## A New Framework for Declarative Programming (2001)

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Citations: | 8 - 3 self |

### BibTeX

@MISC{Finkelstein01anew,

author = {Stacy E. Finkelstein and Peter Freyd and James Lipton},

title = {A New Framework for Declarative Programming},

year = {2001}

}

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### Abstract

We propose a new indexed-category syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over tau-categories:finite product categories with canonical structure.

### Citations

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Citation Context ...han that of functional or imperative programming. The divide has narrowed in the last ten years, with the development of new denotational, operational, and abstract interpretations for logic programs =-=[11, 39, 40, 14, 31, 38]-=-. There has been a growing interest in a categorical formulation of these ideas, essentially for the same reasons they proved of interest in other programming paradigms.s3 Categorical approaches to lo... |

820 | Constraint Logic Programming: A
- Jaffar, Maher
- 1994
(Show Context)
Citation Context ...he original Horn Clause core [26, 48, 51, 50, 46, 28]) and to add control features and constructs drawn from other language paradigms (e.g. types [55, 32, 49], partial evaluation [31] and constraints =-=[10, 29, 30]-=-, to name just a few). The effect has been to expand the boundaries of the subject and of the very notion of declarative content of a program. A more general syntax and semantics is needed to model th... |

780 | Notions of computation and monads
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- 1991
(Show Context)
Citation Context ...n programming syntax and semantics have enjoyed widespread use for over a decade [56]. Categorical models have been used to give clean, implementation-independent approaches to side effects and state =-=[47, 62, 68, 52]-=-, non-determinism [53], type disciplines [15, 33] and other logics for computation [7, 63]. The mathematical treatment of some features, such as parametricity and polymorphism, have required categoric... |

747 | The Semantics of Predicate Logic as a Programming Language
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- 1976
(Show Context)
Citation Context ...here. 5 Operational Semantics One of our key aims in proposing a categorical semantics is to give a sufficiently general treatment of the Kowalski-van Emden fixed point semantics of logic programming =-=[38, 67]-=-, a remarkably robust approach that has been successfully applied to many variants and extensions of Prolog. Our semantics takes this idea as a cornerstone of a more general treatment of declarative p... |

690 | On the unity of logic - Girard - 1993 |

468 | Comprehending monads
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(Show Context)
Citation Context ...n programming syntax and semantics have enjoyed widespread use for over a decade [56]. Categorical models have been used to give clean, implementation-independent approaches to side effects and state =-=[47, 62, 68, 52]-=-, non-determinism [53], type disciplines [15, 33] and other logics for computation [7, 63]. The mathematical treatment of some features, such as parametricity and polymorphism, have required categoric... |

460 |
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Citation Context ...d use for over a decade [56]. Categorical models have been used to give clean, implementation-independent approaches to side effects and state [47, 62, 68, 52], non-determinism [53], type disciplines =-=[15, 33]-=- and other logics for computation [7, 63]. The mathematical treatment of some features, such as parametricity and polymorphism, have required categorical tools [57, 21]. Logic programming, however, ha... |

422 |
Category Theory for Computing Science
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(Show Context)
Citation Context ...can be recovered from the indexed formulation \Pi b just given via a well-known canonical operation: the so-called Grothendieck construction of a fibration from an indexed category, presented in e.g. =-=[6]-=-, and sketched in the appendix. Let G(C ; \Pi b) be the source of the Grothendieck fibration induced by the indexed category \Pi b, i.e. the category with objects: pairs hoe; Si with oe 2 jC j and S 2... |

402 |
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Citation Context ...han that of functional or imperative programming. The divide has narrowed in the last ten years, with the development of new denotational, operational, and abstract interpretations for logic programs =-=[11, 39, 40, 14, 31, 38]-=-. There has been a growing interest in a categorical formulation of these ideas, essentially for the same reasons they proved of interest in other programming paradigms.s3 Categorical approaches to lo... |

391 | Uniform proofs as a foundation for logic programming
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(Show Context)
Citation Context ...earch, resolution, as the computational engine. However, the demand for more expressive power and efficiency has led language designers to consider logical extensions to the original Horn Clause core =-=[26, 48, 51, 50, 46, 28]-=-) and to add control features and constructs drawn from other language paradigms (e.g. types [55, 32, 49], partial evaluation [31] and constraints [10, 29, 30], to name just a few). The effect has bee... |

391 | Proofs and Types - Girard, Taylor, et al. - 1989 |

309 | Logic programming in a fragment of intuitionistic linear logic - Hodas, Miller - 1994 |

299 | Abstract Interpretation and Applications to Logic Programs - Cousot, Cousot - 1992 |

157 | Higher-order logic programming - Miller, Nadathur - 1986 |

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154 |
A logical analysis of modules in logic programming
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- 1989
(Show Context)
Citation Context ...pleteness has had a remarkable success in logic programming: countless extensions of declarative programming to e.g. constraints [30], abstract interpretation [5, 11], Hereditarily Harrop programming =-=[44]-=-, higher-order logic [17, 18] build on a similar completeness proof. We take this semantic definition as a foundation for a categorical treatment of uniform logic programming. A slight change in the p... |

145 |
A polymorphic type system for Prolog
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(Show Context)
Citation Context ...language designers to consider logical extensions to the original Horn Clause core [26, 48, 51, 50, 46, 28]) and to add control features and constructs drawn from other language paradigms (e.g. types =-=[55, 32, 49]-=-, partial evaluation [31] and constraints [10, 29, 30], to name just a few). The effect has been to expand the boundaries of the subject and of the very notion of declarative content of a program. A m... |

144 | Constraint logic programming - Jaar, Lassez - 1987 |

121 | Negation and constraint logic programming - Stuckey - 1995 |

120 | The s-semantics approach: theory and applications
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Citation Context ...tionally oriented semantics. Also, it would be interesting to capture in a categorical context the structure of other semantics (compositional, open program, unfolding, etc.), studied by Levi et. al. =-=[8, 40, 1, 43]-=-. In addition, an interesting follow-up to the work presented here would be a categorical analysis of the Jaffar-Lassez criteria [29] for constraint domains and of the Lassez-MacAloon [35] constraint ... |

116 | Declarative Modeling of the Operational Behavior of Logic Languages - Falaschi, Levi, et al. - 1989 |

108 | Parametricity and local variables
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- 1995
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Citation Context ...n programming syntax and semantics have enjoyed widespread use for over a decade [56]. Categorical models have been used to give clean, implementation-independent approaches to side effects and state =-=[47, 62, 68, 52]-=-, non-determinism [53], type disciplines [15, 33] and other logics for computation [7, 63]. The mathematical treatment of some features, such as parametricity and polymorphism, have required categoric... |

104 | How to Declare an Imperative - Wadler - 1995 |

97 | Constraint logic programming languages - Cohen - 1990 |

85 |
Categories for Types
- Crole
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(Show Context)
Citation Context ...d use for over a decade [56]. Categorical models have been used to give clean, implementation-independent approaches to side effects and state [47, 62, 68, 52], non-determinism [53], type disciplines =-=[15, 33]-=- and other logics for computation [7, 63]. The mathematical treatment of some features, such as parametricity and polymorphism, have required categorical tools [57, 21]. Logic programming, however, ha... |

85 | A multiple-conclusion meta-logic
- Miller
- 1994
(Show Context)
Citation Context ...ambdasB. It would be interesting to study which operations of this kind (over more general semantic categories) corresponding to other logics (e.g. Girard's LU[24], linear logic programming languages =-=[28, 45, 9]-=-), and which give rise to useful operations that still agree with some notion of conventional semantics in the limiting case.s54 7.2 Directions for future work This foundation opens the way to a categ... |

72 | A compositional semantics for logic programs
- Bossi, Gabbrielli, et al.
- 1994
(Show Context)
Citation Context ...tionally oriented semantics. Also, it would be interesting to capture in a categorical context the structure of other semantics (compositional, open program, unfolding, etc.), studied by Levi et. al. =-=[8, 40, 1, 43]-=-. In addition, an interesting follow-up to the work presented here would be a categorical analysis of the Jaffar-Lassez criteria [29] for constraint domains and of the Lassez-MacAloon [35] constraint ... |

70 | A Uniform Proof-theoretic Investigation of Linear Logic Programming - Pym, Harland - 1994 |

69 |
A Model-theoretic Reconstruction of the Operational Semantics of Logic Programs
- Falaschi, Levi, et al.
- 1993
(Show Context)
Citation Context ...han that of functional or imperative programming. The divide has narrowed in the last ten years, with the development of new denotational, operational, and abstract interpretations for logic programs =-=[11, 39, 40, 14, 31, 38]-=-. There has been a growing interest in a categorical formulation of these ideas, essentially for the same reasons they proved of interest in other programming paradigms.s3 Categorical approaches to lo... |

62 | Higher-order Horn clauses
- Nadathur, Miller
- 1990
(Show Context)
Citation Context ...earch, resolution, as the computational engine. However, the demand for more expressive power and efficiency has led language designers to consider logical extensions to the original Horn Clause core =-=[26, 48, 51, 50, 46, 28]-=-) and to add control features and constructs drawn from other language paradigms (e.g. types [55, 32, 49], partial evaluation [31] and constraints [10, 29, 30], to name just a few). The effect has bee... |

59 | Term assignment for intuitionistic linear logic - Benton, Bierman, et al. - 1992 |

56 | Typed Prolog: A Semantic Reconstruction of the Mycroft-O'Keefe Type System
- Lakshman, Reddy
- 1991
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Citation Context ...language designers to consider logical extensions to the original Horn Clause core [26, 48, 51, 50, 46, 28]) and to add control features and constructs drawn from other language paradigms (e.g. types =-=[55, 32, 49]-=-, partial evaluation [31] and constraints [10, 29, 30], to name just a few). The effect has been to expand the boundaries of the subject and of the very notion of declarative content of a program. A m... |

45 |
First Order Categorical Logic
- Makkai, Reyes
- 1977
(Show Context)
Citation Context ...eveloped independently by Goguen. In 1989, Asperti and Martini [4] formalized the syntax of Horn clause programming over the Herbrand Universe using first-order categorical logic as developed in e.g. =-=[41]-=- and gave a topos-theoretic semantics. In 1992, Corradini, Asperti and Montanari gave a categorical analysis of logic program transitions [13] and of logic program structure using indexed monoidal cat... |

43 | Types in Logic Programming - Pfenning - 1992 |

41 | A functional theory of exceptions - Spivey - 1990 |

40 | Proof Theoretic Approach to Specification Languages
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- 1995
(Show Context)
Citation Context ...ambdasB. It would be interesting to study which operations of this kind (over more general semantic categories) corresponding to other logics (e.g. Girard's LU[24], linear logic programming languages =-=[28, 45, 9]-=-), and which give rise to useful operations that still agree with some notion of conventional semantics in the limiting case.s54 7.2 Directions for future work This foundation opens the way to a categ... |

35 |
An algebraic semantics for structured transition systems and its application to logic programs
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(Show Context)
Citation Context ... using first-order categorical logic as developed in e.g. [41] and gave a topos-theoretic semantics. In 1992, Corradini, Asperti and Montanari gave a categorical analysis of logic program transitions =-=[13]-=- and of logic program structure using indexed monoidal categories [12]. In [54] Panangaden, Scott, Seely, Saraswat, gave a categorical formulation of concurrent constraints for logic programming. In 1... |

35 | C.,: Category Theory for Computing - Barr, Wells - 1990 |

34 | Practical Foundations of Mathematics - Taylor - 1999 |

30 |
Constraint Logic Programming: A Survey. The Jour. of Logic Programming 19
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(Show Context)
Citation Context ...he original Horn Clause core [26, 48, 51, 50, 46, 28]) and to add control features and constructs drawn from other language paradigms (e.g. types [55, 32, 49], partial evaluation [31] and constraints =-=[10, 29, 30]-=-, to name just a few). The effect has been to expand the boundaries of the subject and of the very notion of declarative content of a program. A more general syntax and semantics is needed to model th... |

30 | Semantics of type theory - Streicher - 1991 |

27 | Constraint logic programming: A survey - ar, Maher - 1994 |

26 | Category-based Semantics for Equational and Constraint Logic Programming - Diaconescu - 1994 |

23 |
Extensional PERs
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Citation Context ...erminism [53], type disciplines [15, 33] and other logics for computation [7, 63]. The mathematical treatment of some features, such as parametricity and polymorphism, have required categorical tools =-=[57, 21]-=-. Logic programming, however, has developed within a different semantic tradition than that of functional or imperative programming. The divide has narrowed in the last ten years, with the development... |

21 | A constraint sequent calculus - Lassez, McAloon - 1990 |

20 | Fibrations, Logical Predicates and Indeterminates
- Hermida
- 1993
(Show Context)
Citation Context ...ined (and will subsequently be defined by a program). We now compare this category with a notion of generalized category of predicates introduced in a related (but somewhat different) form by Hermida =-=[27]-=- and Asperti-Corradini [12]. 3.3 From Formula Diagrams to Generalized Formulas Definition 3.12 A (generalized) category of predicates over a base category C is any indexed category q over C . An objec... |

16 | A theory of observables for logic programs - Comini, Levi, et al. |

15 | Constraint Logic Programming - Cohen - 1990 |

14 |
A categorical unification algorithm
- Rydeheard, Burstall
- 1986
(Show Context)
Citation Context ... reasons they proved of interest in other programming paradigms.s3 Categorical approaches to logic programming features appeared in the mid 1980's in Rydeheard and Burstall's treatment of unification =-=[61]-=-, also developed independently by Goguen. In 1989, Asperti and Martini [4] formalized the syntax of Horn clause programming over the Herbrand Universe using first-order categorical logic as developed ... |

13 |
A categorical model for logic programs: Indexed monoidal categories
- Corradini, Asperti
- 1987
(Show Context)
Citation Context ...e a topos-theoretic semantics. In 1992, Corradini, Asperti and Montanari gave a categorical analysis of logic program transitions [13] and of logic program structure using indexed monoidal categories =-=[12]-=-. In [54] Panangaden, Scott, Seely, Saraswat, gave a categorical formulation of concurrent constraints for logic programming. In 1994 Diaconescu [19] formalized equational constraint Horn Clause progr... |