27 lines
1.6 KiB
OCaml
27 lines
1.6 KiB
OCaml
(****************************************************************************)
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(* *)
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(* OCaml *)
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(* *)
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(* INRIA Rocquencourt *)
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(* *)
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(* Copyright 2007 Institut National de Recherche en Informatique et *)
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(* en Automatique. All rights reserved. This file is distributed under *)
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(* the terms of the GNU Library General Public License, with the special *)
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(* exception on linking described in LICENSE at the top of the OCaml *)
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(* source tree. *)
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(* *)
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(****************************************************************************)
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let id = << fun x -> x >>
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(* Imported and traduced from CCT *)
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let zero = << fun s -> fun z -> z >>
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let succ = << fun n -> fun s -> fun z -> s n >>
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let one = << $succ$ $zero$ >>
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let iota = << fun x -> z >>
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let rho = << fun m -> fun r -> (s m (m r $iota$ r)) >>
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let rec_nat =
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<< fun n -> fun s -> fun z -> n $rho$ $iota$ $rho$ >>
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let plus = << fun n -> fun m -> $rec_nat$ n (fun n -> fun p -> $succ$ p) m >>
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let times = << fun n -> fun m -> $rec_nat$ n (fun n -> fun p -> $plus$ m p) $zero$ >>
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let fact = << fun n -> $rec_nat$ n (fun n -> fun p -> $times$ ($succ$ n) p) $one$ >>
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