quox/lib/Quox/Definition.idr

module Quox.Definition

import public Quox.No
import public Quox.Syntax
import public Data.SortedMap
import public Control.Monad.Reader
import Decidable.Decidable


public export
record AnyTerm q where
  constructor T
  get : forall d, n. Term q d n

public export
record Definition' q (isGlobal : Pred q) where
  constructor MkDef'
  qty  : q
  type : AnyTerm q
  term : Maybe $ AnyTerm q
  {auto 0 qtyGlobal : isGlobal qty}

public export
0 Definition : (q : Type) -> IsQty q => Type
Definition q = Definition' q IsGlobal

public export %inline
mkDef : IsQty q => (qty : q) -> (0 _ : IsGlobal qty) =>
        (type, term : forall d, n. Term q d n) -> Definition q
mkDef qty type term = MkDef' {qty, type = T type, term = Just (T term)}

public export %inline
mkAbstract : IsQty q => (qty : q) -> (0 _ : IsGlobal qty) =>
             (type : forall d, n. Term q d n) -> Definition q
mkAbstract qty type = MkDef' {qty, type = T type, term = Nothing}


public export %inline
(.get0) : AnyTerm q -> Term q 0 0
t.get0 = t.get

public export %inline
(.type0) : Definition' q _ -> Term q 0 0
g.type0 = g.type.get

public export %inline
(.term0) : Definition' q _ -> Maybe (Term q 0 0)
g.term0 = map (\t => t.get) g.term

public export %inline
(.qtyP) : forall q, isGlobal. Definition' q isGlobal -> Subset q isGlobal
g.qtyP = Element g.qty g.qtyGlobal


public export %inline
toElim : Definition' q _ -> Maybe $ Elim q d n
toElim def = pure $ (!def.term).get :# def.type.get


public export
0 IsZero : IsQty q => Pred $ Definition q
IsZero g = IsZero g.qty

public export %inline
isZero : (p : IsQty q) => Dec1 $ Definition.IsZero @{p}
isZero g = isZero g.qty


public export
0 Definitions' : (q : Type) -> Pred q -> Type
Definitions' q isGlobal = SortedMap Name $ Definition' q isGlobal

public export
0 Definitions : (q : Type) -> IsQty q => Type
Definitions q = Definitions' q IsGlobal


public export
0 HasDefs' : (q : Type) -> (q -> Type) -> (Type -> Type) -> Type
HasDefs' q isGlobal = MonadReader (Definitions' q isGlobal)

public export
0 HasDefs : (q : Type) -> IsQty q => (Type -> Type) -> Type
HasDefs q = HasDefs' q IsGlobal


public export %inline
lookupElim : forall isGlobal.
             Name -> Definitions' q isGlobal -> Maybe (Elim q d n)
lookupElim x defs = toElim !(lookup x defs)


parameters {0 isGlobal : _} (defs : Definitions' q isGlobal)
  namespace Term
    public export %inline
    isRedex : Term q d n -> Bool
    isRedex = isRedex $ \x => lookupElim x defs

    public export
    0 IsRedex, NotRedex : Pred $ Term q d n
    IsRedex  = So . isRedex
    NotRedex = No . isRedex

  namespace Elim
    public export %inline
    isRedex : Elim q d n -> Bool
    isRedex = isRedex $ \x => lookupElim x defs

    public export
    0 IsRedex, NotRedex : Pred $ Elim q d n
    IsRedex  = So . isRedex
    NotRedex = No . isRedex

public export
0 NonRedexElim, NonRedexTerm :
  (q : Type) -> (d, n : Nat) -> {isGlobal : Pred q} ->
  Definitions' q isGlobal -> Type
NonRedexElim q d n defs = Subset (Elim q d n) (NotRedex defs)
NonRedexTerm q d n defs = Subset (Term q d n) (NotRedex defs)

parameters {0 isGlobal : _} (defs : Definitions' q isGlobal)
  namespace Term
    export covering %inline
    whnfD : Term q d n -> NonRedexTerm q d n defs
    whnfD = whnf $ \x => lookupElim x defs

  namespace Elim
    export covering %inline
    whnfD : Elim q d n -> NonRedexElim q d n defs
    whnfD = whnf $ \x => lookupElim x defs