src/ZF/Resid/Residuals.thy

tidied

(*  Title:      Residuals.thy
    ID:         $Id$
    Author:     Ole Rasmussen
    Copyright   1995  University of Cambridge
    Logic Image: ZF

*)

Residuals = Substitution+

consts
  Sres          :: i
  residuals     :: [i,i,i]=>i
  "|>"          :: [i,i]=>i     (infixl 70)
  
translations
  "residuals(u,v,w)"  == "<u,v,w>:Sres"

inductive
  domains       "Sres" <= "redexes*redexes*redexes"
  intrs
    Res_Var     "n:nat ==> residuals(Var(n),Var(n),Var(n))"
    Res_Fun     "[|residuals(u,v,w)|]==>   
                     residuals(Fun(u),Fun(v),Fun(w))"
    Res_App     "[|residuals(u1,v1,w1);   
                   residuals(u2,v2,w2); b:bool|]==>   
                 residuals(App(b,u1,u2),App(0,v1,v2),App(b,w1,w2))"
    Res_redex   "[|residuals(u1,v1,w1);   
                   residuals(u2,v2,w2); b:bool|]==>   
                 residuals(App(b,Fun(u1),u2),App(1,Fun(v1),v2),w2/w1)"
  type_intrs    "[subst_type]@[e-mail]@bool_typechecks"

rules
  res_func_def  "u |> v == THE w. residuals(u,v,w)"
end