### Table B.2: Selected notation of Isabelle/HOL

### Table 1. Lines of code in Isabelle/HOL, per language and file.

### Table 1. Lines of Isar proof code for different parts of the proof

2006

"... In PAGE 12: ... In total, the proof of the correctness of the transformation from automata to a PLC language contains approximately 1500 lines of proof code. Table1 shows the distribution of lines of proof code for the different parts of the proof. 5 Here, the Isabelle/HOL operator llparenthesis.... ..."

Cited by 1

### Table 1: Running times (in seconds) for TPTP problems

"... In PAGE 7: ... 19 of these 42 problems are rather easy, and were solved in less than a second each by both the existing procedures and the SAT solver approach. Table1 shows the times in seconds required to solve the remaining 23 prob- lems. An x indicates that the procedure ran out of memory or failed to terminate within an hour.... In PAGE 7: ...or the 7 satis able (i.e. unprovable) problems. In contrast, the SAT solver approach solves all problems, takes less than two seconds on all but two problems, and provides actual counterexamples for the unprovable prob- lems. Furthermore, the rightmost column of Table1 already shows the total (combined) time for the invocation of zCha and the following proof recon- struction in Isabelle/HOL. zCha alone terminates after a usually negligible fraction of this time, at which point a de nite answer can already be dis- played to the user { a feature that is particularly useful in our interactive setting.... ..."

### Table 3: The axioms for boolean algebras.

1998

"... In PAGE 9: ... n28We have kept our numbering consistent with Groote and Ponse n281994an29; in their setting Sum2 den0cnes n0b-conversion.n29 Let n06 be a pCRL-signature, then the pCRL-theory n05 n06 for n06 consists of the axioms depicted in Table 2 and the axioms for boolean algebras depicted in Table3 . A n06-algebra A is called a pCRL-algebra if A j=n05 n06... ..."

### Table 1 MTL linear algebra operations.

1998

"... In PAGE 3: ...Table 1 MTL linear algebra operations. 3 MTL Algorithms Table1 lists the principal algorithms provided by MTL. This list seems sparse, but a large number of functions are available by combining the above algorithms with the strided(), scaled(), and trans() iterator adapters.... ..."

Cited by 9

### Table 8: Some common Geometric Algebra operations.

2004

"... In PAGE 42: ... The large number of basic operations. Table8 lists some basic operations that every GA implementation should provide. 3.... ..."

Cited by 4

### Table 1. Operators of the MD algebra. Operator Description

"... In PAGE 13: ...mplemented or can be mapped to statements of a language (e.g., SQL or API) for an existing database server (a relational, a ROLAP, or a MOLAP system). Table1 briefly describes the main operators of the MD algebra.4 Apart from a number of operators that are variants of relational algebra operators, there are three new operators.... ..."