Verification of Parameterised FPGA Circuit Descriptions with Layout ...

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APPENDIX C. PLACED COMBINATOR LIBRARIES 252 by auto end bool,(’t11*’t12)=>(’t13*’t14)=>int)block) *(((’t16=>’t11=>bool,’t16=>’t11=>int)block)*((’t18=>’t12=>bool,’t18=>’t12=> int)block))*(((’t13=>’t20=>bool,’t13=>’t20=>int)block)*((’t14=>’t22=>bool,’ t14=>’t22=>int)block)))=>(’t16*’t18)=>(’t20*’t22)=>bool" height:: "((((’t11*’t12)=>(’t13*’t14)=>bool,(’t11*’t12)=>(’t13*’t14)=>int)block) *(((’t16=>’t11=>bool,’t16=>’t11=>int)block)*((’t18=>’t12=>bool,’t18=>’t12=> int)block))*(((’t13=>’t20=>bool,’t13=>’t20=>int)block)*((’t14=>’t22=>bool,’ t14=>’t22=>int)block)))=>(’t16*’t18)=>(’t20*’t22)=>int" width:: "((((’t11*’t12)=>(’t13*’t14)=>bool,(’t11*’t12)=>(’t13*’t14)=>int)block) *(((’t16=>’t11=>bool,’t16=>’t11=>int)block)*((’t18=>’t12=>bool,’t18=>’t12=> int)block))*(((’t13=>’t20=>bool,’t13=>’t20=>int)block)*((’t14=>’t22=>bool,’ t14=>’t22=>int)block)))=>(’t16*’t18)=>(’t20*’t22)=>int" surround:: "(((((’t11*’t12)=>(’t13*’t14)=>bool,(’t11*’t12)=>(’t13*’t14)=>int) block)*(((’t16=>’t11=>bool,’t16=>’t11=>int)block)*((’t18=>’t12=>bool,’t18=>’ t12=>int)block))*(((’t13=>’t20=>bool,’t13=>’t20=>int)block)*((’t14=>’t22=> bool,’t14=>’t22=>int)block)))=>(’t16*’t18)=>(’t20*’t22)=>bool, ((((’t11*’t12) =>(’t13*’t14)=>bool,(’t11*’t12)=>(’t13*’t14)=>int)block)*(((’t16=>’t11=>bool ,’t16=>’t11=>int)block)*((’t18=>’t12=>bool,’t18=>’t12=>int)block))*(((’t13=>’ t20=>bool,’t13=>’t20=>int)block)*((’t14=>’t22=>bool,’t14=>’t22=>int)block))) =>(’t16*’t18)=>(’t20*’t22)=>int)block" defs struct_def: "struct == % (A, (B, C), (D, E)) (l, t) (b, r). EX (l2::’t11) (t2::’ t12) (b2::’t13) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)" height_def: "height == % (A, (B, C), (D, E)) (l, t) (b, r). let l2 = (THE (l2::’t11). EX (t2::’t12) (b2::’t13) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in

APPENDIX C. PLACED COMBINATOR LIBRARIES 253 let t2 = (THE (t2::’t12). EX (l2::’t11) (b2::’t13) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in let b2 = (THE (b2::’t13). EX (l2::’t11) (t2::’t12) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in let r2 = (THE (r2::’t14). EX (l2::’t11) (t2::’t12) (b2::’t13). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in max ((Height (b2 ;;; D ;;; b)) + (Height (r2 ;;; E ;;; r))) ((max (Height (b2 ;;; D ;;; b)) ((max ((Height (b2 ;;; D ;;; b)) + (Height ((l2, t2) ;;; A ;;; (b2, r2)))) ((max ((max ((Height (b2 ;;; D ;;; b)) + (Height (r2 ;;; E ;;; r))) ((Height (b2 ;;; D ;;; b)) + (Height ((l2, t2) ;;; A ;;; (b2, r2))))) + (Height (t ;;; C ;;; t2))) ((Height (b2 ;;; D ;;; b)) + ( Height (l ;;; B ;;; l2)))))))))" width_def: "width == % (A, (B, C), (D, E)) (l, t) (b, r). let l2 = (THE (l2::’t11). EX (t2::’t12) (b2::’t13) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in let t2 = (THE (t2::’t12). EX (l2::’t11) (b2::’t13) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in let b2 = (THE (b2::’t13). EX (l2::’t11) (t2::’t12) (r2::’t14). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in let r2 = (THE (r2::’t14). EX (l2::’t11) (t2::’t12) (b2::’t13). Def (l ;;; B ;;; l2) & Def (t ;;; C ;;; t2) & Def ((l2, t2) ;;; A ;;; (b2, r2)) & Def (b2 ;;; D ;;; b) & Def (r2 ;;; E ;;; r)) in max ((Width (l ;;; B ;;; l2)) + (Width ((l2, t2) ;;; A ;;; (b2, r2))) + ( Width (r2 ;;; E ;;; r))) ((max ((Width (l ;;; B ;;; l2)) + (Width (b2 ;;; D ;;; b))) ((max ((Width (l ;;; B ;;; l2)) + (Width ((l2, t2) ;;; A ;;; (b2, r2)))) ((max ((Width (l ;;; B ;;; l2)) + (Width (t ;;; C ;;; t2 ))) (Width (l ;;; B ;;; l2))))))))" surround_def: "surround == (| Def = struct, Height = height, Width = width|)" declare width_def [simp] declare height_def [simp] declare struct_def [simp] section {* Validity of width and height functions *} theorem height_ge0_int : "!! (A::(((’t11*’t12)=>(’t13*’t14)=>bool,(’t11*’t12)=>(’t13 *’t14)=>int)block)) (B::((’t16=>’t11=>bool,’t16=>’t11=>int)block)) (C::((’t18=>’ t12=>bool,’t18=>’t12=>int)block)) (D::((’t13=>’t20=>bool,’t13=>’t20=>int)block)) (E::((’t14=>’t22=>bool,’t14=>’t22=>int)block)) (l::’t16) (t::’t18) (b::’t20) (r ::’t22). [| ALL (qs32::(’t11*’t12)) (qs33::(’t13*’t14)). 0

Page 1 and 2: Imperial College of Science, Techno

Page 3 and 4: Acknowledgements Firstly, I’d lik

Page 5 and 6: TABLE OF CONTENTS iv 2.5 Isabelle:

Page 7 and 8: TABLE OF CONTENTS vi 5.3.1 Speciali

Page 9 and 10: TABLE OF CONTENTS viii C.1.1 fst .

Page 11 and 12: Chapter 1 Introduction This thesis

Page 13 and 14: CHAPTER 1. INTRODUCTION 3 B A C Fig

Page 15 and 16: CHAPTER 1. INTRODUCTION 5 pler, all

Page 17 and 18: CHAPTER 2. BACKGROUND AND RELATED W














Page 45 and 46: CHAPTER 3. GENERATING PARAMETERISED















Page 75 and 76: Chapter 4 Verifying Circuit Layouts

Page 77 and 78: CHAPTER 4. VERIFYING CIRCUIT LAYOUT




















Page 117 and 118: Chapter 5 Specialisation In this ch

Page 119 and 120: CHAPTER 5. SPECIALISATION 109 opera

Page 121 and 122: CHAPTER 5. SPECIALISATION 111 // Ha

Page 123 and 124: CHAPTER 5. SPECIALISATION 113 circu

Page 125 and 126: CHAPTER 5. SPECIALISATION 115 const

Page 127 and 128: CHAPTER 5. SPECIALISATION 117 block

Page 129 and 130: CHAPTER 5. SPECIALISATION 119 Modif

Page 131 and 132: CHAPTER 5. SPECIALISATION 121 Buffe

Page 133 and 134: CHAPTER 5. SPECIALISATION 123 a fas

Page 135 and 136: CHAPTER 5. SPECIALISATION 125 block

Page 137 and 138: CHAPTER 5. SPECIALISATION 127 y y y

Page 139 and 140: CHAPTER 5. SPECIALISATION 129 with

Page 141 and 142: CHAPTER 6. LAYOUT CASE STUDIES 131

















Page 175 and 176: CHAPTER 7. CONCLUSION AND FUTURE WO





Page 185 and 186: Bibliography [1] A. Aggoun and N. B

Page 187 and 188: BIBLIOGRAPHY 177 [19] H. Gelernter.

Page 189 and 190: BIBLIOGRAPHY 179 [41] Y. Li and M.

Page 191 and 192: BIBLIOGRAPHY 181 [60] L. C. Paulson

Page 193 and 194: BIBLIOGRAPHY 183 [83] J. Voeten. On

Page 195 and 196: APPENDIX A. QUARTZ LANGUAGE GRAMMAR

Page 197 and 198: Appendix B Theoretical Basis for La

Page 199 and 200: APPENDIX B. THEORETICAL BASIS FOR L









Page 217 and 218: Appendix C Placed Combinator Librar

Page 219 and 220: APPENDIX C. PLACED COMBINATOR LIBRA





















Page 261: APPENDIX C. PLACED COMBINATOR LIBRA








Page 279 and 280: APPENDIX D. CIRCUIT LAYOUT CASE STU
























Page 327: APPENDIX D. CIRCUIT LAYOUT CASE STU

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layout

bits

height

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width

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combinator

theorems

appendix

verification

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