author | lcp |
Fri, 19 Aug 1994 11:02:45 +0200 | |
changeset 115 | 0ec63df3ae04 |
parent 112 | 3fc2f9c40759 |
child 185 | 8325414a370a |
permissions | -rw-r--r-- |
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0ec63df3ae04
HOL/fun.ML: renamed Fun.ML to avoid problems with MLs "fun" keyword
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(* Title: HOL/Prod.thy |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1992 University of Cambridge |
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Ordered Pairs and the Cartesian product type |
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The unit type |
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The type definition admits the following unused axiom: |
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Abs_Unit_inverse "f: Unit ==> Rep_Unit(Abs_Unit(f)) = f" |
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*) |
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115
0ec63df3ae04
HOL/fun.ML: renamed Fun.ML to avoid problems with MLs "fun" keyword
lcp
parents:
112
diff
changeset
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Prod = Fun + |
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types |
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('a,'b) "*" (infixr 20) |
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unit |
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arities |
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"*" :: (term,term)term |
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unit :: term |
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consts |
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Pair_Rep :: "['a,'b] => ['a,'b] => bool" |
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Prod :: "('a => 'b => bool)set" |
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Rep_Prod :: "'a * 'b => ('a => 'b => bool)" |
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Abs_Prod :: "('a => 'b => bool) => 'a * 'b" |
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fst :: "'a * 'b => 'a" |
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snd :: "'a * 'b => 'b" |
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split :: "[['a,'b]=>'c, 'a * 'b] => 'c" |
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prod_fun :: "['a=>'b, 'c=>'d, 'a*'c] => 'b*'d" |
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Pair :: "['a,'b] => 'a * 'b" |
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"@Tuple" :: "args => 'a*'b" ("(1<_>)") |
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Sigma :: "['a set, 'a => 'b set] => ('a*'b)set" |
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Unit :: "bool set" |
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Rep_Unit :: "unit => bool" |
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Abs_Unit :: "bool => unit" |
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Unity :: "unit" ("<>") |
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translations |
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"<x,y,z>" == "<x,<y,z>>" |
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"<x,y>" == "Pair(x,y)" |
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"<x>" => "x" |
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rules |
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Pair_Rep_def "Pair_Rep == (%a b. %x y. x=a & y=b)" |
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Prod_def "Prod == {f. ? a b. f = Pair_Rep(a,b)}" |
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(*faking a type definition...*) |
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Rep_Prod "Rep_Prod(p): Prod" |
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Rep_Prod_inverse "Abs_Prod(Rep_Prod(p)) = p" |
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Abs_Prod_inverse "f: Prod ==> Rep_Prod(Abs_Prod(f)) = f" |
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(*defining the abstract constants*) |
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Pair_def "Pair(a,b) == Abs_Prod(Pair_Rep(a,b))" |
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fst_def "fst(p) == @a. ? b. p = <a,b>" |
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snd_def "snd(p) == @b. ? a. p = <a,b>" |
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split_def "split(c,p) == c(fst(p),snd(p))" |
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prod_fun_def "prod_fun(f,g) == split(%x y.<f(x), g(y)>)" |
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Sigma_def "Sigma(A,B) == UN x:A. UN y:B(x). {<x,y>}" |
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Unit_def "Unit == {p. p=True}" |
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(*faking a type definition...*) |
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Rep_Unit "Rep_Unit(u): Unit" |
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Rep_Unit_inverse "Abs_Unit(Rep_Unit(u)) = u" |
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(*defining the abstract constants*) |
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Unity_def "Unity == Abs_Unit(True)" |
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end |