127 lines
2.6 KiB
Idris
127 lines
2.6 KiB
Idris
module Quox.Syntax.Qty.Three
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import Quox.Pretty
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import public Quox.Syntax.Qty
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import Derive.Prelude
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%default total
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%language ElabReflection
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public export
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data Three = Zero | One | Any
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%name Three pi, rh
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%runElab derive "Three" [Eq, Ord, Show]
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export
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PrettyHL Three where
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prettyM pi = hl Qty <$>
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case pi of
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Zero => pure "0"
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One => pure "1"
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Any => ifUnicode "ω" "#"
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public export
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DecEq Three where
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decEq Zero Zero = Yes Refl
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decEq Zero One = No $ \case _ impossible
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decEq Zero Any = No $ \case _ impossible
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decEq One Zero = No $ \case _ impossible
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decEq One One = Yes Refl
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decEq One Any = No $ \case _ impossible
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decEq Any Zero = No $ \case _ impossible
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decEq Any One = No $ \case _ impossible
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decEq Any Any = Yes Refl
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public export
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plus : Three -> Three -> Three
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plus Zero rh = rh
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plus pi Zero = pi
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plus _ _ = Any
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public export
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times : Three -> Three -> Three
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times Zero _ = Zero
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times _ Zero = Zero
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times One rh = rh
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times pi One = pi
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times Any Any = Any
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public export
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data Compat3 : Rel Three where
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CmpRefl : Compat3 rh rh
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CmpAny : Compat3 rh Any
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public export
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compat3 : Dec2 Compat3
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compat3 pi rh with (decEq pi rh) | (decEq rh Any)
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compat3 pi pi | Yes Refl | _ = Yes CmpRefl
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compat3 pi Any | No _ | Yes Refl = Yes CmpAny
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compat3 pi rh | No ne | No na =
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No $ \case CmpRefl => ne Refl; CmpAny => na Refl
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public export
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data IsSubj3 : Pred Three where
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SZero : IsSubj3 Zero
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SOne : IsSubj3 One
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public export
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isSubj3 : Dec1 IsSubj3
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isSubj3 Zero = Yes SZero
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isSubj3 One = Yes SOne
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isSubj3 Any = No $ \case _ impossible
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public export
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timesSubj3 : forall pi, rh. IsSubj3 pi -> IsSubj3 rh -> IsSubj3 (times pi rh)
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timesSubj3 SZero SZero = SZero
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timesSubj3 SZero SOne = SZero
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timesSubj3 SOne SZero = SZero
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timesSubj3 SOne SOne = SOne
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public export
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data IsGlobal3 : Pred Three where
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GZero : IsGlobal3 Zero
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GAny : IsGlobal3 Any
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public export
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isGlobal3 : Dec1 IsGlobal3
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isGlobal3 Zero = Yes GZero
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isGlobal3 One = No $ \case _ impossible
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isGlobal3 Any = Yes GAny
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public export
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IsQty Three where
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zero = Zero
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one = One
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(+) = plus
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(*) = times
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IsZero = Equal Zero
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isZero = decEq Zero
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zeroIsZero = Refl
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Compat = Compat3
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compat = compat3
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IsSubj = IsSubj3
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isSubj = isSubj3
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zeroIsSubj = \Refl => SZero
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oneIsSubj = SOne
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timesSubj = timesSubj3
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IsGlobal = IsGlobal3
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isGlobal = isGlobal3
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zeroIsGlobal = \Refl => GZero
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export Uninhabited (IsGlobal3 One) where uninhabited _ impossible
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export Uninhabited (IsSubj3 Any) where uninhabited _ impossible
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