src/ZF/README
changeset 488 52f7447d4f1b
parent 0 a5a9c433f639
child 958 f2c225386348
equal deleted inserted replaced
487:af83700cb771 488:52f7447d4f1b
     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)