-- | Church-encoded @nat@ and related functions.

{-# LANGUAGE OverloadedStrings #-}

module PlutusCore.StdLib.Data.ChurchNat
    ( churchNat
    , churchZero
    , churchSucc
    ) where

import PlutusCore.Core
import PlutusCore.MkPlc
import PlutusCore.Name
import PlutusCore.Quote

-- | Church-encoded @Nat@ as a PLC type.
--
-- > all (r :: *). r -> (r -> r) -> r
churchNat :: Type TyName uni ()
churchNat :: Type TyName uni ()
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-- | Church-encoded '0' as a PLC term.
--
-- > /\(r :: *) -> \(z : r) (f : r -> r) -> z
churchZero :: TermLike term TyName Name uni fun => term ()
churchZero :: term ()
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-- | Church-encoded 'succ' as a PLC term.
--
-- > \(n : nat) -> /\(r :: *) -> \(z : r) (f : r -> r) -> f (n {r} z f)
churchSucc :: TermLike term TyName Name uni fun => term ()
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