quox/lib/Quox/Syntax/Qty.idr

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||| quantities count how many times a bound variable is used [@nuttin; @qtt].
|||
||| i tried grtt [@grtt] for a bit but i think it was more complex than
||| it's worth in a language that has other stuff going on too
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module Quox.Syntax.Qty
import Quox.Pretty
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import Quox.Decidable
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import Quox.PrettyValExtra
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import Data.DPair
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import Derive.Prelude
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%default total
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%language ElabReflection
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||| the possibilities we care about are:
|||
||| - 0: a variable is used only at compile time, not run time
||| - 1: a variable is used exactly once at run time
||| - ω (or #): don't care. an ω variable *can* also be used 0/1 time
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public export
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data Qty = Zero | One | Any
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%runElab derive "Qty" [Eq, Ord, Show, PrettyVal]
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%name Qty.Qty pi, rh
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export
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prettyQty : {opts : _} -> Qty -> Eff Pretty (Doc opts)
prettyQty Zero = hl Qty $ text "0"
prettyQty One = hl Qty $ text "1"
prettyQty Any = hl Qty =<< ifUnicode (text "ω") (text "#")
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||| prints in a form that can be a suffix of "case"
public export
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prettySuffix : {opts : _} -> Qty -> Eff Pretty (Doc opts)
prettySuffix = prettyQty
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||| e.g. if in the expression `(s, t)`, the variable `x` is
||| used π times in `s` and ρ times in `t`, then it's used
||| (π + ρ) times in the whole expression
public export
(+) : Qty -> Qty -> Qty
Zero + rh = rh
pi + Zero = pi
_ + _ = Any
||| e.g. if a function `f` uses its argument π times,
||| and `f x` occurs in a σ context, then `x` is used `πσ` times overall
public export
(*) : Qty -> Qty -> Qty
Zero * _ = Zero
_ * Zero = Zero
One * rh = rh
pi * One = pi
Any * Any = Any
||| "π ≤ ρ"
|||
||| if a variable is bound with quantity ρ, then it can be used with a total
||| quantity π as long as π ≤ ρ. for example, an ω variable can be used any
||| number of times, so π ≤ ω for any π.
public export
compat : Qty -> Qty -> Bool
compat pi Any = True
compat pi rh = pi == rh
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||| "π ρ"
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|||
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||| returns a quantity τ with π ≤ τ and ρ ≤ τ.
||| if π = ρ, then it's that, otherwise it's ω.
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public export
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lub : Qty -> Qty -> Qty
lub p q = if p == q then p else Any
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||| to maintain subject reduction, only 0 or 1 can occur
||| for the subject of a typing judgment. see @qtt, §2.3 for more detail
public export
data SQty = SZero | SOne
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%runElab derive "SQty" [Eq, Ord, Show, PrettyVal]
%name Qty.SQty sg
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||| "σ ⨴ π"
|||
||| σ ⨴ π is 0 if either of σ or π are, otherwise it is σ.
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public export
subjMult : SQty -> Qty -> SQty
subjMult _ Zero = SZero
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subjMult sg _ = sg
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||| it doesn't make much sense for a top level declaration to have a
||| quantity of 1, so the only distinction is whether it is present
||| at runtime at all or not
public export
data GQty = GZero | GAny
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%runElab derive "GQty" [Eq, Ord, Show, PrettyVal]
%name GQty rh
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public export
toGlobal : Qty -> Maybe GQty
toGlobal Zero = Just GZero
toGlobal Any = Just GAny
toGlobal One = Nothing
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||| when checking a definition, a 0 definition is checked at 0,
||| but an ω definition is checked at 1 since ω isn't a subject quantity
public export %inline
globalToSubj : GQty -> SQty
globalToSubj GZero = SZero
globalToSubj GAny = SOne
public export
DecEq Qty where
decEq Zero Zero = Yes Refl
decEq Zero One = No $ \case _ impossible
decEq Zero Any = No $ \case _ impossible
decEq One Zero = No $ \case _ impossible
decEq One One = Yes Refl
decEq One Any = No $ \case _ impossible
decEq Any Zero = No $ \case _ impossible
decEq Any One = No $ \case _ impossible
decEq Any Any = Yes Refl
public export
DecEq SQty where
decEq SZero SZero = Yes Refl
decEq SZero SOne = No $ \case _ impossible
decEq SOne SZero = No $ \case _ impossible
decEq SOne SOne = Yes Refl
public export
DecEq GQty where
decEq GZero GZero = Yes Refl
decEq GZero GAny = No $ \case _ impossible
decEq GAny GZero = No $ \case _ impossible
decEq GAny GAny = Yes Refl
namespace SQty
public export %inline
(.qty) : SQty -> Qty
(SZero).qty = Zero
(SOne).qty = One
namespace GQty
public export %inline
(.qty) : GQty -> Qty
(GZero).qty = Zero
(GAny).qty = Any