### Table 2: Transformation Table for Functional Logic Programming.

"... In PAGE 11: ... fib(1,1). 2 PAGE can model this programming paradigm introducing a new transformation table ( Table2 ) which is used in conjunction with the tables used for the LP paradigm. Now we consider that functional arguments have the same notational signi cance as the previously seen ordinary variables.... In PAGE 11: ... Functional arguments are prioritized in the uni cation procedure (the uni cation procedure becomes matching procedure since we are dealing with interpreted functional terms), so that when we have to unify a variable argument which is in the argument list of a functional argument we prefer to unify the latter and discard the former. This can easily be seen in Table 3, where the equivalent AG is given after the use of transformation Table 1 in conjunction with the transformation Table2 . Fig.... In PAGE 12: ....4.1. Multi-pass execution (simple case) The method described so far ( Table2 is used) is operationally incomplete when the minimal elements in the partial ordering induced by the generated dependency graph are unbound (for instance some of the arguments in the argument list of a functional argument are unbound). In such cases, a delayed binding mechanism has to be used.... In PAGE 12: ... 6 we can see the dependency graph for the equivalent AG corresponding to Table 5 generated after the the use of Table 1 in conjunction with Table 4. Here, we do not have functional arguments and so we do not apply the transformation Table2 . Arrows corresponding to Table 1 are designed with solid lines, while arrows corresponding to Table 4 are designed with dashed lines.... In PAGE 15: ...he new inherited attribute). This is shown in Fig. 5 with the dashed lines. 2 It is noteworthy that the same behaviour is possible if we supply the FLP tranformation table ( Table2 ) with extra transformation actions, simulating this way the constraint solver. However, that actions are problem depented and they do not t in a declarative way of programming.... ..."

### Table 1. Full-Sample Estimates of Impact of IMF Programs on Market Access

2000

"... In PAGE 21: ... We are also interested in the differential effects of different types of conditionality. In column (1) of Table1 , we show the results of the probit relating the decision to... ..."

### Table 1: Nondeterministic Logic Programming Reductions

"... In PAGE 84: ... Correspondingly, the expression betray a man to every enemy of him (45) would by our grammar be assigned the denotation dom((B; A) \ (D3 I)) : M: (46) This term is equivalent to the set fxj(9y)(y 2 M ^ (8z)(zAy ! Bxyz))g; (47) which is in line with our intuition about the meaning of (45). In Table1 a grammar was given for a fragment of English that is large enough to derive many of Peirce apos;s English examples to illustrate his operations and their use to construct complex terms. In the next section we use our fragment to check Peirce apos;s constructions.... ..."

### Table 1: Categories of parallelism in logic

"... In PAGE 2: ... It is also possible, however, to view the program to be evaluated as data, which are transformed by certain operations according to a particular inference mechanism, and apply some of these operations in parallel to the whole, or parts of the original program. Table1 shows an overview of the categories of parallelism, arranged according to the granularity and the components of a logic program. It identi es the particular data structures and operations applied in a category.... In PAGE 2: ... It identi es the particular data structures and operations applied in a category. The notation used in Table1 is based on viewing a logic program as a collection of clauses, possibly organized into modules (or objects). The clauses consist of literals, arranged as head and tail.... ..."

### Table 3. The Icarus program induced by our method.

2002

"... In PAGE 7: ... If Icarus evaluates these in order, it can only reach the fth branch if the fourth fails to return an action, meaning there is no imminent collision (TTIA gt; 1:82). We can use this knowledge to simplify the logical tests in the fth subtree, producing the Icarus subplans labeled R1, R2, R21 and R22 in Table3 . This completes the process of inducing a hierarchical control program from observational traces.... In PAGE 9: ...ig. 3. The classi cation hierarchy obtained by our method. ordering simpli ed the required conditions. Taken as a whole, these transforma- tions recovered the Icarus program shown in Table3 , completing the task of inducing a hierarchical program from observations. 4.... In PAGE 10: ... Thus, the hierarchical representation requires only 30% of the e ort. When we compare the learned Icarus program in Table3 with the original program in Table 1 several interesting features emerge. First, the learned pro- gram is simpler.... In PAGE 10: ... Next, the learned program captures much of the natural structure of the driving task; the top-level routines call roughly the same number of functions, and half of those implement identical reactions. Speci cally, R1 in Table3 corresponds to Emergency-brake in Table 1, while R2 represents Avoid-trouble-ahead using a simpler gating condition. Similarly, R4 captures the behavior of Avoid-trouble-behind, although it adds the Slow- down operation found in Get-to-target-speed.... ..."

Cited by 3

### Table 2: Inference Rules of Many Sorted Monadic Equational Logic

1991

"... In PAGE 7: ...omplex assertions, e.g. formulas of rst order logic, then they should be interpreted by subobjects; in particular equality = : A should be interpreted by the diagonal [[A]]. The formal consequence relation on the set of equations is generated by the inference rules for equivalences ((re ), (simm) and (trans)), congruence and substitutivity (see Table2 ). This formal consequence relation is sound and complete w.... In PAGE 12: ...7 Given a signature for the programming language, let be the signature for the metalanguage with the same base types and a function p: 1 ! T 2 for each command p: 1 * 2 in . The translation from programs over to terms over is de ned by induction on raw programs: x [x]T (let x1(e1 in e2) (letT x1(e1 in e2 ) p(e1) (letT x(e1 in p(x)) [e] [e ]T (e) (letT x(e in x) The inference rules for deriving equivalence and existence assertions of the simple programming language can be partitioned as follows: general rules (see Table 6) for terms denoting computations, but with variables ranging over values; these rules replace those of Table2 for many sorted monadic equational logic rules capturing the properties of type- and term-constructors (see Table 7) after interpretation of the programming language; these rules replace the additional rules for the metalanguage given in Table 4.... ..."

Cited by 585

### Table 1 Programming languages and their supported programming paradigms. Progr. language OO Functional Logic Static typing Dynamic typing

"... In PAGE 3: ... 1 The FCA algorithm takes as input a relation, or Boolean table, T between a (potentially large, but finite) set of elements and a set of properties of those elements. An example of such a table is given in Table1 , in which different programming languages and properties are related. A cross in a table cell means that the programming language in the corresponding row has the property of the corresponding column.... ..."

### Table 1 Programming languages and their supported programming paradigms. Progr. language OO Functional Logic Static typing Dynamic typing

"... In PAGE 3: ... 1 The FCA algorithm takes as input a relation, or Boolean table, T between a (potentially large, but finite) set of elements and a set of properties of those elements. An example of such a table is given in Table1 , in which different programming languages and properties are related. A mark in a table cell means that the programming language in the corresponding row has the property of the corresponding column.... ..."

### Table 3. Succinct ow logic for the functional fragment.

1998

"... In PAGE 6: ... We express this as follows: (Rd F ; Rc F ; MF ; SF ; WF ) satis es R; M e : S1 ! S2 amp; W Here the proposed solution consists of the ve caches of Table 2 and the entities R; M; S1; S2 and W: R 2 d Env is the environment in which e is to be analysed, M 2 P(Mem) is the set of contexts in which e is to be analysed, S1 2 d Store is the store that is possible immediately before e, S2 2 d Store is the store that is possible immediately after e, and W 2 c Val is the value that e can evaluate to. Since the ve caches of Table 2 remain \constant quot; throughout the veri cation we shall dispense with listing them when de ning the \ quot; relation in Table3 . Note that the clauses are de ned compositionally and hence clearly are well-de ned.... In PAGE 6: ... Given the caches of Example 4 we may verify the following formula for the program of Example 1 [ ]; f g program : [ ] ! [ ] amp; f( ; (y; 3))g re ecting that the initial environment is empty, that the initial context is the empty call string, that the program does not manipulate the store (which hence is empty) and that the nal value is described by f( ; (y; 3))g. The veri cation will amount to a proof using the clauses of Table3 as rules and axioms; if successful, the proof and the caches constitute the analysis of the program. 2 The clause for variables merely demands that the store after x equals the store possible before x and that the value associated with x in the environment equals... In PAGE 8: ... Containments versus equalities. Since the speci cation in Table3 is concerned with verifying whether or not a proposed solution is acceptable it is sensible that the clause for function application employs a containment like takek(l; M) MF ( ) rather than an equality like takek(l; M) = MF ( ). The reason is that there might be other instances of the clause where the label of the application... In PAGE 9: ... In fact it would be incorrect to replace the containment by an equality: if M 6 = ;, k gt; 0 and li1 6 = li2 then it is impossible to obtain takek(li; M) = MF ( ) for all i. Although the clauses in Table3 contain no explicit equalities they do contain a lot of implicit equalities because the same ow variable is used more than once in the same clause. One can avoid this by introducing new variables and then linking them explicitly by containments as illustrated below.... In PAGE 10: ...F ( )dXl dc(M; W1; )e v Rc F( ) ^ takek(l; M) MF( ) for some R1; M1; S11; S12; W1; R2; M2; S21; S22; W2 Clearly there will be proposed solutions that are acceptable according to the modi ed speci cation but that are not acceptable according to Table3 . This motivates being explicit about what we mean by the best solution.... In PAGE 10: ... In other words, we can change containments to equalities if we \collect quot; all terms de ning the same entity. 3 Attribute Grammar Formulations The ow logic of Table3 can be transformed into an attribute grammar. The basic idea behind attribute grammars is as follows.... In PAGE 10: ... We shall now proceed in two stages. First we show that a minor transformation will turn the speci cation of Table3 into an extended attribute grammar with global attributes and side conditions. The second stage will then transform the extended attribute grammar into an attribute grammar using global attributes and de ning the attributes by containments (rather than equalities).... In PAGE 11: ... The global attributes can be used as constants in the construction of terms for the attributes and their values can be further constrained by explicit conditions associated with the syntactic rules. It is now easy to see that Table 4 can be obtained from Table3 and vice versa by simply changing the notation. Hence it should be clear that the two speci cations admit the same acceptable solutions and therefore that the best solution for one equals the best solution for the other.... In PAGE 15: ... In doing so we shall exploit the presence of labels on all subexpressions. We shall write the analysis of an expression tl as (Rd F ; Rc F ; MF ; SF ; WF ; RL; ML; WL; SL) satis es tl and (as in Table3 ) we shall be explicit about the analysis of subexpressions. Allowing minor changes in notation this results in the speci cation of Table 8.... ..."

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### Table 2: Database and logic programming terms. DB terminology LP terminology

"... In PAGE 3: ... A deductive Datalog database consists of de nite database clauses with no function symbols. Table2 relates basic database and logic programming terms. For a full treatment of logic programming, RDBs, and deductive databases, we refer the reader to [31] and... ..."