src/Cube/Cube.ML
author clasohm
Tue, 24 Oct 1995 14:45:35 +0100
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(*  Title:      Cube/Cube.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1990  University of Cambridge
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For Cube.thy.  The systems of the Lambda-cube that extend simple types
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*)
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open Cube;
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val simple = [s_b,strip_s,strip_b,app,lam_ss,pi_ss];
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val L2_thy =
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  Cube.thy
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  |> add_axioms
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   [("pi_bs",  "[| A:[]; !!x. x:A ==> B(x):* |] ==> Prod(A,B):*"),
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    ("lam_bs", "[| A:[]; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):* |] \
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     \  ==> Abs(A,f) : Prod(A,B)")]
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  |> add_thyname "L2";
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val lam_bs = get_axiom L2_thy "lam_bs";
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val pi_bs = get_axiom L2_thy "pi_bs";
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val L2 = simple @ [lam_bs,pi_bs];
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val Lomega_thy =
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  Cube.thy
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  |> add_axioms
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   [("pi_bb",  "[| A:[]; !!x. x:A ==> B(x):[] |] ==> Prod(A,B):[]"),
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    ("lam_bb", "[| A:[]; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):[] |] \
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     \  ==> Abs(A,f) : Prod(A,B)")]
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  |> add_thyname "Lomega";
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val lam_bb = get_axiom Lomega_thy "lam_bb";
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val pi_bb = get_axiom Lomega_thy "pi_bb";
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val Lomega = simple @ [lam_bb,pi_bb];
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val LOmega_thy = merge_theories(L2_thy,Lomega_thy);
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val LOmega = simple @ [lam_bs,pi_bs,lam_bb,pi_bb];
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val LP_thy =
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  Cube.thy
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  |> add_axioms
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   [("pi_sb",  "[| A:*; !!x. x:A ==> B(x):[] |] ==> Prod(A,B):[]"),
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    ("lam_sb", "[| A:*; !!x. x:A ==> f(x):B(x); !!x. x:A ==> B(x):[] |] \
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     \  ==> Abs(A,f) : Prod(A,B)")]
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  |> add_thyname "LP";
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val lam_sb = get_axiom LP_thy "lam_sb";
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val pi_sb = get_axiom LP_thy "pi_sb";
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val LP = simple @ [lam_sb,pi_sb];
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val LP2_thy = merge_theories(L2_thy,LP_thy);
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val LP2 = simple @ [lam_bs,pi_bs,lam_sb,pi_sb];
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val LPomega_thy = merge_theories(LP_thy,Lomega_thy);
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val LPomega = simple @ [lam_bb,pi_bb,lam_sb,pi_sb];
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val CC_thy = merge_theories(L2_thy,LPomega_thy);
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val CC = simple @ [lam_bs,pi_bs,lam_bb,pi_bb,lam_sb,pi_sb];