New techniques for constructing a distributive law of a monad over another are studied using subm... more New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product mon-ads, recursively-defined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad approximations for compositions which fail to be a monad.
The way in which Pfn (sets and partial functions) provides a setting for the semantics of determi... more The way in which Pfn (sets and partial functions) provides a setting for the semantics of deterministic programs [and Rel (sets and relations) provides a setting for the semantics of nondeterministic programs] has led us to axiomatize the notion of a partially-additive monoid. We show that programs incorporating procedure calls may be represented by graph grammars, with one non-terminal and production for each distinct procedure (including the program itself). Program execution may be construed as a process of interpretation of graphs obtained by repeated graph substitution. We show that the resultant interpretive semantics yields the same result as our theory of the canonical fixpoint for abstract recursion schemes introduced in an earlier paper.
A critical element of a pressure-tolerant fiber optic sonar link (FOSL) is the pressure tolerant ... more A critical element of a pressure-tolerant fiber optic sonar link (FOSL) is the pressure tolerant electronic (PTE) light-emitting diode (LED)/fiber optic cable interface. The term PTE denotes that the interface is capable of meeting performance specifications without the use of a pressure vessel while exposed to hydrostatic and hydrodynamic pressures external to the submarine hull. The paper begins with a description of the FOSL system and its requirements as well as a discussion of the PTE environmental requirements. The present PTE technology base is assessed briefly for its adequacy in meeting PTE FOSL system requirements. The design of the PTE LED/fiber optic interface was optimized by selecting the design with the best expected performance estimated by calculating total power coupled. The effects of temperature and pressure on the total power coupled were analyzed and compared with experimental measurements of power coupling at pressures up to 2 klbf/in.2gauge. It was concluded ...
The last 30 years have seen the growth of a new branch of mathematics called CATEGORY THEORY whic... more The last 30 years have seen the growth of a new branch of mathematics called CATEGORY THEORY which provides a general perspective on many different branches of mathematics. Many workers (see Lawvere, 1972) have argued that it is category theory, rather than SET THEORY, that provides the proper setting for the study of the FOUNDATIONS OF MATHEMATICS. The aim of
Abstract. We present for the first time a general definition of machines in an arbitrary category... more Abstract. We present for the first time a general definition of machines in an arbitrary category which unifies the theories of sequential machines, linear control systems, tree automata and stochastic automata. To make the paper relatively accessible, we provide a careful ...
ABSTRACT In this paper we introduce the concept of Kleisli strength for monads in an arbitrary sy... more ABSTRACT In this paper we introduce the concept of Kleisli strength for monads in an arbitrary symmetric monoidal category. This generalises the notion of commutative monad and gives us new examples, even in the cartesian-closed category of sets. We exploit the presence of Kleisli strength to derive methods for generating distributive laws. We also introduce linear equations to extend the results to certain quotient monads. Mechanisms are described for finding strengths that produce a large collection of new distributive laws, and consequently monad compositions, including the composition of monadic data types such as lists, trees, exceptions and state.
... 9. Godement, R. (1958) Theorie des Faisceux, Hermann. 10. Irwin R. Goodman , Hung T. Nguyen, ... more ... 9. Godement, R. (1958) Theorie des Faisceux, Hermann. 10. Irwin R. Goodman , Hung T. Nguyen, Uncertainty Models for Knowledge-Based Systems; A Unified Approach to the Measurement of Uncertainty, Elsevier Science Inc., New York, NY, 1985. ... Ernie G. Manes: colleagues. ...
New techniques for constructing a distributive law of a monad over another are studied using subm... more New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product mon-ads, recursively-defined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad approximations for compositions which fail to be a monad.
The way in which Pfn (sets and partial functions) provides a setting for the semantics of determi... more The way in which Pfn (sets and partial functions) provides a setting for the semantics of deterministic programs [and Rel (sets and relations) provides a setting for the semantics of nondeterministic programs] has led us to axiomatize the notion of a partially-additive monoid. We show that programs incorporating procedure calls may be represented by graph grammars, with one non-terminal and production for each distinct procedure (including the program itself). Program execution may be construed as a process of interpretation of graphs obtained by repeated graph substitution. We show that the resultant interpretive semantics yields the same result as our theory of the canonical fixpoint for abstract recursion schemes introduced in an earlier paper.
A critical element of a pressure-tolerant fiber optic sonar link (FOSL) is the pressure tolerant ... more A critical element of a pressure-tolerant fiber optic sonar link (FOSL) is the pressure tolerant electronic (PTE) light-emitting diode (LED)/fiber optic cable interface. The term PTE denotes that the interface is capable of meeting performance specifications without the use of a pressure vessel while exposed to hydrostatic and hydrodynamic pressures external to the submarine hull. The paper begins with a description of the FOSL system and its requirements as well as a discussion of the PTE environmental requirements. The present PTE technology base is assessed briefly for its adequacy in meeting PTE FOSL system requirements. The design of the PTE LED/fiber optic interface was optimized by selecting the design with the best expected performance estimated by calculating total power coupled. The effects of temperature and pressure on the total power coupled were analyzed and compared with experimental measurements of power coupling at pressures up to 2 klbf/in.2gauge. It was concluded ...
The last 30 years have seen the growth of a new branch of mathematics called CATEGORY THEORY whic... more The last 30 years have seen the growth of a new branch of mathematics called CATEGORY THEORY which provides a general perspective on many different branches of mathematics. Many workers (see Lawvere, 1972) have argued that it is category theory, rather than SET THEORY, that provides the proper setting for the study of the FOUNDATIONS OF MATHEMATICS. The aim of
Abstract. We present for the first time a general definition of machines in an arbitrary category... more Abstract. We present for the first time a general definition of machines in an arbitrary category which unifies the theories of sequential machines, linear control systems, tree automata and stochastic automata. To make the paper relatively accessible, we provide a careful ...
ABSTRACT In this paper we introduce the concept of Kleisli strength for monads in an arbitrary sy... more ABSTRACT In this paper we introduce the concept of Kleisli strength for monads in an arbitrary symmetric monoidal category. This generalises the notion of commutative monad and gives us new examples, even in the cartesian-closed category of sets. We exploit the presence of Kleisli strength to derive methods for generating distributive laws. We also introduce linear equations to extend the results to certain quotient monads. Mechanisms are described for finding strengths that produce a large collection of new distributive laws, and consequently monad compositions, including the composition of monadic data types such as lists, trees, exceptions and state.
... 9. Godement, R. (1958) Theorie des Faisceux, Hermann. 10. Irwin R. Goodman , Hung T. Nguyen, ... more ... 9. Godement, R. (1958) Theorie des Faisceux, Hermann. 10. Irwin R. Goodman , Hung T. Nguyen, Uncertainty Models for Knowledge-Based Systems; A Unified Approach to the Measurement of Uncertainty, Elsevier Science Inc., New York, NY, 1985. ... Ernie G. Manes: colleagues. ...
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