author | berghofe |
Fri, 24 Jul 1998 13:39:47 +0200 | |
changeset 5191 | 8ceaa19f7717 |
parent 5186 | 439e292b5b87 |
child 5305 | 513925de8962 |
permissions | -rw-r--r-- |
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(* Title: HOL/HOL.thy |
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ID: $Id$ |
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Author: Tobias Nipkow |
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Copyright 1993 University of Cambridge |
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Higher-Order Logic. |
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*) |
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HOL = CPure + |
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(** Core syntax **) |
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global |
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classes |
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term < logic |
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default |
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term |
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types |
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bool |
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arities |
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fun :: (term, term) term |
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bool :: term |
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consts |
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(* Constants *) |
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Trueprop :: bool => prop ("(_)" 5) |
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Not :: bool => bool ("~ _" [40] 40) |
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True, False :: bool |
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If :: [bool, 'a, 'a] => 'a ("(if (_)/ then (_)/ else (_))" 10) |
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arbitrary :: 'a |
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(* Binders *) |
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Eps :: ('a => bool) => 'a |
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All :: ('a => bool) => bool (binder "! " 10) |
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Ex :: ('a => bool) => bool (binder "? " 10) |
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Ex1 :: ('a => bool) => bool (binder "?! " 10) |
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Let :: ['a, 'a => 'b] => 'b |
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(* Infixes *) |
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o :: ['b => 'c, 'a => 'b, 'a] => 'c (infixl 55) |
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"=" :: ['a, 'a] => bool (infixl 50) |
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"&" :: [bool, bool] => bool (infixr 35) |
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"|" :: [bool, bool] => bool (infixr 30) |
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"-->" :: [bool, bool] => bool (infixr 25) |
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(* Overloaded Constants *) |
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axclass |
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plus < term |
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axclass |
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minus < term |
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axclass |
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times < term |
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axclass |
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power < term |
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consts |
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"+" :: ['a::plus, 'a] => 'a (infixl 65) |
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"-" :: ['a::minus, 'a] => 'a (infixl 65) |
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"*" :: ['a::times, 'a] => 'a (infixl 70) |
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(*See Nat.thy for "^"*) |
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(** Additional concrete syntax **) |
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nonterminals |
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letbinds letbind |
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case_syn cases_syn |
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syntax |
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"~=" :: ['a, 'a] => bool (infixl 50) |
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"@Eps" :: [pttrn, bool] => 'a ("(3@ _./ _)" [0, 10] 10) |
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(* Alternative Quantifiers *) |
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"*All" :: [idts, bool] => bool ("(3ALL _./ _)" [0, 10] 10) |
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"*Ex" :: [idts, bool] => bool ("(3EX _./ _)" [0, 10] 10) |
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"*Ex1" :: [idts, bool] => bool ("(3EX! _./ _)" [0, 10] 10) |
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(* Let expressions *) |
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"_bind" :: [pttrn, 'a] => letbind ("(2_ =/ _)" 10) |
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"" :: letbind => letbinds ("_") |
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"_binds" :: [letbind, letbinds] => letbinds ("_;/ _") |
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"_Let" :: [letbinds, 'a] => 'a ("(let (_)/ in (_))" 10) |
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(* Case expressions *) |
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"@case" :: ['a, cases_syn] => 'b ("(case _ of/ _)" 10) |
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"@case1" :: ['a, 'b] => case_syn ("(2_ =>/ _)" 10) |
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"" :: case_syn => cases_syn ("_") |
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"@case2" :: [case_syn, cases_syn] => cases_syn ("_/ | _") |
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translations |
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"x ~= y" == "~ (x = y)" |
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"@ x. b" == "Eps (%x. b)" |
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"ALL xs. P" => "! xs. P" |
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"EX xs. P" => "? xs. P" |
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"EX! xs. P" => "?! xs. P" |
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"_Let (_binds b bs) e" == "_Let b (_Let bs e)" |
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"let x = a in e" == "Let a (%x. e)" |
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syntax ("" output) |
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"op =" :: ['a, 'a] => bool ("(_ =/ _)" [51, 51] 50) |
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"op ~=" :: ['a, 'a] => bool ("(_ ~=/ _)" [51, 51] 50) |
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syntax (symbols) |
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Not :: bool => bool ("\\<not> _" [40] 40) |
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"op &" :: [bool, bool] => bool (infixr "\\<and>" 35) |
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"op |" :: [bool, bool] => bool (infixr "\\<or>" 30) |
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"op -->" :: [bool, bool] => bool (infixr "\\<midarrow>\\<rightarrow>" 25) |
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"op o" :: ['b => 'c, 'a => 'b, 'a] => 'c (infixl "\\<circ>" 55) |
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"op ~=" :: ['a, 'a] => bool (infixl "\\<noteq>" 50) |
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"@Eps" :: [pttrn, bool] => 'a ("(3\\<epsilon>_./ _)" [0, 10] 10) |
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"! " :: [idts, bool] => bool ("(3\\<forall>_./ _)" [0, 10] 10) |
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"? " :: [idts, bool] => bool ("(3\\<exists>_./ _)" [0, 10] 10) |
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"?! " :: [idts, bool] => bool ("(3\\<exists>!_./ _)" [0, 10] 10) |
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"@case1" :: ['a, 'b] => case_syn ("(2_ \\<Rightarrow>/ _)" 10) |
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(*"@case2" :: [case_syn, cases_syn] => cases_syn ("_/ \\<orelse> _")*) |
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syntax (symbols output) |
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"op ~=" :: ['a, 'a] => bool ("(_ \\<noteq>/ _)" [51, 51] 50) |
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"*All" :: [idts, bool] => bool ("(3\\<forall>_./ _)" [0, 10] 10) |
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"*Ex" :: [idts, bool] => bool ("(3\\<exists>_./ _)" [0, 10] 10) |
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"*Ex1" :: [idts, bool] => bool ("(3\\<exists>!_./ _)" [0, 10] 10) |
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(** Rules and definitions **) |
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local |
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rules |
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eq_reflection "(x=y) ==> (x==y)" |
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(* Basic Rules *) |
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refl "t = (t::'a)" |
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subst "[| s = t; P(s) |] ==> P(t::'a)" |
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ext "(!!x::'a. (f x ::'b) = g x) ==> (%x. f x) = (%x. g x)" |
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selectI "P (x::'a) ==> P (@x. P x)" |
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impI "(P ==> Q) ==> P-->Q" |
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mp "[| P-->Q; P |] ==> Q" |
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defs |
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True_def "True == ((%x::bool. x) = (%x. x))" |
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All_def "All(P) == (P = (%x. True))" |
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Ex_def "Ex(P) == P(@x. P(x))" |
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False_def "False == (!P. P)" |
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not_def "~ P == P-->False" |
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and_def "P & Q == !R. (P-->Q-->R) --> R" |
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or_def "P | Q == !R. (P-->R) --> (Q-->R) --> R" |
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Ex1_def "Ex1(P) == ? x. P(x) & (! y. P(y) --> y=x)" |
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rules |
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(* Axioms *) |
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iff "(P-->Q) --> (Q-->P) --> (P=Q)" |
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True_or_False "(P=True) | (P=False)" |
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defs |
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(*misc definitions*) |
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Let_def "Let s f == f(s)" |
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o_def "(f::'b=>'c) o g == (%(x::'a). f(g(x)))" |
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if_def "If P x y == @z::'a. (P=True --> z=x) & (P=False --> z=y)" |
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(*arbitrary is completely unspecified, but is made to appear as a |
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definition syntactically*) |
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arbitrary_def "False ==> arbitrary == (@x. False)" |
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(** initial HOL theory setup **) |
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setup Simplifier.setup |
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setup ClasetThyData.setup |
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end |
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ML |
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(** Choice between the HOL and Isabelle style of quantifiers **) |
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val HOL_quantifiers = ref true; |
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fun alt_ast_tr' (name, alt_name) = |
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let |
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fun ast_tr' (*name*) args = |
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if ! HOL_quantifiers then raise Match |
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else Syntax.mk_appl (Syntax.Constant alt_name) args; |
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in |
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(name, ast_tr') |
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end; |
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val print_ast_translation = |
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map alt_ast_tr' [("! ", "*All"), ("? ", "*Ex"), ("?! ", "*Ex1")]; |