Tutorial on Isabelle/HOL

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Contentsxi9. Advanced Simplification and Induction . . . . . . . . . . . . . . . . . . . 1779.1 Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1779.1.1 Advanced Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1779.1.2 How the Simplifier Works . . . . . . . . . . . . . . . . . . . . . . . . . 1799.2 Advanced Induction Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 1809.2.1 Massaging the Proposition . . . . . . . . . . . . . . . . . . . . . . . . . 1809.2.2 Beyond Structural and Recursion Induction . . . . . . . . . . 1829.2.3 Derivation of New Induction Schemas . . . . . . . . . . . . . . . 1849.2.4 CTL Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18410. Case Study: Verifying a Security Protocol . . . . . . . . . . . . . . . . 18910.1 The Needham-Schroeder Public-Key Protocol . . . . . . . . . . . . . . 18910.2 Agents and Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19110.3 Modelling the Adversary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19210.4 Event Traces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19310.5 Modelling the Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19410.6 Proving Elementary Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 19510.7 Proving Secrecy Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197A. Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
xiiContents
Page 1 and 2: Tobias NipkowMarkus WenzelLawrence
Page 3 and 4: viPrefacegives the best performance
Page 5 and 6: viiiContents3.1.3 The simp Method .
Page 7: xContents6.6 Case Study: Verified M
Page 12 and 13: 1. The Basics1.1 IntroductionThis b
Page 14 and 15: 1.3 Types, Terms and Formulae 5base
Page 16 and 17: 1.4 Variables 71.4 VariablesIsabell
Page 18: 2. Functional Programming in HOLThi
Page 21 and 22: 12 2. Functional Programming in HOL
Page 36 and 37: 3. More Functional ProgrammingThe p
Page 38 and 39: 3.1 Simplification 29could have bee
Page 40 and 41: 3.1 Simplification 31lemma "(let xs
Page 42 and 43: 3.1 Simplification 33lemma "rev [a]
Page 44 and 45: 3.2 Induction Heuristics 35Proof Ge
Page 46 and 47: 3.3 Case Study: Compiling Expressio
Page 48 and 49: 3.4 Advanced Datatypes 39two case-e
Page 50 and 51: apply simp_all3.4 Advanced Datatype
Page 52 and 53: 3.4 Advanced Datatypes 43lemma [sim
Page 54 and 55: 3.4 Advanced Datatypes 45✑◗ ✑
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"ack2 n 0 = Suc n" |"ack2 0 (Suc m)
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3.5 Total Recursive Functions: fun
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54 4. Presenting Theoriesdefinition
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56 4. Presenting Theories| Yen nat
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58 4. Presenting Theories4.2.1 Isab
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60 4. Presenting Theoriesheader {*
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62 4. Presenting Theoriestext {*Thi
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64 4. Presenting TheoriesTagged com
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5. The Rules of the GameThis chapte
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70 5. The Rules of the GameThe assu
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74 5. The Rules of the Game¬(P →
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76 5. The Rules of the GameOther me
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78 5. The Rules of the Gamere-orien
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80 5. The Rules of the Gamelemma "[
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82 5. The Rules of the GameAs befor
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84 5. The Rules of the Gamelemma "[
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86 5. The Rules of the Game5.10.1 D
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88 5. The Rules of the Game5.11 Som
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90 5. The Rules of the GameThe next
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92 5. The Rules of the Gameit can p
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94 5. The Rules of the Game5.15.1 M
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96 5. The Rules of the Game5.15.2 M
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98 5. The Rules of the Game5.16.1 T
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100 5. The Rules of the Game5.17 Ma
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102 5. The Rules of the GameWe deci
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104 5. The Rules of the Gamegcd ?m1
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6. Sets, Functions and RelationsThi
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6.1 Sets 1096.1.1 Finite Set Notati
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6.2 Functions 111The internal form
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6.3 Relations 1131. ∀ x y. f x =
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Induction over the reflexive transi
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inv_image r f ≡ {(x,y). (f x, f y
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6.6 Case Study: Verified Model Chec
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6.6.2 Computation Tree Logic — CT
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130 7. Inductively Defined Setsan e
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132 7. Inductively Defined Sets1. n
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134 7. Inductively Defined Setsindu
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136 7. Inductively Defined SetsNow
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138 7. Inductively Defined Sets7.3.
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140 7. Inductively Defined Setswher
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142 7. Inductively Defined Sets7.3.
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144 7. Inductively Defined Sets| "[
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146 7. Inductively Defined Setstheo
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Part IIIAdvanced Material
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152 8. More about TypesThe intuitiv
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154 8. More about Typesthe simplifi
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156 8. More about Typesmore is impl
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158 8. More about TypesThe cases me
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160 8. More about Types8.3 Axiomati
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162 8. More about Typesprefix_def:"
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164 8. More about TypesLinear Order
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166 8. More about Types8.4 NumbersU
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168 8. More about Types2 + n = Suc
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170 8. More about Typeswhen the lef
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172 8. More about Types((c::’a::r
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174 8. More about Types8.5.2 Defini
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176 8. More about TypesThe fact tha
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178 9. Advanced Simplification and
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10. Case Study: Verifying a Securit
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10.2 Agents and Messages 1911. A
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analz (synth H) = analz H ∪ synth
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10.6 Proving Elementary Properties
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10.7 Proving Secrecy Theorems 197No
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10.7 Proving Secrecy Theorems 199ca
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201You know my methods. Apply them!
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204 A. AppendixConstant Type Syntax
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206 BIBLIOGRAPHY[13] Florian Haftma
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Index!, 203?, 203∃! , 203?!, 203&
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210 Index- defining inductively, 12
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212 Index- and fun, 48patterns- hig
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Tutorial on Isabelle/HOL

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