## The logic of recursive equations (1998)

Venue: | the Journal of Symbolic Logic |

Citations: | 12 - 5 self |

### BibTeX

@ARTICLE{Mcarthur98thelogic,

author = {Monica Mcarthur and Yiannis N. Moschovakis and Lawrence S. Moss and Glen T. Whitney and A. J. C. Hurkens and Monica Mcarthur and Yiannis N. Moschovakis and Lawrence S. Moss and Glen and T. Whitney},

title = {The logic of recursive equations},

journal = {the Journal of Symbolic Logic},

year = {1998},

pages = {451--478}

}

### Years of Citing Articles

### OpenURL

### Abstract

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### Citations

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Citation Context ...; this type of intensionality is at the core of many studies of concurrent computation. Early attempts to understand and prove properties of recursive definitions in various specific contexts include =-=[5, 6, 15, 13]-=-. The general study of recursion equations has been pursued under several guises since then: I as recursive applicative program schemes [4], u-calculus [2], and perhaps most notably as the iteration t... |

473 |
Denotational Semantics: the Scott-Strachey Approach to Programming Languages Theory
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Citation Context ... "Functorial Dagger Implication" (for base morphisms) of Bloom and E'sik [1]. However, one may regard (RI) as a descendent of the principle called "Scott induction" or "fix-point induction" (see Stoy =-=[22]-=-). The rule (RI) formulates a set of instances of this principle which are valid for general (not necessarily continuous, as in [22]) least fixed points, and which suffice to establish all valid ident... |

28 | Iteration theories: the equational logic of iterative processes
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Citation Context ...ctional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The 'pure," propositional fragment FLRo turns out to coincide with the iteration theories of =-=[1]-=-. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models. In [18, 17], Moschovaki... |

16 |
Monadic computation and iterative algebraic theories, Logic colloquium
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Citation Context ...e latter work builds on Lawvere's introduction of algebraic theories [14] in order to get categorical presentations of universal algebra, and Elgot's use of these in connection with flowchart schemes =-=[7]-=-. Thus, the relationship of this paper and [1] is roughly that between ordinary equational logic and algebraic theories. In particular, we will provide an explicit "dictionary" showing that the catego... |

12 |
Algorithmes d’equivalence et de reduction a des expressions minimales dans une classe d’equations recursives simples
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Citation Context ... definitions in various specific contexts include [5, 6, 15, 13]. The general study of recursion equations has been pursued under several guises since then: I as recursive applicative program schemes =-=[4]-=-, u-calculus [2], and perhaps most notably as the iteration theories [10, 1] of Bloom and Esik. The latter work builds on Lawvere's introduction of algebraic theories [14] in order to get categorical ... |

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Citation Context ...o compute (A( -)E) (dT, first suppose that none of the x1 happen to coincide with any of the 2These classes are not themselves new; indeed, Cont is the standard environment of "domain theory," and in =-=[9]-=-, Mon is called ./1 and Wk is the class of "concrete Park theories."454 HURKENS, McARTHUR, MOSCHOVAKIS, MOSS, AND WHITNEY yi. Let f i = A(yl,. . ., yy, x) E for i from 0 to m. The functions f I throu... |

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Recursive Procedures
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Citation Context ...; this type of intensionality is at the core of many studies of concurrent computation. Early attempts to understand and prove properties of recursive definitions in various specific contexts include =-=[5, 6, 15, 13]-=-. The general study of recursion equations has been pursued under several guises since then: I as recursive applicative program schemes [4], u-calculus [2], and perhaps most notably as the iteration t... |

5 |
The logic of functional recursion. To appear
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Citation Context ...ract. We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in "propositional" fragments of the functional language of recursion FLR =-=[18, 17]-=-, i.e., without the value passing or abstraction allowed in FLR. The 'pure," propositional fragment FLRo turns out to coincide with the iteration theories of [1]. Our main focus here concerns the shar... |

4 | Recursion structures for non-determinism and concurrency - Whitney - 1994 |

2 |
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Citation Context ...; this type of intensionality is at the core of many studies of concurrent computation. Early attempts to understand and prove properties of recursive definitions in various specific contexts include =-=[5, 6, 15, 13]-=-. The general study of recursion equations has been pursued under several guises since then: I as recursive applicative program schemes [4], u-calculus [2], and perhaps most notably as the iteration t... |

1 |
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Citation Context ...lates a set of instances of this principle which are valid for general (not necessarily continuous, as in [22]) least fixed points, and which suffice to establish all valid identities. The references =-=[9, 8]-=- investigate this connection in greater detail. The following proposition is straightforward; the case of Recursion Inference is proved by induction on the stages of a recursion. PROPOSITION 1 (Soundn... |

1 |
in iterative and rational algebraic theories
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Citation Context ...neral study of recursion equations has been pursued under several guises since then: I as recursive applicative program schemes [4], u-calculus [2], and perhaps most notably as the iteration theories =-=[10, 1]-=- of Bloom and Esik. The latter work builds on Lawvere's introduction of algebraic theories [14] in order to get categorical presentations of universal algebra, and Elgot's use of these in connection w... |

1 |
Algebraic recursion theory, Ellis Horwood Limited
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Citation Context ...he plain symbol g will abbreviate go for nullary function symbols (i.e., constant symbols). The special symbol I will I Another approach to axiomatic theories of recursion, algebraic recursion theory =-=[21, 11, 12]-=-, has a different emphasis: it confines itself to least (or initial) fixed points, and seeks to understand the additional combinatorial properties needed to support stronger results analogous to class... |

1 |
generalization of algebraic recursion theory
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Citation Context ...he plain symbol g will abbreviate go for nullary function symbols (i.e., constant symbols). The special symbol I will I Another approach to axiomatic theories of recursion, algebraic recursion theory =-=[21, 11, 12]-=-, has a different emphasis: it confines itself to least (or initial) fixed points, and seeks to understand the additional combinatorial properties needed to support stronger results analogous to class... |

1 |
Functorial semantics of algebraic theories, Proceedings of the National Academy of Sciences of the United
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Citation Context ...e applicative program schemes [4], u-calculus [2], and perhaps most notably as the iteration theories [10, 1] of Bloom and Esik. The latter work builds on Lawvere's introduction of algebraic theories =-=[14]-=- in order to get categorical presentations of universal algebra, and Elgot's use of these in connection with flowchart schemes [7]. Thus, the relationship of this paper and [1] is roughly that between... |

1 |
Powerdornains, powiverstructures, andfairness, Proceedings of computer science logic '94
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- 1995
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Citation Context ...well known that many classes of structures have the same collection of valid identities: [1] surveys a wide range of such classes, and we would also like to call attention to the player structures of =-=[19, 20]-=-, which are a class of highly intensional models of concurrency which satisfy exactly the standard identities. The results of this section illustrate two other, important aspects of this robustness. F... |

1 |
Computability in combinatory spaces
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Citation Context ...he plain symbol g will abbreviate go for nullary function symbols (i.e., constant symbols). The special symbol I will I Another approach to axiomatic theories of recursion, algebraic recursion theory =-=[21, 11, 12]-=-, has a different emphasis: it confines itself to least (or initial) fixed points, and seeks to understand the additional combinatorial properties needed to support stronger results analogous to class... |