Verification of Parameterised FPGA Circuit Descriptions with Layout ...

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APPENDIX B. THEORETICAL BASIS FOR LAYOUT REASONING 206 theorem min_max_corres: "!! (a::int) (b::int). min a b = - (max (-a) (-b))" apply (simp add: max_def min_def) done section {* minf function and correspondance with maxf *} consts minf :: "(int*int*(int=>int))=>int" recdef minf "measure (%(b, t, f). nat(t+1-b))" "minf (bot, top, fun) = (if (top < bot) then 0 else ( case (top = bot) of True => fun top | False => ( let one = fun top in let two = minf (bot, top - 1, fun) in min one two) ))" theorem minf_maxf_corres: "!! (f::int=>int) b t. minf(b,t,f) = - maxf (b,t,% x.- f x) " apply (case_tac "b
Appendix C Placed Combinator Libraries This appendix contains the Quartz descriptions and layout correctness proofs for some Quartz libraries. The wide range of wiring blocks in the Quartz prelude library have been omitted, since they are all defined to have size 0 × 0, as have many combinators which have similar functions to the one shown. For example, the snd block is structurally very similar to the fst block and has been omitted, as has the col block which is very similar to row. C.1 Prelude Library C.1.1 fst /∗∗ Apply block R to the first element of a tuple ∗/ block fst (block R ‘a ∼ ‘b) (‘a i1, ‘c i2) ∼ (‘b o1, ‘c o2) attributes { height = height(i1 ;R ; o1). width = width(i1 ;R ;o1). layout−proved. } { o2 = i2. i1 ; R ; o1 at (0,0). } theory fst = QuartzLayout: section {* Function definitions *} consts struct:: "((’t276=>’t277=>bool,’t276=>’t277=>int)block)=>(’t276*’t284)=>(’t277*’ t284)=>bool" 207
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Imperial College of Science, Techno
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Acknowledgements Firstly, I’d lik
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TABLE OF CONTENTS iv 2.5 Isabelle:
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TABLE OF CONTENTS vi 5.3.1 Speciali
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TABLE OF CONTENTS viii C.1.1 fst .
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Chapter 1 Introduction This thesis
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CHAPTER 1. INTRODUCTION 3 B A C Fig
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CHAPTER 1. INTRODUCTION 5 pler, all
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CHAPTER 2. BACKGROUND AND RELATED W
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CHAPTER 3. GENERATING PARAMETERISED
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Chapter 4 Verifying Circuit Layouts
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CHAPTER 4. VERIFYING CIRCUIT LAYOUT
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Chapter 5 Specialisation In this ch
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CHAPTER 5. SPECIALISATION 109 opera
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CHAPTER 5. SPECIALISATION 111 // Ha
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CHAPTER 5. SPECIALISATION 113 circu
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CHAPTER 5. SPECIALISATION 115 const
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CHAPTER 5. SPECIALISATION 117 block
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CHAPTER 5. SPECIALISATION 119 Modif
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CHAPTER 5. SPECIALISATION 121 Buffe
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CHAPTER 5. SPECIALISATION 123 a fas
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CHAPTER 5. SPECIALISATION 125 block
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CHAPTER 5. SPECIALISATION 127 y y y
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CHAPTER 5. SPECIALISATION 129 with
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CHAPTER 6. LAYOUT CASE STUDIES 131
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