| author | wenzelm |
| Wed, 12 Dec 2001 20:37:31 +0100 | |
| changeset 12484 | 7ad150f5fc10 |
| parent 243 | c22b85994e17 |
| permissions | -rw-r--r-- |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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(* Title: HOLCF/cont.thy |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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Results about continuity and monotonicity |
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*) |
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Cont = Fun3 + |
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(* |
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Now we change the default class! Form now on all untyped typevariables are |
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of default class pcpo |
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*) |
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default pcpo |
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consts |
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monofun :: "('a::po => 'b::po) => bool" (* monotonicity *)
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contlub :: "('a => 'b) => bool" (* first cont. def *)
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contX :: "('a => 'b) => bool" (* secnd cont. def *)
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rules |
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monofun "monofun(f) == ! x y. x << y --> f(x) << f(y)" |
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contlub "contlub(f) == ! Y. is_chain(Y) --> \ |
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\ f(lub(range(Y))) = lub(range(% i.f(Y(i))))" |
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contX "contX(f) == ! Y. is_chain(Y) --> \ |
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\ range(% i.f(Y(i))) <<| f(lub(range(Y)))" |
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(* ------------------------------------------------------------------------ *) |
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(* the main purpose of cont.thy is to show: *) |
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(* monofun(f) & contlub(f) <==> contX(f) *) |
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(* ------------------------------------------------------------------------ *) |
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end |