## Functions as Passive Constraints in LIFE (1994)

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Venue: | ACM Transactions on Programming Languages and Systems |

Citations: | 12 - 4 self |

### BibTeX

@ARTICLE{Aït-Kaci94functionsas,

author = {Hassan Aït-Kaci and Andreas Podelski},

title = {Functions as Passive Constraints in LIFE},

journal = {ACM Transactions on Programming Languages and Systems},

year = {1994},

volume = {16}

}

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### Abstract

LIFE is an experimental programming language proposing to integrate logic programming, functional programming, and object-oriented programming. It replaces first-order terms with ψ-terms, data structures which allow computing with partial information. These are approximation structures denoting sets of values. LIFE further enriches the expressiveness of ψ-terms with functional dependency constraints. We must explain the meaning and use of functions in LIFE declaratively as solving partial information constraints. These constraints do not attempt to generate their solutions but behave as demons filtering out anything else.

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Citation Context ... as defining a relation r by considering them as simple Horn-clauses; i.e., by ignoring the operational meaning of the guard. This amounts to using Clark’s completion, yielding a definite equivalence =-=[10]-=-. In the scheme of Smolka [24], a relation r is first defined by a definite equivalence defining the semantics of this relation, and only then guarded rules are added, helping to enforce deterministic... |

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Citation Context ... i �� j n i � � V n i & V j n i : si � j j then s 0 i is chosen as some sort such that si j �s 0 i � �for all i j, ij � 1� ...� m. 5 A general residuation framework Constraint Logic Programming (CLP) =-=[18]-=-, the guarded Horn-clause scheme of Maher (ALPS) [20], Concurrent Constraint Programming (CCP) [23], and Kernel Andorra Prolog [15] (KAP) are recent logic programming frameworks that exploit the separ... |

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Citation Context ...test-and-generate” search. � Communication with the external world is made simple and clean [9]. � More generally, it allows concurrent computation. Synchronization is obtained by checking entailment =-=[20, 23]-=-. There are two orthogonal dimensions to elucidate regarding the use of functions in LIFE: � characterizing functions as approximation-driven coroutines; and, � constructing a higher-order model of LI... |

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Citation Context ...nd s 0 in S. � for each feature � in F, � A is a total unary function from the domain into the domain; i.e., � A : D A 7� D A ; 7 In fact, the reader familiar with implementation techniques of Prolog =-=[2]-=- should recognize that they are of the exact same granularity as WAM term representation and instructions. June 1991 (Revised, November 1992) Digital PRLsFunctions as Passive Constraints in LIFE 19 Th... |

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Citation Context ...ion � & � & U � � X. Proof: This is an immediate consequence of Theorem 3 and Proposition 8. 4.3 Independence The following theorem states that the OSF-constraint system has the independence property =-=[19]-=-. It is well-known that in any constraint system with this property it is possible to solve constraints which are conjunctions of constraints and negated constraints by testing entailment. Namely, � &... |

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Citation Context ...nstructor terms; and, � allowing interpretable functional expressions as bona fide terms. The first extension is based on �-terms which are attributed partially-ordered sorts denoting sets of objects =-=[1, 3]-=-. In particular, �-terms generalize first-order constructor terms in their rôle as data structures in that they are endowed with a unification operation denoting type intersection. This gives an elega... |

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Citation Context ...ee unfoldings are equal. A tree unfolding is obtained from a �-term by associating a unique node to every feature path. It is well known that a rooted directed graph represents a unique rational tree =-=[14]-=-. In our case, we obtain trees whose nodes are labeled by sorts and whose 8 Refer to Figure 2 on Page 8 for an example. 9 If an OSF-constraint is satisfiable in some interpretation, then it is also sa... |

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Citation Context ...test-and-generate” search. � Communication with the external world is made simple and clean [9]. � More generally, it allows concurrent computation. Synchronization is obtained by checking entailment =-=[20, 23]-=-. There are two orthogonal dimensions to elucidate regarding the use of functions in LIFE: � characterizing functions as approximation-driven coroutines; and, � constructing a higher-order model of LI... |

123 | Towards a meaning of LIFE
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(Show Context)
Citation Context ...otion of fully defined element, or ground term, is no longer available. Hence, such familiar tools as variable substitutions, instantiation, unification, etc., must be reformulated in the new setting =-=[5]-=-. The second extension deals with building into the unification operation a means to reduce functional expressions using definitions of interpretable symbols over data patterns. 1 Our basic idea is th... |

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Citation Context ...e.g., by rewrite-rules) into an incremental one (e.g., by adding or modifying the rules). Our experience is limited to cases (essentially to the constraint systems over finite or rational first-order =-=[11, 13]-=- or feature trees [7, 25]) where incrementality came for free. 5.3 Operational semantics of residuation We assume a constraint system with an incremental relative-simplification system as described in... |

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Citation Context ...ure constraint of the form X�� � � Y for each �; and, � no other occurrence of the variable X if it contains the equality constraint X � � Y. 10 T is essentially the feature tree structure of [7] and =-=[8, 25]-=-. The difference lies in our using partially-ordered sorts and total, as opposed to partial, features. June 1991 (Revised, November 1992) Digital PRLsFunctions as Passive Constraints in LIFE 23 In [6,... |

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Citation Context ...-clause program has a least model. Proof: It is a well-known fact that a system of predicate definitions such as (2) has a least model extending the model of the theory of the constraint domain (cf., =-=[18, 17]-=-). The statement then follows from the assumption and Proposition 13. For the sake of completely relating our approach to others, let us mention one idea which is not (yet) implemented in LIFE. Given ... |

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Citation Context ...d to what has been quoted to us as the “Andorra Principle” [15], a strategy of preferentially selecting goals which have at most one alternative, and is a basic principle underlying the Andorra Model =-=[22]-=-. 17 This is an example of a useful redundancy; cf., Footnote 13. June 1991 (Revised, November 1992) Digital PRLsFunctions as Passive Constraints in LIFE 43 5.2 Incremental relative-simplification sys... |

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Citation Context ...e.g., by rewrite-rules) into an incremental one (e.g., by adding or modifying the rules). Our experience is limited to cases (essentially to the constraint systems over finite or rational first-order =-=[11, 13]-=- or feature trees [7, 25]) where incrementality came for free. 5.3 Operational semantics of residuation We assume a constraint system with an incremental relative-simplification system as described in... |

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Citation Context ...framework of concurrent constraint logic programming, represented by, e.g., the guarded Horn-clause scheme of Maher [20], Concurrent Constraint Programming (CCP) [23], and Kernel Andorra Prolog (KAP) =-=[15]-=-. These schemes are Research Report No. 13 June 1991 (Revised, November 1992)s4 Hassan Aït-Kaci and Andreas Podelski parameterized with respect to an abstract class of constraint systems. An increment... |

69 | A feature-based constraint system for logic programming with entailment
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(Show Context)
Citation Context ...to an incremental one (e.g., by adding or modifying the rules). Our experience is limited to cases (essentially to the constraint systems over finite or rational first-order [11, 13] or feature trees =-=[7, 25]-=-) where incrementality came for free. 5.3 Operational semantics of residuation We assume a constraint system with an incremental relative-simplification system as described in the previous section. Le... |

55 |
An algebraic semantics approach to the effective resolution of type equations
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(Show Context)
Citation Context ...nstructor terms; and, � allowing interpretable functional expressions as bona fide terms. The first extension is based on �-terms which are attributed partially-ordered sorts denoting sets of objects =-=[1, 3]-=-. In particular, �-terms generalize first-order constructor terms in their rôle as data structures in that they are endowed with a unification operation denoting type intersection. This gives an elega... |

53 | Warren's Abstract Machine, A Tutorial Reconstruction - A't-Kaci - 1991 |

34 | The definition of Standard ML (version 2 - Harper, Milner, et al. - 1988 |

30 |
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Citation Context ...ides a powerful search-space pruning facility by changing “generate-and-test” search into demon-controlled “test-and-generate” search. � Communication with the external world is made simple and clean =-=[9]-=-. � More generally, it allows concurrent computation. Synchronization is obtained by checking entailment [20, 23]. There are two orthogonal dimensions to elucidate regarding the use of functions in LI... |

29 | Research Report 3: Introduction to Programmable Active Memories - Vuillemin - 1989 |

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18 |
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Citation Context ... [4]. This simple idea turns out invaluable in practice. Here are a few benefits. � Such non-declarative heresies as the is predicate in Prolog and the freeze meta-predicate in some of its extensions =-=[21, 12]-=- are not needed. � Functional computations are determinate and do not incur the overhead of the search strategy needed by logic programming. 1 Several patterns specifying a same function may possibly ... |

17 |
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Citation Context ...match a definiens of the function in question, it is simply left untouched. Resolution may proceed until the arguments are proven to match a definition from the accumulated constraints in the context =-=[4]-=-. This simple idea turns out invaluable in practice. Here are a few benefits. � Such non-declarative heresies as the is predicate in Prolog and the freeze meta-predicate in some of its extensions [21,... |

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16 | Research Report 32: Order-Sorted Feature Theory Unification - Podelski, Goldstein - 1993 |

14 | Warrens' Abstract Machine: A Tutorial Reconstruction - aet-Kaci, H - 1991 |

13 | Aït-Kaci and Andreas Podelski. Towards a Meaning of LIFE - Hassan - 1993 |

12 | ome Barraquand - er - 1993 |

10 | Research Report 7: The Siphon: Managing Distant Replicated Repositories - Prusker, Wobber - 1991 |

10 | Incremental algorithms for constraint solving and entailment over rational trees - Ramachandran, Hentenryck - 1993 |

9 | Integrating Logic and Functional Programming - At-Kaci, Nasr - 1989 |

8 | A feature-based constraint system for logic programming with entailment - At-Kaci, Podelski, et al. - 1994 |

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7 |
The Definition of Standard
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Citation Context ...unction may possibly have overlapping denotations. Therefore, the order of the specified patterns defines an implicit priority, as is usual in functional programming using first-order patterns (e.g., =-=[16]-=-). Research Report No. 13 June 1991 (Revised, November 1992)s2 Hassan Aït-Kaci and Andreas Podelski � Higher-order functions are easy to return or pass as arguments since functional variables can be b... |

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7 | PRL Research Reports The following documents may be ordered by regular mail from: Librarian -- Research Reports Digital Equipment Corporation Paris Research Laboratory 85, avenue Victor Hugo 92563 Rueil-Malmaison Cedex France. It is also possible to obtai - No - 1994 |