quox/lib/Quox/Syntax/Dim.idr

139 lines
3.1 KiB
Idris

module Quox.Syntax.Dim
import Quox.Loc
import Quox.Name
import Quox.Var
import Quox.Syntax.Subst
import Quox.Pretty
import Quox.Context
import Decidable.Equality
import Control.Function
import Derive.Prelude
%default total
%language ElabReflection
public export
data DimConst = Zero | One
%name DimConst e
%runElab derive "DimConst" [Eq, Ord, Show]
||| `ends l r e` returns `l` if `e` is `Zero`, or `r` if it is `One`.
public export
ends : Lazy a -> Lazy a -> DimConst -> a
ends l r Zero = l
ends l r One = r
export Uninhabited (Zero = One) where uninhabited _ impossible
export Uninhabited (One = Zero) where uninhabited _ impossible
public export
DecEq DimConst where
decEq Zero Zero = Yes Refl
decEq Zero One = No absurd
decEq One Zero = No absurd
decEq One One = Yes Refl
public export
data Dim : Nat -> Type where
K : DimConst -> Loc -> Dim d
B : Var d -> Loc -> Dim d
%name Dim.Dim p, q
%runElab deriveIndexed "Dim" [Eq, Ord, Show]
||| `endsOr l r x p` returns `ends l r ε` if `p` is a constant ε, and
||| `x` otherwise.
public export
endsOr : Lazy a -> Lazy a -> Lazy a -> Dim n -> a
endsOr l r x (K e _) = ends l r e
endsOr l r x (B _ _) = x
export
Located (Dim d) where
(K _ loc).loc = loc
(B _ loc).loc = loc
export
Relocatable (Dim d) where
setLoc loc (K e _) = K e loc
setLoc loc (B i _) = B i loc
export
prettyDimConst : {opts : _} -> DimConst -> Eff Pretty (Doc opts)
prettyDimConst = hl Dim . text . ends "0" "1"
export
prettyDim : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
prettyDim names (K e _) = prettyDimConst e
prettyDim names (B i _) = prettyDBind $ names !!! i
public export %inline
toConst : Dim 0 -> DimConst
toConst (K e _) = e
public export
DSubst : Nat -> Nat -> Type
DSubst = Subst Dim
public export FromVar Dim where fromVarLoc = B
export
CanShift Dim where
K e loc // _ = K e loc
B i loc // by = B (i // by) loc
export
CanSubstSelf Dim where
K e loc // _ = K e loc
B i loc // th = getLoc th i loc
export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
export Uninhabited (K e loc1 = B i loc2) where uninhabited _ impossible
public export
data Eqv : Dim d1 -> Dim d2 -> Type where
EK : K e _ `Eqv` K e _
EB : i `Eqv` j -> B i _ `Eqv` B j _
export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
export
injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
injectiveB (EB e) = e
export
injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
injectiveK EK = Refl
public export
decEqv : Dec2 Dim.Eqv
decEqv (K e _) (K f _) = case decEq e f of
Yes Refl => Yes EK
No n => No $ n . injectiveK
decEqv (B i _) (B j _) = case decEqv i j of
Yes y => Yes $ EB y
No n => No $ \(EB y) => n y
decEqv (B _ _) (K _ _) = No absurd
decEqv (K _ _) (B _ _) = No absurd
||| abbreviation for a bound variable like `BV 4` instead of
||| `B (VS (VS (VS (VS VZ))))`
public export %inline
BV : (i : Nat) -> (0 _ : LT i d) => (loc : Loc) -> Dim d
BV i loc = B (V i) loc
export
weakD : (by : Nat) -> Dim d -> Dim (by + d)
weakD by p = p // shift by