### Table References: Lu,7 Qureshi,8 Harwood,9 Sanjur,10 Vontress,11 Spector,12 Giger,13

2002

### Table 6: Truth table representing Lazy-GA-predicate. Acknowledgements The authors wish to thank Professor Aaron Sloman and the Cognition and A ect Group of the School of Computer Science, The University of Birm- ingham, for useful suggestions and help in developing the system described in this paper.

1995

Cited by 3

### Table 1. Partipants, affiliations, and methods Name Affiliation Method Andrea Baronchelli, et al. Rome Entropy-based informatic distance Aaron Coburn Middlebury Contextual network graph Hans van Haltern Nijmegen Linguistic Profiling

### Table 1: List of interviewees Name Organisation Martin Foreman Department of Natural Resources (New South Wales) Stuart Critchell Department of Sustainability and Environment (Victoria) Julie Cann Department of Water, Land and Biodiversity Conservation (South Australia) Randall Cox Department of Natural Resources, Mines and Water (Queensland) Aaron Stasi Department of Natural Resources, Mines and Water (Queensland) Victor Fazakerley Department of Water (Western Australia)

in Contents

2006

### Table 1: Fiscal adjustments in Ireland

"... In PAGE 6: ... According to our definition of adjustment,7 Ireland had three episodes of fiscal adjustment since the early 80s: 1983-84, 1987-89 and 1996. The main features of these fiscal adjustments are summarized in Table1 . Of the three adjustments, those in 1983-84 and 1987-89 were successful, while the 1996 adjustment was not successful.... In PAGE 6: ... The 1996 adjustment, on the other hand, lowered potential but raised actual GDP growth, whereas the 1983-84 adjustment loweredbothgrowthrates. The third and fourth rows of Table1 report the size of the fiscal impulse for each episode; these are, respectively, the average and total improvement in the primary balance to GDP. The fiscal impulse in 1987-89 was the strongest and it coincided with the peak in the public debt to GDP ratio.... In PAGE 6: ... The fiscal impulse in 1987-89 was the strongest and it coincided with the peak in the public debt to GDP ratio. Row six in Table1 reports the (average) composition of the fiscal adjustment, indicating what fraction of the primary surplus improvement was due to a reduction in government disbursements versus an increase in tax revenues.8 Most of the fiscal improvement in 1983-84 came through cuts in discretionary taxation, including increases in duties, VAT, a temporary levy on income and new residential property taxes.... In PAGE 6: ... The 1996 fiscal improvement came both from lower public spending and higher tax revenues, mainly originating from higher income taxes on households. Table1 reports the developments in Irish monetary policy during the fiscal adjustments, i.e.... ..."

### Table 1: Rewrite rules for monotonic functions.

"... In PAGE 8: ... The simple equations yield the same inferences as the originals with much less work. We nd the simple equations by collapsing redundant M functions with the rewrite rules shown in Table1 . The proof that the rules preserve the SPQR semantics is straightforward.... In PAGE 22: ... We now consider the other cases. M + P = U: We can write the expression M+ + P as M+ + (P + k) for any constant k by rule 5 of Table1 . We can write any f on [a; b] as P + k with k the absolute value of the in mum of f on [a; b].... In PAGE 22: ... Divide the interval [a; b] into four subintervals (some possibly empty): (i) f; g gt; 0, (ii) f; g lt; 0, (iii) f gt; 0; g lt; 0, and (iv) f lt; 0; g gt; 0. The result is M+ on (i) by rule 1 of Table1 and M? on (ii) by rule 2 because (fg)0 = f0g + fg0 and f0; g0 gt; 0. On interval (iii), we have fg = ?elog(?fg) = ?elog(f)+log(?g) = ?eM++M? = ?eU = ?P = N: The third equality holds because any function can be written as the log of a positive function; the fourth holds by Lemma 1; and the fth holds because any positive function can be written as the exponential of a function.... ..."

### Table 2: The system CDV not necessarily identical, since they may consist of di erent algorithms, in contrast to the set-theoretic extensional notion where functions are identi ed with their graphs. Extensionality in the untyped calculus may be recovered, as is well known, through the introduction of the -reduction rule: x:Mx ! M if x 62 FV(M): With the subsequent notion of -convertibility one obtains that any two functions being extensionally equal are identi ed. A type system for the -calculus with the -rule must also contain an -typing- rule, in order to satisfy the minimal requirement of type invariance by -reduction: ? ` x:Mx: x 62 FV(M) ? ` M:

"... In PAGE 20: ... By the way it is easy to check that the de nition given in (2) is equivalent. The subsumption rule, along with the theory of the subtyping relation, dispenses with the intersection- elimination rules, which become derived rules: ? ` M: ^ ^ ? ` M: (sub) ? ` M: ^ ^ ? ` M: (sub) More precisely, the type system CDV, with intersection introduction and elimina- tion, is equivalent to the system CDV , reported in Table2 , where the elimination rules have been replaced by the subsumption rule and the subtype rules; among these the axiom ! becomes super uous and might be omitted, since the typing axiom ? ` M: ! is already stronger (we keep it as it will again be necessary in the expanded systems considered in the next sections). Analogously, the restricted system CDV6 ! is equivalent to the system CDV ;6 !, which of course is the system CDV with the two resp.... ..."

### Table 2: The system CDV not necessarily identical, since they may consist of di erent algorithms, in contrast to the set-theoretic extensional notion where functions are identi ed with their graphs. Extensionality in the untyped calculus may be recovered, as is well known, through the introduction of the -reduction rule: x:Mx ! M if x 62 FV(M): With the subsequent notion of -convertibility one obtains that any two functions being extensionally equal are identi ed. A type system for the -calculus with the -rule must also contain an -typing- rule, in order to satisfy the minimal requirement of type invariance by -reduction: ? ` x:Mx: x 62 FV(M) ? ` M:

"... In PAGE 20: ... By the way it is easy to check that the de nition given in (2) is equivalent. The subsumption rule, along with the theory of the subtyping relation, dispenses with the intersection- elimination rules, which become derived rules: ? ` M: ^ ^ ? ` M: (sub) ? ` M: ^ ^ ? ` M: (sub) More precisely, the type system CDV, with intersection introduction and elimina- tion, is equivalent to the system CDV , reported in Table2 , where the elimination rules have been replaced by the subsumption rule and the subtype rules; among these the axiom ! becomes super uous and might be omitted, since the typing axiom ? ` M: ! is already stronger (we keep it as it will again be necessary in the expanded systems considered in the next sections). Analogously, the restricted system CDV6 ! is equivalent to the system CDV ;6 !, which of course is the system CDV with the two resp.... ..."

### Table 2: The system CDV not necessarily identical, since they may consist of di erent algorithms, in contrast to the set-theoretic extensional notion where functions are identi ed with their graphs. Extensionality in the untyped calculus may be recovered, as is well known, through the introduction of the -reduction rule: x:Mx ! M if x 62 FV(M): With the subsequent notion of -convertibility one obtains that any two functions being extensionally equal are identi ed. A type system for the -calculus with the -rule must also contain an -typing- rule, in order to satisfy the minimal requirement of type invariance by -reduction: ? ` x:Mx: x 62 FV(M) ? ` M:

"... In PAGE 20: ... By the way it is easy to check that the de nition given in (2) is equivalent. The subsumption rule, along with the theory of the subtyping relation, dispenses with the intersection- elimination rules, which become derived rules: ? ` M: ^ ^ ? ` M: (sub) ? ` M: ^ ^ ? ` M: (sub) More precisely, the type system CDV, with intersection introduction and elimina- tion, is equivalent to the system CDV , reported in Table2 , where the elimination rules have been replaced by the subsumption rule and the subtype rules; among these the axiom ! becomes super uous and might be omitted, since the typing axiom ? ` M: ! is already stronger (we keep it as it will again be necessary in the expanded systems considered in the next sections). Analogously, the restricted system CDV6 ! is equivalent to the system CDV ;6 !, which of course is the system CDV with the two resp.... ..."

### Table 5. Well-typed terms.

1999

Cited by 16