A Tight, Practical Integration of Relations and Functions

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Springer Science & Business Media, Sep 29, 1999 - Computers - 176 pages
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As in other fields, in computer science certain objects of study can be synthesized from different basic elements, in different ways, and with different resulting stabilities. In subfields such as artificial intelligence, computational logic, and programming languages various relational and functional ingredients and techniques have been tried for the synthesis of declarative programs.
This text considers the notions of relations, as found in logic programming or in relational databases, and of functions, as found in functional programming or in equational languages. We study a declarative integration which is tight, because it takes place right at the level of these notions, and which is still practical, because it preserves the advantages of the widely used relational and functional languages PROLOG and LISP. The resulting relational and functional language, RELFUN, is used here for exemplifying all integration principles.
 

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Contents

An Overview of the RelationalFunctional Language RELFUN
1
12 From Relations and Functions to Operators
5
13 PROLOGLISPRELFUN Comparison
8
14 Semantics and Implementation
11
15 Applications
14
16 Related Work
16
17 Readers Guide
19
Extended LogicplusFunctional Programming
21
37 Completeness of SLVResolution
85
38 Conclusions
87
Finite Domains and Exclusions as FirstClass Citizens
89
42 Domain Terms
91
43 Exclusion Terms
93
44 Occurrence Bindings
95
45 DomainsExclusions in Relation Definitions
97
452 Clauses and bndto Reductions
99

22 Relations Defined by Hornish Clauses
23
222 PROLOGlike Structures and Lists
25
223 VaryingArity Structures
26
224 VaryingArity Relationships
28
225 HigherOrder Constructors and Relations
29
23 Functions Defined by Footed Clauses
31
2312 Footed Rules and the density Example
33
2313 Nondeterminism DATALOG Relationalizing and WAM Compilation
35
232 Full RELFUN Exemplified by SelfFunctions
36
233 HigherOrder Constructors and Functions
39
24 The LogicFunctional Style in Use
42
OntheFly Construction of Proof Trees
45
Interpreting a LISP Subset in RELFUN
48
25 Conclusions
50
The RELFUN Syntax
52
A Direct Semantic Characterization of RELFUN
55
32 Extending FirstOrder Theories to First Order RelationalFunctional Theories
61
33 RelationalFunctional Interpretations and Models
65
34 SLVResolution
72
35 Soundness of SLVResolution
78
36 Least Herbrand Crossbase Models as Fix points
80
46 FiniteDomainExclusion Functional Programming
101
461 DomainsExclusions as Function Arguments
102
462 Functions with DomainExclusion Values
103
47 Domain and Exclusion Antiunification
105
48 Operational Semantics
109
49 Conclusions
111
The RELFUN Metaunify
114
MultipleValued Horn Clauses and Their WAM Compilation
117
52 A MultipleValued RelationalFunctional Language
120
522 SingleValued and MultipleValued Clauses
123
Refining the palindrome Operator
128
524 HigherOrder Functions and Relations
134
53 RelationalFunctional WAM Compilation
137
532 Evaluative Foots and Denotative Normalization
140
533 Nondeterministic MultipleValued Nestings and Static Flattening
143
534 HigherOrder Clauses and ConstantOperator Reduction
148
535 Translation to WAM Instructions
151
54 Conclusions
157
Bibliography
161
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