quox/lib/Quox/Typing/Context.idr

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module Quox.Typing.Context
import Quox.Syntax
import Quox.Context
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import Quox.Pretty
import public Data.Singleton
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%default total
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public export
QContext : Type -> Nat -> Type
QContext = Context'
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public export
TContext : Type -> Nat -> Nat -> Type
TContext q d = Context (Term q d)
public export
QOutput : Type -> Nat -> Type
QOutput = Context'
public export
DimAssign : Nat -> Type
DimAssign = Context' DimConst
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public export
record TyContext q d n where
constructor MkTyContext
{auto dimLen : Singleton d}
{auto termLen : Singleton n}
dctx : DimEq d
dnames : NContext d
tctx : TContext q d n
tnames : NContext n
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qtys : QContext q n -- only used for printing
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%name TyContext ctx
public export
record EqContext q n where
constructor MkEqContext
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{dimLen : Nat}
{auto termLen : Singleton n}
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dassign : DimAssign dimLen -- only used for printing
dnames : NContext dimLen -- only used for printing
tctx : TContext q 0 n
tnames : NContext n
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qtys : QContext q n -- only used for printing
%name EqContext ctx
namespace TContext
export %inline
pushD : TContext q d n -> TContext q (S d) n
pushD tel = map (// shift 1) tel
export %inline
zeroFor : IsQty q => Context tm n -> QOutput q n
zeroFor ctx = zero <$ ctx
private
extendLen : Telescope a from to -> Singleton from -> Singleton to
extendLen [<] x = x
extendLen (tel :< _) x = [|S $ extendLen tel x|]
namespace TyContext
public export %inline
empty : TyContext q 0 0
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empty =
MkTyContext {dctx = new, dnames = [<], tctx = [<], tnames = [<], qtys = [<]}
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public export %inline
null : TyContext q d n -> Bool
null ctx = null ctx.dnames && null ctx.tnames
export %inline
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extendTyN : Telescope (\n => (q, BaseName, Term q d n)) from to ->
TyContext q d from -> TyContext q d to
extendTyN xss (MkTyContext {termLen, dctx, dnames, tctx, tnames, qtys}) =
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let (qs, xs, ss) = unzip3 xss in
MkTyContext {
dctx, dnames,
termLen = extendLen xss termLen,
tctx = tctx . ss,
tnames = tnames . xs,
qtys = qtys . qs
}
export %inline
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extendTy : q -> BaseName -> Term q d n -> TyContext q d n ->
TyContext q d (S n)
extendTy q x s = extendTyN [< (q, x, s)]
export %inline
extendDim : BaseName -> TyContext q d n -> TyContext q (S d) n
extendDim x (MkTyContext {dimLen, dctx, dnames, tctx, tnames, qtys}) =
MkTyContext {
dctx = dctx :<? Nothing,
dnames = dnames :< x,
dimLen = [|S dimLen|],
tctx = pushD tctx,
tnames, qtys
}
export %inline
eqDim : Dim d -> Dim d -> TyContext q d n -> TyContext q d n
eqDim p q = {dctx $= set p q, dimLen $= id, termLen $= id}
export
injectT : TyContext q d n -> Term q 0 0 -> Term q d n
injectT (MkTyContext {dimLen = Val d, termLen = Val n, _}) tm =
tm // shift0 d // shift0 n
export
injectE : TyContext q d n -> Elim q 0 0 -> Elim q d n
injectE (MkTyContext {dimLen = Val d, termLen = Val n, _}) el =
el // shift0 d // shift0 n
namespace QOutput
parameters {auto _ : IsQty q}
export %inline
(+) : QOutput q n -> QOutput q n -> QOutput q n
(+) = zipWith (+)
export %inline
(*) : q -> QOutput q n -> QOutput q n
(*) pi = map (pi *)
export %inline
zeroFor : TyContext q _ n -> QOutput q n
zeroFor ctx = zeroFor ctx.tctx
export
makeDAssign : DSubst d 0 -> DimAssign d
makeDAssign (Shift SZ) = [<]
makeDAssign (K e ::: th) = makeDAssign th :< e
export
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makeEqContext' : {d : Nat} -> TyContext q d n -> DSubst d 0 -> EqContext q n
makeEqContext' ctx th = MkEqContext {
termLen = ctx.termLen,
dassign = makeDAssign th,
dnames = ctx.dnames,
tctx = map (// th) ctx.tctx,
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tnames = ctx.tnames,
qtys = ctx.qtys
}
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export
makeEqContext : TyContext q d n -> DSubst d 0 -> EqContext q n
makeEqContext ctx@(MkTyContext {dnames, _}) th =
let (d' ** Refl) = lengthPrf0 dnames in makeEqContext' ctx th
namespace EqContext
public export %inline
empty : EqContext q 0
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empty = MkEqContext {
dassign = [<], dnames = [<], tctx = [<], tnames = [<], qtys = [<]
}
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public export %inline
null : EqContext q n -> Bool
null ctx = null ctx.dnames && null ctx.tnames
export %inline
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extendTyN : Telescope (\n => (q, BaseName, Term q 0 n)) from to ->
EqContext q from -> EqContext q to
extendTyN xss (MkEqContext {termLen, dassign, dnames, tctx, tnames, qtys}) =
let (qs, xs, ss) = unzip3 xss in
MkEqContext {
termLen = extendLen xss termLen,
tctx = tctx . ss,
tnames = tnames . xs,
qtys = qtys . qs,
dassign, dnames
}
export %inline
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extendTy : q -> BaseName -> Term q 0 n -> EqContext q n -> EqContext q (S n)
extendTy q x s = extendTyN [< (q, x, s)]
export %inline
extendDim : BaseName -> DimConst -> EqContext q n -> EqContext q n
extendDim x e (MkEqContext {dassign, dnames, tctx, tnames, qtys}) =
MkEqContext {dassign = dassign :< e, dnames = dnames :< x,
tctx, tnames, qtys}
export
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toTyContext : (e : EqContext q n) -> TyContext q e.dimLen n
toTyContext (MkEqContext {dimLen, dassign, dnames, tctx, tnames, qtys}) =
MkTyContext {
dctx = fromGround dassign,
tctx = map (// shift0 dimLen) tctx,
dnames, tnames, qtys
}
export
injectT : EqContext q n -> Term q 0 0 -> Term q 0 n
injectT (MkEqContext {termLen = Val n, _}) tm = tm // shift0 n
export
injectE : EqContext q n -> Elim q 0 0 -> Elim q 0 n
injectE (MkEqContext {termLen = Val n, _}) el = el // shift0 n
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private
data CtxBinder a = MkCtxBinder BaseName a
PrettyHL a => PrettyHL (CtxBinder a) where
prettyM (MkCtxBinder x t) = pure $
sep [hsep [!(pretty0M $ TV x), colonD], !(pretty0M t)]
parameters {auto _ : (Eq q, PrettyHL q, IsQty q)} (unicode : Bool)
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private
pipeD : Doc HL
pipeD = hl Syntax "|"
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export covering
prettyTContext : QContext q n -> NContext n -> TContext q d n -> Doc HL
prettyTContext qs ns ctx = separate comma $ toList $ go qs ns ctx where
go : QContext q m -> NContext m -> TContext q d m -> SnocList (Doc HL)
go [<] [<] [<] = [<]
go (qs :< q) (xs :< x) (ctx :< t) =
let bind = MkWithQty q $ MkCtxBinder x t in
go qs xs ctx :< runPretty unicode (pretty0M bind)
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export covering
prettyTyContext : TyContext q d n -> Doc HL
prettyTyContext (MkTyContext dctx dnames tctx tnames qtys) =
case dctx of
C [<] => prettyTContext qtys tnames tctx
_ => sep [prettyDimEq dnames dctx <++> pipeD,
prettyTContext qtys tnames tctx]
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export covering
prettyEqContext : EqContext q n -> Doc HL
prettyEqContext (MkEqContext dassign dnames tctx tnames qtys) =
case dassign of
[<] => prettyTContext qtys tnames tctx
_ => sep [prettyDimEq dnames (fromGround dassign) <++> pipeD,
prettyTContext qtys tnames tctx]