### Table 2: Sequent rules corresponding to circuit links

"... In PAGE 6: ... In valid (or sequential) nets C will havetobevalid as well;; this will be checked using the sequentialization process of Appendix B, or, equivalently,by showing that the circuit can be built inductively. Since some of these connectives will not be familiar (and because we use a di erent notation from just about anyone else!|Lambek uses n ;;=for ; ;; ;,and : ; ;; ; : for 5;; 4), the sequent rules that correspond to these links are given in Table2 . In commutative logics the reader can add the exchange rule for himself.... In PAGE 12: ...n the noncommutative logic. In Appendix B we presentavalid sequentialization process. An example of a planar non-sequential circuit which satis es the net criterion is given in Figure 16. The sequent rules given in Table2 are all valid in the noncommutative logics;; for the commutative logics, where the circuits need not be planar, one must add the exchange rules in the obvious way. In Figure 3 are some (valid) circuits.... In PAGE 15: ... Logical theories and categorical doctrines We shall deal with several logical theories (and the corresponding categorical structures) in this paper. The full system using all the binary connectives ;; ;; ; ;; ;;; 4;; 5 and the constants gt;;; ? and using the sequent rules of Table2 (or equivalently the circuit links of Table 1) is Lambek apos;s bilinear logic BILL.We also consider the fragment of bilinear logic which omits the connectives 4;; 5;;we call this noncommutative logic GILL.... In PAGE 15: ....1. Remark. (Cut elimination and FILL) Neither the commutative nor noncommuta- tiveversions of FILL, if presented as a sequent calculus (as in Table2 , with the restriction of Remark 1.1) satis es cut elimination.... In PAGE 18: ...102 in Table2 ) corresponds categorically to having an inverse (costrength) to this family of maps: A ; (B C) ;! (A ; B) C.Wecancheck that in the category of circuits with the more general \boxed quot; links we do indeed havesuch an isomorphism;; half of this exercise is illustrated in Figure 4.... ..."

### Table 1: Degrees of causal indirection. There is a natural trend from simpler to more complicated tasks. The more time-delayed an e ect, the more di cult it is to model.

2003

"... In PAGE 1: ... We present results for two important steps along the way, and describe how we plan to proceed. Table1 shows three levels of causal complexity. The simplest causal chain that the robot experiences is the perception of its own actions.... ..."

Cited by 4

### Table 1: Degrees of causal indirection. There is a natural trend from simpler to more complicated tasks. The more time-delayed an e ect, the more di cult it is to model.

2003

"... In PAGE 1: ... We present results for two important steps along the way, and describe how we plan to proceed. Table1 shows three levels of causal complexity. The simplest causal chain that the robot experiences is the perception of its own actions.... ..."

Cited by 4

### Table 1: Degrees of causal indirection. There is a natural trend from simpler to more complicated tasks. The more time-delayed an e ect, the more di cult it is to model.

2003

"... In PAGE 1: ... We present results for two important steps along the way, and describe how we plan to proceed. Table1 shows three levels of causal complexity. The simplest causal chain that the robot experiences is the perception of its own actions.... ..."

Cited by 4

### Table 1. Typing Judgements for the -calculus

1999

"... In PAGE 5: ... Contexts are lists x1: A1; : : : xn: An where the x apos;s are distinct variables and the A apos;s are types | the domain of the context is fx1; : : : ; xng and we write ? ?0 if the domain of ? is contained in the domain of ?0. The -calculus has term judgements ? ` t : A and substitution judgements ? ` f : | these judgements are generated by the inference rules of Table1 . The inference rules for declaring variables and the introduction and elimination rules for function spaces and conjunctions are standard.... ..."

Cited by 1

### Table 1. Typing Judgements for the -calculus

1999

"... In PAGE 5: ... Contexts are lists x1: A1; : : : xn: An where the x apos;s are distinct variables and the A apos;s are types | the domain of the context is fx1; : : : ; xng and we write ? ?0 if the domain of ? is contained in the domain of ?0. The -calculus has term judgements ? ` t : A and substitution judgements ? ` f : | these judgements are generated by the inference rules of Table1 . The inference rules for declaring variables and the introduction and elimination rules for function spaces and conjunctions are standard.... ..."

Cited by 1

### Table 5: The total size of the compiled system (binary)

in 1

"... In PAGE 11: ... The di culty of the integration task depends largely on the usage patterns of the data structures in the legacy system whichhave not been migrated yet and therefore need be shadowed, so that the new version of the system can be compiled and linked as a whole. Fi- nally,in Table5 the size of the old and the new version of the overall system is compared. As it is shown, the new system is approximately 5% larger in size than the original one.... ..."

### Table 2: Java binary compatibility summary: interfaces.

2002

"... In PAGE 6: ...ffordable. Reflection is an additional complication. 4 Our Approach In this section we present our solution for static com- pilers to support Java binary compatibility. Table 1 and Table2 summarize all the binary changes to classes and interfaces specified in Chapter 13 of the Java language specification [11]. Compatible changes are marked with B7 and incompatible changes are marked with A0 .... ..."

Cited by 2

### Table 2: Java binary compatibility summary: interfaces.

"... In PAGE 6: ...ffordable. Reflection is an additional complication. 4 Our Approach In this section we present our solution for static com- pilers to support Java binary compatibility. Table 1 and Table2 summarize all the binary changes to classes and interfaces specified in Chapter 13 of the Java language specification [12]. Compatible changes are marked with B7 and incompatible changes are marked with A0 .... ..."

### Table 2: Java binary compatibility summary: interfaces.

"... In PAGE 6: ...ffordable. Reflection is an additional complication. 4 Our Approach In this section we present our solution for static com- pilers to support Java binary compatibility. Table 1 and Table2 summarize all the binary changes to classes and interfaces specified in Chapter 13 of the Java language specification [11]. Compatible changes are marked with B7 and incompatible changes are marked with A0 .... ..."