### Table 1. Overview of automated transformations Phase Transformation Source Target Proof-of-concept

2005

"... In PAGE 6: ... Then, third parties can discover and use the composed service. 5 Additional Aspects of the Methodology Our methodology identifies eleven model transformation steps that can be automated ( Table1 ). For each transforma- tion we specify to which phase it belongs, the source and target in the transformation, and if there exist any proof-of- concept transformations or tools described in the literature.... ..."

Cited by 2

### Table 3. Transformations Associated to Rules of S2

1998

"... In PAGE 22: ... We now specify in full the language of the linear dialectic -calculus. Examples of all constructs can be found in Table3 below. Terms are built up from variables a; b; : : : ; x; y; : : : and types A; B; : : : using -abstraction, application, and pairing.... In PAGE 23: ...When the variable a of a -abstraction is positively typed by a con- junction or negatively typed by an implication (in which case we will have usually written x rather than a), a may be expanded as the pair (a1; a2) where the ai apos;s are variables of the appropriate type and sign depending on A and its sign. This expansion may be applied recursively to the ai apos;s, as for example in rule A1 of Table3 below. When a is positively typed by an implication, a may be written (a1; a2) but the ai apos;s do not have any type of their own independent of that of a.... In PAGE 24: ...interpret successive theorems in a proof by applying the following transfor- mations, each associated with the correspondingly labeled inference rule of S2. In the derivation A ` B via rule R, the transformation associated by Table3 to rule R maps the -term interpreting A to that interpreting B. A1 ((a; b); c) : (A B) C : (a; (b; c)) : A (B C) A2 f : (A B)? C : a : A : b : B : f(a; b) : C A20 f : (A? B) ?C : a : A : y B : f(a; y) C A200 f : (A ?B) ?C : x A : b : B : f(x; b) C C1 (a; b) : A B : (b; a) : B A C2 (f; f0) : A? B : (f0; f) : B ?A C20 (f; f0) : A ?B : (f0; f) : B? A D (f; c) : (A? B) C : a : A : (f(a); c) : B C D0 (f; c) : (A ?B) C : x A : (f(x); c) B ?C E1 (a; b) : A B : (f(a); g(b)) : A0 B0... In PAGE 24: ... The remaining rules are interpreted along the same lines. Theorem 4 Every theorem of S2 is interpreted by Table3 as a transfor- mation represented by a closed term of the linear dialectic -calculus. Proof: This is a straightforward consequence of the form of Table 3.... In PAGE 24: ... Theorem 4 Every theorem of S2 is interpreted by Table 3 as a transfor- mation represented by a closed term of the linear dialectic -calculus. Proof: This is a straightforward consequence of the form of Table3 . The interpretations of the axiom instances and the rules are in the language, con- tain no free variables, -bind exactly one variable, and are typed compatibly with the rules.... ..."

Cited by 10

### Table 2. Proof System

2004

"... In PAGE 8: ... We now see that it also forms the basis of a sound and complete proof theory, and a decision procedure based on proof-search. The rules of the proof system are shown in Table2 . Since there is no Cut rule, the rules have a rather odd form.... ..."

Cited by 34

### Table 2. Proof System

2004

"... In PAGE 8: ... We now see that it also forms the basis of a sound and complete proof theory, and a decision procedure based on proof-search. The rules of the proof system are shown in Table2 . Since there is no Cut rule, the rules have a rather odd form.... ..."

Cited by 34

### Table 2. Proof System

2004

"... In PAGE 8: ... We now see that it also forms the basis of a sound and complete proof theory, and a decision procedure based on proof-search. The rules of the proof system are shown in Table2 . Since there is no Cut rule, the rules have a rather odd form.... ..."

Cited by 34

### Table 2. Proof System

2004

Cited by 34

### Table 2. Proof System

2004

Cited by 34

### Table 2. Proof System

2004

Cited by 34

### Table 3: Proof rules for page thrashing

"... In PAGE 12: ... The last rule proofs a locality bottleneck for a specific variable. Table3 outlines the proof rules for a specific reason of a locality bottleneck, namely thrashing. A vague hint for page thrashing results from the inspection of the pagefault sums of this region in all processes.... ..."

### Table 2. Proof rules for vertical implementation

"... In PAGE 7: ... If dom ; = ?, we write ` t v u r or simply t v r u. Anumber of proof rules for v r are given in Table2 . We rst discuss the case for closed terms;; i.... In PAGE 8: ... In R 12 , nally, the synchronisation set A of the speci cation is re ned in the im- plementation;; moreover, there is a restriction on the re nement function, which will be discussed below in more detail. There are some side conditions in Table2 whose rationale is not immediately obvious. In particular, the re nement function is constrained to be A-preserving in the rule for hiding (R 9 ), and distinct and preserving in the rule for parallel composition (R 12 ).... In PAGE 8: ... Assume A = C = fa;; bg and let r: a 7 ! a;; b;; b 7 ! b. Then the rules of Table2 allow the following derivation: (R 6 ) a v r a;; b (R 6 ) b v r b (R 8 ) a;; b v r a;; b;; b (R 9 ) (a;; b)=a v id (a;; b;; b)=a;; b (R 2 ) (a;; b)=a (a;; b;; b)=a;; b However, (a;; b)=a gives rise to a non-deadlocking term when substituted for x in x jj b b, whereas (a;; b;; b)=a;; b does not. This contradicts the requirement that preserves deadlock freedom.... In PAGE 9: ...! c;; a and b 7 ! c;; b. The rules of Table2 then allowtoderive((a+d)jj a;;b (b+d))=a;; b ((c;; a+d)jj a;;b;;c (c;; b+d))=a;; b;; c. The left hand term contains no deadlock, whereas the righthand term has a -transition to the deadlocked state (1;; b jj b;;c;;d 1;; d)=b;; c;; d.... In PAGE 9: ... [15]) seems inapplicable. 4 Vertical bisimulation Wenow come to the de nition of an actual vertical implementation relation that satis es the derivation rules of Table2 . We build on the principles of observation congruence.... In PAGE 10: ... 6, it follows that vertical bisimilarityuptoid equals ob- servation congruence. Furthermore, the rules in Table2 are sound for . r , To formalise this, we write x .... In PAGE 11: ... r satis es all the rules in Table 2. Note that, although Table2 gives no recipe for deriving implementations from speci cations, in many cases, one particular implementation can be obtained through the syntactic substitution of all abstract actions by their re nements. Abstraction.... ..."