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(* Title: Residuals.thy
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ID: $Id$
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Author: Ole Rasmussen
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Copyright 1995 University of Cambridge
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Logic Image: ZF
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*)
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Residuals = Substitution+
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consts
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Sres :: "i"
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residuals :: "[i,i,i]=>i"
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"|>" :: "[i,i]=>i" (infixl 70)
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translations
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"residuals(u,v,w)" == "<u,v,w>:Sres"
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inductive
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domains "Sres" <= "redexes*redexes*redexes"
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intrs
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Res_Var "n:nat ==> residuals(Var(n),Var(n),Var(n))"
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Res_Fun "[|residuals(u,v,w)|]==> \
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\ residuals(Fun(u),Fun(v),Fun(w))"
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Res_App "[|residuals(u1,v1,w1); \
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\ residuals(u2,v2,w2); b:bool|]==> \
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\ residuals(App(b,u1,u2),App(0,v1,v2),App(b,w1,w2))"
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Res_redex "[|residuals(u1,v1,w1); \
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\ residuals(u2,v2,w2); b:bool|]==> \
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\ residuals(App(b,Fun(u1),u2),App(1,Fun(v1),v2),w2/w1)"
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type_intrs "[subst_type]@nat_typechecks@redexes.intrs@bool_typechecks"
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rules
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res_func_def "u |> v == THE w.residuals(u,v,w)"
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end
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