system components (object, process, project, environmental economic theories) is determined. Based on the example of institutional economic theory, it is shown that the expansion of its terminology and conceptual apparatus within the framework of the construction of a unified multi-level economic theory allows minimizing the contradictions between the “old” and “new” institutionalism, methodological individualism and methodological holism. This expansion is carried out following the principle of the maximum possible system community in two lines. The first line is expanding the subject area (along with organizations as systems of the object type, systems of the process, project, the environment types are also considered as the focal subject of study). The second line is the expanding the instrumental area (analysis of the influence on the behavior of agents from not only institutional subsystems but also information, infrastructural, network, mental, and other environmental subsystems). As a result, each system receives the compact and maximum volumetric internal systemic content and, at the same time, the minimum volumetric external systemic environment, which creates conditions for the effective application of the duality principle in the theory of economic systems. Thus, the system expansion of institutional theory should take place in two lines: content of the theory per se and creation of its immediate environment.


2015 ◽  
Vol 27 (5) ◽  
pp. 603-625 ◽  
Author(s):  
MARIO COPPO ◽  
MARIANGIOLA DEZANI-CIANCAGLINI ◽  
INES MARGARIA ◽  
MADDALENA ZACCHI

This paper gives a complete characterisation of type isomorphism definable by terms of a λ-calculus with intersection and union types. Unfortunately, when union is considered the Subject Reduction property does not hold in general. However, it is well known that in the λ-calculus, independently of the considered type system, the isomorphism between two types can be realised only by invertible terms. Notably, all invertible terms are linear terms. In this paper, the isomorphism of intersection and union types is investigated using a relevant type system for linear terms enjoying the Subject Reduction property. To characterise type isomorphism, a similarity between types and a type reduction are introduced. Types have a unique normal form with respect to the reduction rules and two types are isomorphic if and only if their normal forms are similar.


1999 ◽  
Vol 9 (6) ◽  
pp. 625-647 ◽  
Author(s):  
TRISTAN CROLARD

We derive a confluent λ-calculus with a catch/throw mechanism (called λct-calculus) from Parigot's λμ-calculus. We also present several translations from one calculus into the other which are morphisms for the reduction. We use them to show that the λct-calculus is a retract of λμ-calculus (these calculi are isomorphic if we consider only convertibility). As a by-product, we obtain the subject reduction property for the λct-calculus, as well as the strong normalization for λct-terms typable in the second order classical natural deduction.


2008 ◽  
Vol 8 (1) ◽  
pp. 171-188 ◽  
Author(s):  
Zbigniew Smalko ◽  
Janusz Szpytko

The Man - Machine Type Systems Modeling ApproachThe subject of this paper deals with selected usable characteristics of man - machine systems described by the selected basic attributes. The paper is describing also major objectives of safety engineering, based on the system approach, understanding the structure of safety management system, including the human factor, and all interrelationships between the system components. The part of the paper is example of safety engineering implementations in practice.


1998 ◽  
Vol 11 (4) ◽  
pp. 481-492 ◽  
Author(s):  
A. A. Martynyuk ◽  
I. P. Stavroulakis

This paper investigates the absolute stability on ℊs of the zero solution of Lurie-Postnikov systems with impulses and structural perturbation. A number of absolutely stable on ℊs theorems of the Lyapunov type for Lurie-Postnikov systems are proved, extending and generalizing previous work on the subject. These results are applied to some fourth-order Lurie-Postnikov type systems decomposed into two systems.


1995 ◽  
Vol 2 (31) ◽  
Author(s):  
Jens Palsberg ◽  
Peter Ørbæk

This paper introduces trust analysis for higher-order languages. Trust<br />analysis encourages the programmer to make explicit the trustworthiness of<br />data, and in return it can guarantee that no mistakes with respect to trust will<br />be made at run-time. We present a confluent lambda-calculus with explicit trust<br />operations, and we equip it with a trust-type system which has the subject<br />reduction property. Trust information in presented as two annotations of each<br />function type constructor, and type inference is computable in O(n^3) time.


PMLA ◽  
1935 ◽  
Vol 50 (4) ◽  
pp. 1320-1327
Author(s):  
Colbert Searles

THE germ of that which follows came into being many years ago in the days of my youth as a university instructor and assistant professor. It was generated by the then quite outspoken attitude of colleagues in the “exact sciences”; the sciences of which the subject-matter can be exactly weighed and measured and the force of its movements mathematically demonstrated. They assured us that the study of languages and literature had little or nothing scientific about it because: “It had no domain of concrete fact in which to work.” Ergo, the scientific spirit was theirs by a stroke of “efficacious grace” as it were. Ours was at best only a kind of “sufficient grace,” pleasant and even necessary to have, but which could, by no means ensure a reception among the elected.


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