7 ROOT.ML -- loads all source files. Enter an ML image containing FOL and |
7 ROOT.ML -- loads all source files. Enter an ML image containing FOL and |
8 type: use "ROOT.ML"; |
8 type: use "ROOT.ML"; |
9 |
9 |
10 Makefile -- compiles the files under Poly/ML or SML of New Jersey |
10 Makefile -- compiles the files under Poly/ML or SML of New Jersey |
11 |
11 |
|
12 IMP -- subdirectory containing a semantics equivalence proof between |
|
13 operational and denotational definitions of a simple programming language. |
|
14 To execute, enter an ML image containing ZF and type: use "IMP/ROOT.ML"; |
|
15 |
12 ex -- subdirectory containing examples. To execute them, enter an ML image |
16 ex -- subdirectory containing examples. To execute them, enter an ML image |
13 containing ZF and type: use "ex/ROOT.ML"; |
17 containing ZF and type: use "ex/ROOT.ML"; |
|
18 |
|
19 Isabelle/ZF formalizes the greater part of elementary set theory, including |
|
20 relations, functions, injections, surjections, ordinals and cardinals. |
|
21 Results proved include Cantor's Theorem, the Recursion Theorem, the |
|
22 Schroeder-Bernstein Theorem, and (assuming AC) the Wellordering Theorem. |
|
23 |
|
24 Isabelle/ZF also provides theories of lists, trees, etc., for formalizing |
|
25 computational notions. It supports inductive definitions of |
|
26 infinite-branching trees for any cardinality of branching. |
|
27 |
|
28 Useful references for Isabelle/ZF: |
|
29 |
|
30 Lawrence C. Paulson, |
|
31 Set theory for verification: I. From foundations to functions. |
|
32 J. Automated Reasoning 11 (1993), 353-389. |
|
33 |
|
34 Lawrence C. Paulson, |
|
35 Set theory for verification: II. Induction and recursion. |
|
36 Report 312, Computer Lab (1993). |
|
37 |
|
38 Lawrence C. Paulson, |
|
39 A fixedpoint approach to implementing (co)inductive definitions. |
|
40 In: A. Bundy (editor), |
|
41 CADE-12: 12th International Conference on Automated Deduction, |
|
42 (Springer LNAI 814, 1994), 148-161. |
14 |
43 |
15 Useful references on ZF set theory: |
44 Useful references on ZF set theory: |
16 |
45 |
17 Paul R. Halmos, Naive Set Theory (Van Nostrand, 1960) |
46 Paul R. Halmos, Naive Set Theory (Van Nostrand, 1960) |
18 |
47 |
19 Patrick Suppes, Axiomatic Set Theory (Dover, 1972) |
48 Patrick Suppes, Axiomatic Set Theory (Dover, 1972) |
20 |
49 |
21 Keith J. Devlin, |
50 Keith J. Devlin, |
22 Fundamentals of Contemporary Set Theory (Springer, 1979) |
51 Fundamentals of Contemporary Set Theory (Springer, 1979) |
|
52 |
|
53 Kenneth Kunen |
|
54 Set Theory: An Introduction to Independence Proofs |
|
55 (North-Holland, 1980) |