## Lagois Connections - a Counterpart to Galois Connections - (1993)

Venue: | Theoretical Computer Science |

Citations: | 4 - 0 self |

### BibTeX

@ARTICLE{Melton93lagoisconnections,

author = {Austin Melton and Bernd S.W. Schröder and George E. Strecker},

title = {Lagois Connections - a Counterpart to Galois Connections -},

journal = {Theoretical Computer Science},

year = {1993},

volume = {136},

pages = {79--107}

}

### OpenURL

### Abstract

In this paper we define a Lagois connection, which is a generalization of a special type of Galois connection. We begin by introducing two examples of Lagois connections. We then recall the definition of Galois connection and some of its properties; next we define Lagois connection, establish some of its properties, and compare these with properties of Galois connections; and then we (further) develop examples of Lagois connections. Via these examples it is shown that, as is the case of Galois connections, there is a plethora of Lagois connections. Also it is shown that several fundamental situations in computer science and mathematics that cannot be interpreted in terms of Galois connections naturally fit into the theory of Lagois connections. key words: Galois connection, Galois insertion, Lagois connection, quasiinverse, poset system, closure operator, interior operator AMS subject classification: Primary: 06A15, 06A10 Secondary: 68F05, 68F99, 54B99 The authors were p...

### Citations

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Citation Context ...ents not true, nF represents not false, nN represents not neutral, and ? represents no knowledge. The order on ExtB is given in Figure 10. In trying 29 oe - * ) * ) * ) * ) * ) * ) * ) * ) g [-2] (-1-=-=[1]-=-) (-1-(5-[4])) (-1-([5]-4)) (-1-((2-[-3])-4)) (-1-(([2]- -3)-4)) (-1-(([2- -3])-4)) (-1-([(2- -3)]-4)) (-1-([(2- -3)-4])) (-1-[((2- -3)-4)]) ([-1]-((2- -3)-4)) ([-1-((2- -3)-4)]) [(-1-((2- -3)-4))] f ... |

90 | Laws of programming
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Citation Context ...sents not false, nN represents not neutral, and ? represents no knowledge. The order on ExtB is given in Figure 10. In trying 29 oe - * ) * ) * ) * ) * ) * ) * ) * ) g [-2] (-1-[1]) (-1-(5-[4])) (-1-(=-=[5]-=--4)) (-1-((2-[-3])-4)) (-1-(([2]- -3)-4)) (-1-(([2- -3])-4)) (-1-([(2- -3)]-4)) (-1-([(2- -3)-4])) (-1-[((2- -3)-4)]) ([-1]-((2- -3)-4)) ([-1-((2- -3)-4)]) [(-1-((2- -3)-4))] f (nil,-1:2:-3:neg:add:4:... |

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Residuation Theory
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Citation Context ... a Galois insertion iff f is one-to-one or, equivalently, iff g is onto (cf. Proposition 1.2(13).) 1.2 Facts about Galois connections The following results are well-known. Proofs of them are given in =-=[2]-=-, [3], [6], [7], and [8]. In that which follows we will show that results similar to many of them hold for Lagois connections but that for others no reasonable Lagois analogue is available. Propositio... |

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Galois connexions
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Citation Context ...tion iff f is one-to-one or, equivalently, iff g is onto (cf. Proposition 1.2(13).) 1.2 Facts about Galois connections The following results are well-known. Proofs of them are given in [2], [3], [6], =-=[7]-=-, and [8]. In that which follows we will show that results similar to many of them hold for Lagois connections but that for others no reasonable Lagois analogue is available. Proposition 1.2 Let ((P; ... |

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Citation Context ...ch under Contract N00014-88-K-0455. 1 1 Introduction A Galois connection is an elegant and easily defined relationship among pairs of partially ordered sets and order preserving maps between them. In =-=[6]-=- it is shown that some activities which commonly occur in computer science are examples of Galois connections; these examples include showing correctness of a translator and defining a coercion map be... |

22 |
et al, A Compendium of Continuous Lattice
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Citation Context ...lois insertion iff f is one-to-one or, equivalently, iff g is onto (cf. Proposition 1.2(13).) 1.2 Facts about Galois connections The following results are well-known. Proofs of them are given in [2], =-=[3]-=-, [6], [7], and [8]. In that which follows we will show that results similar to many of them hold for Lagois connections but that for others no reasonable Lagois analogue is available. Proposition 1.2... |

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Citation Context ...then nothing gets pushed onto stk), and place the rest of the postfix expression in con remembering that a sub must be put in con as neg : add. For example given the marked expression (2 \Gamma ((3 + =-=[4]-=-) + (7 \Gamma 8))), we get: 1) 4 is ticked, e.g., we have 4#. 2) 2 3 4# add 7 8 sub add sub 3) (4s3s2 ; add : 7 : 8 : neg : add : add : neg : add) So f((2 \Gamma ((3 + [4]) + (7 \Gamma 8)))) = (4s3s2 ... |

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Citation Context ...f is one-to-one or, equivalently, iff g is onto (cf. Proposition 1.2(13).) 1.2 Facts about Galois connections The following results are well-known. Proofs of them are given in [2], [3], [6], [7], and =-=[8]-=-. In that which follows we will show that results similar to many of them hold for Lagois connections but that for others no reasonable Lagois analogue is available. Proposition 1.2 Let ((P; ); f; g; ... |

1 |
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Citation Context ...eters S and T are equivalent, a Lagois connection between their state sets arises naturally. The form of interpreter equivalence we consider is inspired by McGowan's mapping technique as presented in =-=[10]-=-. The exposition here is also influenced by [6]. 4.1.1 An operational interpreter model We assume that an interpreter S consists of a set M of states and a next state or successor relation ) on M . We... |