Verification of Parameterised FPGA Circuit Descriptions with Layout ...

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APPENDIX A. QUARTZ LANGUAGE GRAMMAR 186 〈rangeval〉 ::= 〈arg〉 〈arg〉 ::= 〈id〉 〈vecindex 〉 | 〈expr〉 | ( ) | ( 〈arg〉 (, 〈arg〉)* ) 〈expr〉 ::= 〈expr〉 〈bop〉 〈expr〉 | 〈uop〉 〈expr〉 | 〈id〉 | 〈num〉 | true | false | 〈expr〉..〈expr〉 | ( 〈expr〉 ) | height ( 〈blkinst〉 ) | width ( 〈blkinst〉 ) | max ( 〈expr〉, 〈expr〉 (, 〈expr〉)* ) | if ( 〈expr〉 , 〈expr〉 , 〈expr〉 ) | sum ( 〈id〉 = 〈expr〉 .. 〈expr〉 , 〈expr〉 ) | maxf ( 〈id〉 = 〈expr〉 .. 〈expr〉 , 〈expr〉 ) 〈bop〉 ::= and | or | nand | nor | xor | xnor | + | - | * | / | ** | mod | == | != | < | | >= 〈uop〉 ::= - | abs | not 〈id〉 ::= (‘A’-‘Z’ | ‘a’-‘z’)+ (‘A’-‘Z’ | ‘a’-‘z’ | ‘0’-‘9’ | ‘ ’)* 〈num〉 ::= (‘0’-‘9’)*
Appendix B Theoretical Basis for Layout Reasoning This appendix contains Isabelle theories which form the QuartzLayout library. IntAlgebra defines Quartz operators that are not already present in HOL, including > and a power operation for integers. It also includes many useful theorems that can be used to rewrite integer expressions. Types declares the Quartz types of wires and vectors. Block defines Quartz blocks as Isabelle records consisting of their functional definition, height function and width function. The theory also defines the block instantiation operation and a number of simplification theorems. Inbuilt defines the layout interpretations of language constructs that are treated as inbuilt blocks (such as zip). SeriesComposition defines the semantics and layout interpretation of Quartz series com- position. It also includes proofs of useful properties for the layout of series compositions. 187
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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 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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CHAPTER 6. LAYOUT CASE STUDIES 133
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