(* 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