equal
deleted
inserted
replaced
1 chapter ZF |
1 chapter ZF |
2 |
2 |
3 session ZF (main timing) = Pure + |
3 session ZF (main timing) = Pure + |
4 description {* |
4 description \<open> |
5 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
5 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
6 Copyright 1995 University of Cambridge |
6 Copyright 1995 University of Cambridge |
7 |
7 |
8 Zermelo-Fraenkel Set Theory. This theory is the work of Martin Coen, |
8 Zermelo-Fraenkel Set Theory. This theory is the work of Martin Coen, |
9 Philippe Noel and Lawrence Paulson. |
9 Philippe Noel and Lawrence Paulson. |
39 |
39 |
40 Keith J. Devlin, Fundamentals of Contemporary Set Theory (Springer, 1979) |
40 Keith J. Devlin, Fundamentals of Contemporary Set Theory (Springer, 1979) |
41 |
41 |
42 Kenneth Kunen, Set Theory: An Introduction to Independence Proofs, |
42 Kenneth Kunen, Set Theory: An Introduction to Independence Proofs, |
43 (North-Holland, 1980) |
43 (North-Holland, 1980) |
44 *} |
44 \<close> |
45 sessions |
45 sessions |
46 FOL |
46 FOL |
47 theories |
47 theories |
48 ZF (global) |
48 ZF (global) |
49 ZFC (global) |
49 ZFC (global) |
50 document_files "root.tex" |
50 document_files "root.tex" |
51 |
51 |
52 session "ZF-AC" in AC = ZF + |
52 session "ZF-AC" in AC = ZF + |
53 description {* |
53 description \<open> |
54 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
54 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
55 Copyright 1995 University of Cambridge |
55 Copyright 1995 University of Cambridge |
56 |
56 |
57 Proofs of AC-equivalences, due to Krzysztof Grabczewski. |
57 Proofs of AC-equivalences, due to Krzysztof Grabczewski. |
58 |
58 |
61 |
61 |
62 The report |
62 The report |
63 http://www.cl.cam.ac.uk/Research/Reports/TR377-lcp-mechanising-set-theory.ps.gz |
63 http://www.cl.cam.ac.uk/Research/Reports/TR377-lcp-mechanising-set-theory.ps.gz |
64 "Mechanizing Set Theory", by Paulson and Grabczewski, describes both this |
64 "Mechanizing Set Theory", by Paulson and Grabczewski, describes both this |
65 development and ZF's theories of cardinals. |
65 development and ZF's theories of cardinals. |
66 *} |
66 \<close> |
67 theories |
67 theories |
68 WO6_WO1 |
68 WO6_WO1 |
69 WO1_WO7 |
69 WO1_WO7 |
70 AC7_AC9 |
70 AC7_AC9 |
71 WO1_AC |
71 WO1_AC |
76 AC18_AC19 |
76 AC18_AC19 |
77 DC |
77 DC |
78 document_files "root.tex" "root.bib" |
78 document_files "root.tex" "root.bib" |
79 |
79 |
80 session "ZF-Coind" in Coind = ZF + |
80 session "ZF-Coind" in Coind = ZF + |
81 description {* |
81 description \<open> |
82 Author: Jacob Frost, Cambridge University Computer Laboratory |
82 Author: Jacob Frost, Cambridge University Computer Laboratory |
83 Copyright 1995 University of Cambridge |
83 Copyright 1995 University of Cambridge |
84 |
84 |
85 Coind -- A Coinduction Example. |
85 Coind -- A Coinduction Example. |
86 |
86 |
97 |
97 |
98 Written up as |
98 Written up as |
99 Jacob Frost, A Case Study of Co_induction in Isabelle |
99 Jacob Frost, A Case Study of Co_induction in Isabelle |
100 Report, Computer Lab, University of Cambridge (1995). |
100 Report, Computer Lab, University of Cambridge (1995). |
101 http://www.cl.cam.ac.uk/Research/Reports/TR359-jf10008-co-induction-in-isabelle.dvi.gz |
101 http://www.cl.cam.ac.uk/Research/Reports/TR359-jf10008-co-induction-in-isabelle.dvi.gz |
102 *} |
102 \<close> |
103 theories ECR |
103 theories ECR |
104 |
104 |
105 session "ZF-Constructible" in Constructible = ZF + |
105 session "ZF-Constructible" in Constructible = ZF + |
106 description {* |
106 description \<open> |
107 Relative Consistency of the Axiom of Choice: |
107 Relative Consistency of the Axiom of Choice: |
108 Inner Models, Absoluteness and Consistency Proofs. |
108 Inner Models, Absoluteness and Consistency Proofs. |
109 |
109 |
110 Gödel's proof of the relative consistency of the axiom of choice is |
110 Gödel's proof of the relative consistency of the axiom of choice is |
111 mechanized using Isabelle/ZF. The proof builds upon a previous |
111 mechanized using Isabelle/ZF. The proof builds upon a previous |
119 of further material from that book. It also serves as an example of what to |
119 of further material from that book. It also serves as an example of what to |
120 expect when deep mathematics is formalized. |
120 expect when deep mathematics is formalized. |
121 |
121 |
122 A paper describing this development is |
122 A paper describing this development is |
123 http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-551.pdf |
123 http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-551.pdf |
124 *} |
124 \<close> |
125 theories |
125 theories |
126 DPow_absolute |
126 DPow_absolute |
127 AC_in_L |
127 AC_in_L |
128 Rank_Separation |
128 Rank_Separation |
129 document_files "root.tex" "root.bib" |
129 document_files "root.tex" "root.bib" |
130 |
130 |
131 session "ZF-IMP" in IMP = ZF + |
131 session "ZF-IMP" in IMP = ZF + |
132 description {* |
132 description \<open> |
133 Author: Heiko Loetzbeyer & Robert Sandner, TUM |
133 Author: Heiko Loetzbeyer & Robert Sandner, TUM |
134 Copyright 1994 TUM |
134 Copyright 1994 TUM |
135 |
135 |
136 Formalization of the denotational and operational semantics of a |
136 Formalization of the denotational and operational semantics of a |
137 simple while-language, including an equivalence proof. |
137 simple while-language, including an equivalence proof. |
139 The whole development essentially formalizes/transcribes |
139 The whole development essentially formalizes/transcribes |
140 chapters 2 and 5 of |
140 chapters 2 and 5 of |
141 |
141 |
142 Glynn Winskel. The Formal Semantics of Programming Languages. |
142 Glynn Winskel. The Formal Semantics of Programming Languages. |
143 MIT Press, 1993. |
143 MIT Press, 1993. |
144 *} |
144 \<close> |
145 theories Equiv |
145 theories Equiv |
146 document_files |
146 document_files |
147 "root.tex" |
147 "root.tex" |
148 "root.bib" |
148 "root.bib" |
149 |
149 |
150 session "ZF-Induct" in Induct = ZF + |
150 session "ZF-Induct" in Induct = ZF + |
151 description {* |
151 description \<open> |
152 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
152 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
153 Copyright 2001 University of Cambridge |
153 Copyright 2001 University of Cambridge |
154 |
154 |
155 Inductive definitions. |
155 Inductive definitions. |
156 *} |
156 \<close> |
157 theories |
157 theories |
158 (** Datatypes **) |
158 (** Datatypes **) |
159 Datatypes (*sample datatypes*) |
159 Datatypes (*sample datatypes*) |
160 Binary_Trees (*binary trees*) |
160 Binary_Trees (*binary trees*) |
161 Term (*recursion over the list functor*) |
161 Term (*recursion over the list functor*) |
179 document_files |
179 document_files |
180 "root.bib" |
180 "root.bib" |
181 "root.tex" |
181 "root.tex" |
182 |
182 |
183 session "ZF-Resid" in Resid = ZF + |
183 session "ZF-Resid" in Resid = ZF + |
184 description {* |
184 description \<open> |
185 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
185 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
186 Copyright 1995 University of Cambridge |
186 Copyright 1995 University of Cambridge |
187 |
187 |
188 Residuals -- a proof of the Church-Rosser Theorem for the |
188 Residuals -- a proof of the Church-Rosser Theorem for the |
189 untyped lambda-calculus. |
189 untyped lambda-calculus. |
194 J. Functional Programming 4(3) 1994, 371-394. |
194 J. Functional Programming 4(3) 1994, 371-394. |
195 |
195 |
196 See Rasmussen's report: The Church-Rosser Theorem in Isabelle: A Proof |
196 See Rasmussen's report: The Church-Rosser Theorem in Isabelle: A Proof |
197 Porting Experiment. |
197 Porting Experiment. |
198 http://www.cl.cam.ac.uk/ftp/papers/reports/TR364-or200-church-rosser-isabelle.ps.gz |
198 http://www.cl.cam.ac.uk/ftp/papers/reports/TR364-or200-church-rosser-isabelle.ps.gz |
199 *} |
199 \<close> |
200 theories Confluence |
200 theories Confluence |
201 |
201 |
202 session "ZF-UNITY" (timing) in UNITY = "ZF-Induct" + |
202 session "ZF-UNITY" (timing) in UNITY = "ZF-Induct" + |
203 description {* |
203 description \<open> |
204 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
204 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
205 Copyright 1998 University of Cambridge |
205 Copyright 1998 University of Cambridge |
206 |
206 |
207 ZF/UNITY proofs. |
207 ZF/UNITY proofs. |
208 *} |
208 \<close> |
209 theories |
209 theories |
210 (*Simple examples: no composition*) |
210 (*Simple examples: no composition*) |
211 Mutex |
211 Mutex |
212 |
212 |
213 (*Basic meta-theory*) |
213 (*Basic meta-theory*) |
215 |
215 |
216 (*Prefix relation; the Allocator example*) |
216 (*Prefix relation; the Allocator example*) |
217 Distributor Merge ClientImpl AllocImpl |
217 Distributor Merge ClientImpl AllocImpl |
218 |
218 |
219 session "ZF-ex" in ex = ZF + |
219 session "ZF-ex" in ex = ZF + |
220 description {* |
220 description \<open> |
221 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
221 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
222 Copyright 1993 University of Cambridge |
222 Copyright 1993 University of Cambridge |
223 |
223 |
224 Miscellaneous examples for Zermelo-Fraenkel Set Theory. |
224 Miscellaneous examples for Zermelo-Fraenkel Set Theory. |
225 |
225 |
229 Several (co)inductive and (co)datatype definitions are presented. The |
229 Several (co)inductive and (co)datatype definitions are presented. The |
230 report http://www.cl.cam.ac.uk/Research/Reports/TR312-lcp-set-II.ps.gz |
230 report http://www.cl.cam.ac.uk/Research/Reports/TR312-lcp-set-II.ps.gz |
231 describes the theoretical foundations of datatypes while |
231 describes the theoretical foundations of datatypes while |
232 href="http://www.cl.cam.ac.uk/Research/Reports/TR320-lcp-isabelle-ind-defs.dvi.gz |
232 href="http://www.cl.cam.ac.uk/Research/Reports/TR320-lcp-isabelle-ind-defs.dvi.gz |
233 describes the package that automates their declaration. |
233 describes the package that automates their declaration. |
234 *} |
234 \<close> |
235 theories |
235 theories |
236 misc |
236 misc |
237 Ring (*abstract algebra*) |
237 Ring (*abstract algebra*) |
238 Commutation (*abstract Church-Rosser theory*) |
238 Commutation (*abstract Church-Rosser theory*) |
239 Primes (*GCD theory*) |
239 Primes (*GCD theory*) |