### Table 14. Deduction rules for sequential composition

2007

Cited by 3

### Table 6: SOS rules for sequential composition

2001

Cited by 2

### Table 2: Extracting Sequential-Composition Statements

1990

Cited by 1

### Table 4. Rewriting Rules for Sequential Composition

2006

"... In PAGE 52: ...45 Table4 . Examples of schematic expressions and their instantiation t (t) f(te) fte 7! g(a)g f(g(a)) f(va) fva 7! xg f(x) 8va: p(va) fva 7! xg 8x: p(x) 8va: p(te) fva 7! x; te 7! xg 8x: p(x) 8va: phi fva 7! x; phi 7! p(x)g 8x: p(x) phi ^ p(te) fphi 7! q _ r; te 7! f(a)g (q _ r) ^ p(f(a)) p(sk) ! 9va: p(va) fsk 7! c; va 7! xg p(c) ! 9x: p(x) fnsubst va; skg(phi) ! 9va: phi fsk 7! c; va 7! x; phi 7! p(x)g p(c) ! 9x: p(x) { (p(t1; : : : ; tn)) := p( (t1); : : : ; (tn)) { (true) := true and (false) := false, { (: ) := : ( ), { ( ^ ) := ( ) ^ ( ) (and correspondingly for _ and ! ), { (8va: ) := 8 (va): ( ) and (9va: ) := 9 (va): ( ), { (fnsubst va; sg( )) := [ (va)= (s)]( ( )).... In PAGE 52: ... Example 4. Table4 illustrates the instantiation of the di erent kinds of schema variables for rst-order logic. We use the following schema variables: KeY a38a30a62a12a51a4a55a44a46a6a63a71a50a8a72a52a50a8a45a41a40a19a50a19a73a49a48a19a46a44a62 { a38a29a66a52a50a23a45a41a40a19a50a29a73a49a48a16a46a44a62 A va; a38a19a54a30a46a23a45a29a63 A te; a38a19a39a30a74a23a45a29a63a52a68a71a48a16a50 phi; a38a30a62a4a77a44a74a44a48a16a46a6a63a44a78a52a46a23a45a29a63 A sk; } KeY Apart from that, we assume that f; g : A ! A are function symbols, a; c : A are constants, p : A and q, r are predicates and x : A is a logical variable.... In PAGE 52: ... We use the following schema variables: KeY a38a30a62a12a51a4a55a44a46a6a63a71a50a8a72a52a50a8a45a41a40a19a50a19a73a49a48a19a46a44a62 { a38a29a66a52a50a23a45a41a40a19a50a29a73a49a48a16a46a44a62 A va; a38a19a54a30a46a23a45a29a63 A te; a38a19a39a30a74a23a45a29a63a52a68a71a48a16a50 phi; a38a30a62a4a77a44a74a44a48a16a46a6a63a44a78a52a46a23a45a29a63 A sk; } KeY Apart from that, we assume that f; g : A ! A are function symbols, a; c : A are constants, p : A and q, r are predicates and x : A is a logical variable. The most interesting instantiation takes place in the last line of Table4 , where rst the schema variables are replaced with terms and variables and then the substitution is applied: (fnsubst va; skg(phi) ! 9va: phi) = [x=c](p(x)) ! 9x: p(x)) = p(c) ! 9x: p(x) Note 4. Example 4 demonstrates the interrelation between schema variables \variables, \term and \formula.... ..."

### Table 4: Deduction rules for generalised weak sequential composition: S

1997

"... In PAGE 13: ... Please note that the operational rules also deal with the resolving of choices. Note that the operational rules for weak sequential composition in Table4 are similar to the operational rules for parallel composition. The main di erence is that an event from the right operand can only be executed if the left operand allows the execution of that event.... ..."

Cited by 8

### Table 4 Complexity Rules for Sequential Composition, Conditional Statements and Loops

"... In PAGE 9: ... Without loss of generality we assume all expressions use basic operations of the domain D, only. Table4 contains rules de ning sequential composition, conditional statements, and loops. For brevity, we omit the rules for static and cumulative measures.... ..."

### Table 4 Deduction rules for generalised weak sequential composition. X

1997

"... In PAGE 12: ..... VC 1 . The operational rules for vertical composition in Table4 are similar to the operational rules for horizontal composition. The main difference is that an event from the right operand can only be executed if the left operand allows the execution of that event.... ..."

Cited by 8

### Table 5: Operational semantics of HyPA, alternative and sequential composition

2004

Cited by 2

### Table 2 where ; is function composition, applied sequentially so that

"... In PAGE 6: ... L(G) is crucial to Kracht 2001. This fact should not be lost when replacing L(G) in Table 1 by tm(G) in Table2 . The prominence Table 1 gives to expressions/exponents ought to be balanced against the centrality of L(G), hinted by the last row of Table 2.... ..."