src/ZF/Resid/Reduction.thy
author clasohm
Tue Feb 06 12:27:17 1996 +0100 (1996-02-06)
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
child 11319 8b84ee2cc79c
permissions -rw-r--r--
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(*  Title:      Reduction.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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Reduction = Terms+
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consts
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  Sred1, Sred,  Spar_red1,Spar_red    :: i
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  "-1->","--->","=1=>",   "===>"      :: [i,i]=>o (infixl 50)
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translations
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  "a -1-> b" == "<a,b>:Sred1"
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  "a ---> b" == "<a,b>:Sred"
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  "a =1=> b" == "<a,b>:Spar_red1"
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  "a ===> b" == "<a,b>:Spar_red"
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inductive
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  domains       "Sred1" <= "lambda*lambda"
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  intrs
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    beta        "[|m:lambda; n:lambda|] ==> Apl(Fun(m),n) -1-> n/m"
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    rfun        "[|m -1-> n|] ==> Fun(m) -1-> Fun(n)"
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    apl_l       "[|m2:lambda; m1 -1-> n1|] ==>   
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                                  Apl(m1,m2) -1-> Apl(n1,m2)"
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    apl_r       "[|m1:lambda; m2 -1-> n2|] ==>   
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                                  Apl(m1,m2) -1-> Apl(m1,n2)"
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  type_intrs    "red_typechecks"
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inductive
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  domains       "Sred" <= "lambda*lambda"
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  intrs
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    one_step    "[|m-1->n|] ==> m--->n"
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    refl        "m:lambda==>m --->m"
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    trans       "[|m--->n; n--->p|]==>m--->p"
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  type_intrs    "[Sred1.dom_subset RS subsetD]@red_typechecks"
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inductive
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  domains       "Spar_red1" <= "lambda*lambda"
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  intrs
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    beta        "[|m =1=> m';   
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                 n =1=> n'|] ==> Apl(Fun(m),n) =1=> n'/m'"
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    rvar        "n:nat==> Var(n) =1=> Var(n)"
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    rfun        "[|m =1=> m'|]==> Fun(m) =1=> Fun(m')"
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    rapl        "[|m =1=> m';   
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                 n =1=> n'|] ==> Apl(m,n) =1=> Apl(m',n')"
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  type_intrs    "red_typechecks"
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  inductive
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  domains       "Spar_red" <= "lambda*lambda"
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  intrs
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    one_step    "[|m =1=> n|] ==> m ===> n"
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    trans       "[|m===>n; n===>p|]==>m===>p"
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  type_intrs    "[Spar_red1.dom_subset RS subsetD]@red_typechecks"
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end
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