### Table 1. Comparison of the ASCII size of programs and proofs.

2003

"... In PAGE 11: ... There is however, the disadvantage that formalising the programs in type theory is a time consuming process; the amount of automation and heuristics available in present day theorem provers is far from being satisfactory. Table1 shows the relative size (in kilobytes) of the various phases of for- malisation. During this project we used the most novel facilities of Coq.... In PAGE 11: ... During this project we used the most novel facilities of Coq. The statistics in Table1 might thus discourage people from using type theoretical tools for veriflcation purposes. Our answer is that, without the existing automa- tion tools in recent versions of Coq, and without the recent theoretical advances, such a project seemed impossible only a couple of years ago.... ..."

Cited by 9

### Table 1. Comparison of the ASCII size of programs and proofs.

2003

"... In PAGE 11: ... There is however, the disadvantage that formalising the programs in type theory is a time consuming process; the amount of automation and heuristics available in present day theorem provers is far from being satisfactory. Table1 shows the relative size (in kilobytes) of the various phases of for- malisation. During this project we used the most novel facilities of Coq.... In PAGE 11: ... During this project we used the most novel facilities of Coq. The statistics in Table1 might thus discourage people from using type theoretical tools for veriflcation purposes. Our answer is that, without the existing automa- tion tools in recent versions of Coq, and without the recent theoretical advances, such a project seemed impossible only a couple of years ago.... ..."

Cited by 9

### Table 3. Proof transformations: Subtyping derivations T-ArrowRef

"... In PAGE 6: ... Lemma 4.1 For any derivation C, the application of a transformation rule from Table3 yields an equivalent derivation Cprime. Proof It is easy to see that each rule transforms a derivation C into a derivation Cprime of the same judgement.... ..."

### Table 6.1: Program transformations used in manually transformed programs

1998

Cited by 4

### Table 6.1: Program transformations used in manually transformed programs

1998

Cited by 4

### Table 1: Benchmark Programs and Transformations

"... In PAGE 2: ... 2 Transformation Space Charac- teristics This paper is concerned with studying the via- bility of iterative compilation by means of 18 case studies. We selected three important and exten- sively studied kernels and examined their behav- iour across three separate platforms and two dif- ferent data sizes (see Table1 ). This section is pri- marily concerned with examining the characteris- tics of the transformation space and is followed in section 3 by evaluation of an iterative approach to nding the global minima.... ..."

### 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. 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 1. Proofs, theories and programs, according to Fetzer (1988;2001).

"... In PAGE 4: ... 2.5 The comparison advanced by Fetzer (1988;2001), which we reproduce in Table1 , suggests that the differences between theorems and programs may outweigh their similarities. Programs, like scientific theories, have semantical significance that mathematical proofs do not possess.... ..."

Cited by 1