The Experts below are selected from a list of 144 Experts worldwide ranked by ideXlab platform
Rasmus Ejlers Møgelberg - One of the best experts on this subject based on the ideXlab platform.
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Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes
2013 28th Annual ACM IEEE Symposium on Logic in Computer Science, 2013Co-Authors: Lars Birkedal, Rasmus Ejlers MøgelbergAbstract:Guarded recursive functions and types are useful for giving semantics to advanced programming languages and for higher-order programming with infinite data types, such as streams, e.g., for modeling reactive systems. We propose an extension of intensional type theory with rules for forming fixed points of guarded recursive functions. Guarded recursive types can be formed simply by taking fixed points of guarded recursive functions on the universe of types. Moreover, we present a general model construction for constructing models of the intensional type theory with guarded recursive functions and types. When applied to the groupoid model of intensional type theory with the universe of small discrete groupoids, the construction gives a model of guarded recursion for which there is a one-to-one correspondence between fixed points of functions on the universe of types and fixed points of (suitable) operators on types. In particular, we find that the functor category Grpdωop from the Preordered Set of natural numbers to the category of groupoids is a model of intensional type theory with guarded recursive types.
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LICS - Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes
2013 28th Annual ACM IEEE Symposium on Logic in Computer Science, 2013Co-Authors: Lars Birkedal, Rasmus Ejlers MøgelbergAbstract:Guarded recursive functions and types are useful for giving semantics to advanced programming languages and for higher-order programming with infinite data types, such as streams, e.g., for modeling reactive systems. We propose an extension of intensional type theory with rules for forming fixed points of guarded recursive functions. Guarded recursive types can be formed simply by taking fixed points of guarded recursive functions on the universe of types. Moreover, we present a general model construction for constructing models of the intensional type theory with guarded recursive functions and types. When applied to the groupoid model of intensional type theory with the universe of small discrete groupoids, the construction gives a model of guarded recursion for which there is a one-to-one correspondence between fixed points of functions on the universe of types and fixed points of (suitable) operators on types. In particular, we find that the functor category Grpdωop from the Preordered Set of natural numbers to the category of groupoids is a model of intensional type theory with guarded recursive types.
Lars Birkedal - One of the best experts on this subject based on the ideXlab platform.
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Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes
2013 28th Annual ACM IEEE Symposium on Logic in Computer Science, 2013Co-Authors: Lars Birkedal, Rasmus Ejlers MøgelbergAbstract:Guarded recursive functions and types are useful for giving semantics to advanced programming languages and for higher-order programming with infinite data types, such as streams, e.g., for modeling reactive systems. We propose an extension of intensional type theory with rules for forming fixed points of guarded recursive functions. Guarded recursive types can be formed simply by taking fixed points of guarded recursive functions on the universe of types. Moreover, we present a general model construction for constructing models of the intensional type theory with guarded recursive functions and types. When applied to the groupoid model of intensional type theory with the universe of small discrete groupoids, the construction gives a model of guarded recursion for which there is a one-to-one correspondence between fixed points of functions on the universe of types and fixed points of (suitable) operators on types. In particular, we find that the functor category Grpdωop from the Preordered Set of natural numbers to the category of groupoids is a model of intensional type theory with guarded recursive types.
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LICS - Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes
2013 28th Annual ACM IEEE Symposium on Logic in Computer Science, 2013Co-Authors: Lars Birkedal, Rasmus Ejlers MøgelbergAbstract:Guarded recursive functions and types are useful for giving semantics to advanced programming languages and for higher-order programming with infinite data types, such as streams, e.g., for modeling reactive systems. We propose an extension of intensional type theory with rules for forming fixed points of guarded recursive functions. Guarded recursive types can be formed simply by taking fixed points of guarded recursive functions on the universe of types. Moreover, we present a general model construction for constructing models of the intensional type theory with guarded recursive functions and types. When applied to the groupoid model of intensional type theory with the universe of small discrete groupoids, the construction gives a model of guarded recursion for which there is a one-to-one correspondence between fixed points of functions on the universe of types and fixed points of (suitable) operators on types. In particular, we find that the functor category Grpdωop from the Preordered Set of natural numbers to the category of groupoids is a model of intensional type theory with guarded recursive types.
Mykola Khrypchenko - One of the best experts on this subject based on the ideXlab platform.
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Lie derivations of incidence algebras
Linear Algebra and its Applications, 2017Co-Authors: Xian Zhang, Mykola KhrypchenkoAbstract:Abstract Let X be a locally finite Preordered Set, R a commutative ring with identity and I ( X , R ) the incidence algebra of X over R . In this note we prove that each Lie derivation of I ( X , R ) is proper, provided that R is 2-torsion free.
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Jordan derivations of finitary incidence rings
Linear & Multilinear Algebra, 2016Co-Authors: Mykola KhrypchenkoAbstract:Let P be a Preordered Set, R a ring and FI(P, R) the finitary incidence ring of P over R. We find a criterion for all the Jordan derivations of FI(P, R) to be derivations. In particular, we prove that each Jordan derivation of the ring of row-finite -matrices over R is a derivation, if .
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Jordan derivations of finitary incidence rings
arXiv: Rings and Algebras, 2015Co-Authors: Mykola KhrypchenkoAbstract:Let $P$ be a Preordered Set, $R$ a ring and $FI(P,R)$ the finitary incidence ring of $P$ over $R$. We find a criterion for all Jordan derivations of $FI(P,R)$ to be derivations and generalize Theorem 3.3 from arXiv:1411.6123. In particular, we prove that each Jordan derivation of the ring $RFM_I(R)$ of row-finite $I\times I$-matrices over $R$ is a derivation, if $|I|>1$.
Yuping Yang - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear derivations of incidence algebras
Acta Mathematica Hungarica, 2019Co-Authors: Yuping YangAbstract:Let ($$X,\leq$$) be a locally finite Preordered Set and R a 2-torsion free commutative ring with unity, I(X, R) the incidence algebra of X over R. We prove that each nonlinear derivation of I(X, R) is a sum of an inner derivation, a transitive induced derivation and an additive induced derivation. In particular, every nonlinear derivation of I(X, R) is automatically additive.
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Lie n-derivations of incidence algebras
Communications in Algebra, 2019Co-Authors: Zhankui Xiao, Yuping YangAbstract:AbstractLet n be a positive integer with n≥2. Let X be a locally finite Preordered Set, R a commutative ring with unity and I(X, R) the incidence algebra of X over R. We prove in this article that ...
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Nonlinear Lie derivations of incidence algebras of finite rank
Linear & Multilinear Algebra, 2019Co-Authors: Yuping YangAbstract:ABSTRACTLet (X,≤) be a finite Preordered Set, R a 2-torsion free commutative ring with unity and I(X,R) the incidence algebra of X over R. In this paper we prove that every nonlinear Lie derivation of I(X,R) is of the standard form. More explicitly, each nonlinear Lie derivation of I(X,R) is a sum of an inner derivation, a transitive induced derivation, an additive induced derivation and a central-valued map.
Noam Zeilberger - One of the best experts on this subject based on the ideXlab platform.
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LICS - A theory of linear typings as flows on 3-valent graphs
Proceedings of the 33rd Annual ACM IEEE Symposium on Logic in Computer Science, 2018Co-Authors: Noam ZeilbergerAbstract:Building on recently established enumerative connections between lambda calculus and the theory of embedded graphs (or "maps"), this paper develops an analogy between typing (of lambda terms) and coloring (of maps). Our starting point is the classical notion of an abelian group-valued "flow" on an abstract graph (Tutte, 1954). Typing a linear lambda term may be naturally seen as constructing a flow (on an embedded 3-valent graph with boundary) valued in a more general algebraic structure consisting of a Preordered Set equipped with an "implication" operation and unit satisfying composition, identity, and unit laws. Interesting questions and results from the theory of flows (such as the existence of nowhere-zero flows) may then be re-examined from the standpoint of lambda calculus and logic. For example, we give a characterization of when the local flow relations (across vertices) may be categorically lifted to a global flow relation (across the boundary), proving that this holds just in case the underlying map has the orientation of a lambda term. We also develop a basic theory of rewriting of flows that suggests topological meanings for classical completeness results in combinatory logic, and introduce a polarized notion of flow, which draws connections to the theory of proof-nets in linear logic and to bidirectional typing.
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A theory of linear typings as flows on 3-valent graphs
arXiv: Logic in Computer Science, 2018Co-Authors: Noam ZeilbergerAbstract:Building on recently established enumerative connections between lambda calculus and the theory of embedded graphs (or "maps"), this paper develops an analogy between typing (of lambda terms) and coloring (of maps). Our starting point is the classical notion of an abelian group-valued "flow" on an abstract graph (Tutte, 1954). Typing a linear lambda term may be naturally seen as constructing a flow (on an embedded 3-valent graph with boundary) valued in a more general algebraic structure consisting of a Preordered Set equipped with an "implication" operation and unit satisfying composition, identity, and unit laws. Interesting questions and results from the theory of flows (such as the existence of nowhere-zero flows) may then be re-examined from the standpoint of lambda calculus and logic. For example, we give a characterization of when the local flow relations (across vertices) may be categorically lifted to a global flow relation (across the boundary), proving that this holds just in case the underlying map has the orientation of a lambda term. We also develop a basic theory of rewriting of flows that suggests topological meanings for classical completeness results in combinatory logic, and introduce a polarized notion of flow, which draws connections to the theory of proof-nets in linear logic and to bidirectional typing.