src/ZF/Resid/Reduction.thy

New example by Ole Rasmussen

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

Reduction = Terms+

consts
  Sred1, Sred,  Spar_red1,Spar_red    :: "i"
  "-1->","--->","=1=>",   "===>"      :: "[i,i]=>o" (infixl 50)

translations
  "a -1-> b" == "<a,b>:Sred1"
  "a ---> b" == "<a,b>:Sred"
  "a =1=> b" == "<a,b>:Spar_red1"
  "a ===> b" == "<a,b>:Spar_red"
  
  
inductive
  domains       "Sred1" <= "lambda*lambda"
  intrs
    beta	"[|m:lambda; n:lambda|] ==> Apl(Fun(m),n) -1-> n/m"
    rfun  	"[|m -1-> n|] ==> Fun(m) -1-> Fun(n)"
    apl_l	"[|m2:lambda; m1 -1-> n1|] ==>   \
\		 	          Apl(m1,m2) -1-> Apl(n1,m2)"
    apl_r	"[|m1:lambda; m2 -1-> n2|] ==>   \
\		 	          Apl(m1,m2) -1-> Apl(m1,n2)"
  type_intrs	"red_typechecks"

inductive
  domains       "Sred" <= "lambda*lambda"
  intrs
    one_step	"[|m-1->n|] ==> m--->n"
    refl  	"m:lambda==>m --->m"
    trans	"[|m--->n; n--->p|]==>m--->p"
  type_intrs	"[Sred1.dom_subset RS subsetD]@red_typechecks"

inductive
  domains       "Spar_red1" <= "lambda*lambda"
  intrs
    beta	"[|m =1=> m';   \
\		 n =1=> n'|] ==> Apl(Fun(m),n) =1=> n'/m'"
    rvar	"n:nat==> Var(n) =1=> Var(n)"
    rfun	"[|m =1=> m'|]==> Fun(m) =1=> Fun(m')"
    rapl	"[|m =1=> m';   \
\		 n =1=> n'|] ==> Apl(m,n) =1=> Apl(m',n')"
  type_intrs	"red_typechecks"

  inductive
  domains       "Spar_red" <= "lambda*lambda"
  intrs
    one_step	"[|m =1=> n|] ==> m ===> n"
    trans	"[|m===>n; n===>p|]==>m===>p"
  type_intrs	"[Spar_red1.dom_subset RS subsetD]@red_typechecks"


end