New unified treatment of sequent calculi by Sara Kalvala
combines the old LK and Modal with the new ILL (Int. Linear Logic)
(* Title: HOLCF/fix.thy
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
definitions for fixed point operator and admissibility
*)
Fix = Cfun3 +
consts
iterate :: "nat=>('a->'a)=>'a=>'a"
Ifix :: "('a->'a)=>'a"
fix :: "('a->'a)->'a"
adm :: "('a=>bool)=>bool"
admw :: "('a=>bool)=>bool"
chain_finite :: "'a=>bool"
flat :: "'a=>bool"
rules
iterate_def "iterate(n,F,c) == nat_rec(n,c,%n x.F[x])"
Ifix_def "Ifix(F) == lub(range(%i.iterate(i,F,UU)))"
fix_def "fix == (LAM f. Ifix(f))"
adm_def "adm(P) == !Y. is_chain(Y) --> \
\ (!i.P(Y(i))) --> P(lub(range(Y)))"
admw_def "admw(P)== (!F.((!n.P(iterate(n,F,UU)))-->\
\ P(lub(range(%i.iterate(i,F,UU))))))"
chain_finite_def "chain_finite(x::'a)==\
\ !Y. is_chain(Y::nat=>'a) --> (? n.max_in_chain(n,Y))"
flat_def "flat(x::'a) ==\
\ ! x y. x::'a << y --> (x = UU) | (x=y)"
end