### Table 2: Expression evaluation

"... In PAGE 7: ... Expression evaluation. Table2 lists the semantics for evaluating an expression e in an environment . The evalu- ation rules are given as a big step semantics with the evalu- ation operator eval : Exp ! U, that takes an expression and a lattice element and produces a value.... ..."

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### Table 1. Attributes for Expression Evaluation

2003

"... In PAGE 5: ... The attribute nt : fOCCg speci es the set of possible tasks to be executed next. Table1 summarizes the attributes required for expression evaluation. Figure 1 shows an example expression ((i = 2 i) == i ++) amp; amp;(++ i == i).... In PAGE 5: ... The dotted arrows denote the root attribute. The other attributes shown in Table1 are straightforward. We de ne the state space of imperative languages.... ..."

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### Table 1: Rules for expression evaluation.

1996

"... In PAGE 23: ... Let Can denote the subset of Expr consisting of the expressions in canonical form. These are given by: c ::= () j true j false j n j Ini(c) j (c,c) j x: :e : The operational semantics of the programming language can be given via a type-indexed family of evaluation relations e + c (e 2 Expr ; c 2 Can ) : These relations are inductively de ned by the rules in Table1 , which follow the dynamic semantics of the corresponding Standard ML expressions, as speci ed in (Milner, Tofte and Harper, 1990).... In PAGE 27: ... Properties (13) and (14) are simple to prove by induction on the struc- ture of the canonical form c. Property (15) is often called the soundness of the denotational semantics with respect to the operational semantics and can be proved by checking that the relation [[e]] = [[c]] is closed under the rules in Table1 de ning the evaluation relation. So it only remains to prove (16).... ..."

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### Table 1: Rules for expression evaluation.

"... In PAGE 18: ... Let Can denote the subset of Expr consisting of the expressions in canonical form. These are given by: c ::= () j true j false j n j Ini(c) j (c,c) j x: :e : The operational semantics of the programming language can be given via a type-indexed family of evaluation relations e + c (e 2 Expr ; c 2 Can ) : These relations are inductively de ned by the rules in Table1 , which follow the dynamic semantics of the corresponding Standard ML expressions, as speci ed in (Milner, Tofte and Harper, 1990). Turning now to the denotational semantics of this language, for each type , let F (?; +) : Cpoop ? Cpo? ?! Cpo? be the locally continuous functor de ned by: Funit(?; +) def= 1? Fbool(?; +) def= 2? Fint(?; +) def= Z? Fty(?; +) def= (+) F 0(?; +) def= F (?; +) F 0(?; +) F ! 0(?; +) def= (F (+; ?) ( F 0(?; +))? : Here 1?, 2?, and Z? are the cppos obtained by lifting the discrete cpos 1 = f0g, 2 = f0; 1g, and Z = f: : : ; ?1; 0; 1; : : :g.... In PAGE 21: ... Properties (12) and (13) are simple to prove by induction on the structure of the canonical form c. Property (14) is often called the soundness of the denotational semantics with respect to the operational semantics and can be proved by check- ing that the relation [[e]] = [[c]] is closed under the rules in Table1 de ning the evaluation relation. So it only remains to prove (15).... ..."

### Table 2: Evaluation on interpretations of ex- tracted metonymic expressions. Evaluation # of expressions

"... In PAGE 4: ... Incorrect The interpretation is incorrect, or the expression BT AB C8 AB CE AB is not a metonymy. Table2 shows the result, and the examples of the evaluations are shown in Figure 5. 79% of the interpretative expressions were correct.... ..."

### Table 2. Evaluation of expressions

2003

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### Table 3. The expression evaluation rules for arithmetic operations op such as +, -, *, / and logical operations such as ^, _.

"... In PAGE 10: ... In addition, we need rules for evaluating expressions. These rules are sum- marized in Table3 . The case where an operand in an expression has the value > never occurs in PSCC algo- rithm if all the variables are initialized in the original program.... ..."

### Table 2. Evaluating the expressiveness of the model

### Table 3. Regular expressions and evaluations for model checking the dice ex- ample.

2004

"... In PAGE 11: ... Let 0 = trueU Wi=6 i=1 i and i = trueU i for i = 1 : : : 6. Then, the initial state s0 must satisfy the following PCTL formulas, for i = 1 : : : 6: P 1( 0); P 1 6 ( i); P 1 6 ( i) Table3 shows the results from applying our model checking approach to the dice model. For each path formula i, the second column gives the regular ex- pression3 corresponding to L(A i) and the third column gives its evaluation.... ..."

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