710 lines
27 KiB
Idris
710 lines
27 KiB
Idris
module Quox.Reduce
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import Quox.No
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import Quox.Syntax
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import Quox.Definition
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import Quox.Typing.Context
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import Quox.Typing.Error
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import Data.SnocVect
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import Data.Maybe
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import Data.List
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%default total
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public export
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0 RedexTest : TermLike -> Type
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RedexTest tm = {d, n : Nat} -> Definitions -> tm d n -> Bool
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public export
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interface Whnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm
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where
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whnf : {d, n : Nat} -> (defs : Definitions) -> (ctx : WhnfContext d n) ->
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tm d n -> Either Error (Subset (tm d n) (No . isRedex defs))
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public export %inline
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whnf0 : {d, n : Nat} -> {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
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(defs : Definitions) -> WhnfContext d n -> tm d n ->
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Either Error (tm d n)
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whnf0 defs ctx t = fst <$> whnf defs ctx t
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public export
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0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex =>
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Definitions -> Pred (tm d n)
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IsRedex defs = So . isRedex defs
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NotRedex defs = No . isRedex defs
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public export
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0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
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Whnf tm isRedex => (d, n : Nat) -> (defs : Definitions) -> Type
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NonRedex tm d n defs = Subset (tm d n) (NotRedex defs)
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public export %inline
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nred : {0 isRedex : RedexTest tm} -> (0 _ : Whnf tm isRedex) =>
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(t : tm d n) -> (0 nr : NotRedex defs t) =>
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NonRedex tm d n defs
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nred t = Element t nr
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public export %inline
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isLamHead : Elim {} -> Bool
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isLamHead (Lam {} :# Pi {}) = True
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isLamHead (Coe {}) = True
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isLamHead _ = False
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public export %inline
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isDLamHead : Elim {} -> Bool
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isDLamHead (DLam {} :# Eq {}) = True
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isDLamHead (Coe {}) = True
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isDLamHead _ = False
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public export %inline
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isPairHead : Elim {} -> Bool
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isPairHead (Pair {} :# Sig {}) = True
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isPairHead (Coe {}) = True
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isPairHead _ = False
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public export %inline
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isTagHead : Elim {} -> Bool
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isTagHead (Tag t :# Enum _) = True
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isTagHead (Coe {}) = True
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isTagHead _ = False
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public export %inline
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isNatHead : Elim {} -> Bool
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isNatHead (Zero :# Nat) = True
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isNatHead (Succ n :# Nat) = True
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isNatHead (Coe {}) = True
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isNatHead _ = False
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public export %inline
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isBoxHead : Elim {} -> Bool
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isBoxHead (Box {} :# BOX {}) = True
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isBoxHead (Coe {}) = True
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isBoxHead _ = False
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public export %inline
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isE : Term {} -> Bool
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isE (E _) = True
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isE _ = False
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public export %inline
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isAnn : Elim {} -> Bool
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isAnn (_ :# _) = True
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isAnn _ = False
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||| true if a term is syntactically a type.
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public export %inline
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isTyCon : Term {} -> Bool
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isTyCon (TYPE {}) = True
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isTyCon (Pi {}) = True
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isTyCon (Lam {}) = False
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isTyCon (Sig {}) = True
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isTyCon (Pair {}) = False
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isTyCon (Enum {}) = True
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isTyCon (Tag {}) = False
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isTyCon (Eq {}) = True
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isTyCon (DLam {}) = False
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isTyCon Nat = True
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isTyCon Zero = False
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isTyCon (Succ {}) = False
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isTyCon (BOX {}) = True
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isTyCon (Box {}) = False
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isTyCon (E {}) = False
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isTyCon (CloT {}) = False
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isTyCon (DCloT {}) = False
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||| true if a term is syntactically a type, or a neutral.
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public export %inline
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isTyConE : Term {} -> Bool
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isTyConE s = isTyCon s || isE s
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||| true if a term is syntactically a type.
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public export %inline
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isAnnTyCon : Elim {} -> Bool
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isAnnTyCon (ty :# TYPE _) = isTyCon ty
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isAnnTyCon _ = False
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public export %inline
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isK : Dim d -> Bool
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isK (K _) = True
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isK _ = False
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mutual
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public export
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isRedexE : RedexTest Elim
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isRedexE defs (F x) {d, n} =
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isJust $ lookupElim x defs {d, n}
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isRedexE _ (B _) = False
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isRedexE defs (f :@ _) =
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isRedexE defs f || isLamHead f
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isRedexE defs (CasePair {pair, _}) =
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isRedexE defs pair || isPairHead pair
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isRedexE defs (CaseEnum {tag, _}) =
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isRedexE defs tag || isTagHead tag
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isRedexE defs (CaseNat {nat, _}) =
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isRedexE defs nat || isNatHead nat
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isRedexE defs (CaseBox {box, _}) =
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isRedexE defs box || isBoxHead box
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isRedexE defs (f :% p) =
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isRedexE defs f || isDLamHead f || isK p
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isRedexE defs (t :# a) =
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isE t || isRedexT defs t || isRedexT defs a
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isRedexE defs (Coe {val, _}) =
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isRedexT defs val || not (isE val)
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isRedexE defs (Comp {ty, r, _}) =
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isRedexT defs ty || isK r
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isRedexE defs (TypeCase {ty, ret, _}) =
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isRedexE defs ty || isRedexT defs ret || isAnnTyCon ty
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isRedexE _ (CloE {}) = True
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isRedexE _ (DCloE {}) = True
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public export
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isRedexT : RedexTest Term
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isRedexT _ (CloT {}) = True
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isRedexT _ (DCloT {}) = True
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isRedexT defs (E e) = isAnn e || isRedexE defs e
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isRedexT _ _ = False
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public export
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tycaseRhs : (k : TyConKind) -> TypeCaseArms d n ->
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Maybe (ScopeTermN (arity k) d n)
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tycaseRhs k arms = lookupPrecise k arms
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public export
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tycaseRhsDef : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
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ScopeTermN (arity k) d n
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tycaseRhsDef def k arms = fromMaybe (SN def) $ tycaseRhs k arms
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public export
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tycaseRhs0 : (k : TyConKind) -> TypeCaseArms d n ->
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(0 eq : arity k = 0) => Maybe (Term d n)
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tycaseRhs0 k arms {eq} with (tycaseRhs k arms) | (arity k)
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tycaseRhs0 k arms {eq = Refl} | res | 0 = map (.term) res
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public export
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tycaseRhsDef0 : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
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(0 eq : arity k = 0) => Term d n
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tycaseRhsDef0 def k arms = fromMaybe def $ tycaseRhs0 k arms
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private
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weakDS : (by : Nat) -> DScopeTerm d n -> DScopeTerm d (by + n)
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weakDS by (S names (Y body)) = S names $ Y $ weakT by body
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weakDS by (S names (N body)) = S names $ N $ weakT by body
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private
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dweakS : (by : Nat) -> ScopeTerm d n -> ScopeTerm (by + d) n
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dweakS by (S names (Y body)) = S names $ Y $ dweakT by body
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dweakS by (S names (N body)) = S names $ N $ dweakT by body
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private
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coeScoped : {s : Nat} -> DScopeTerm d n -> Dim d -> Dim d ->
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ScopeTermN s d n -> ScopeTermN s d n
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coeScoped ty p q (S names (Y body)) =
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S names $ Y $ E $ Coe (weakDS s ty) p q body
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coeScoped ty p q (S names (N body)) =
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S names $ N $ E $ Coe ty p q body
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mutual
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parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
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||| performs the minimum work required to recompute the type of an elim.
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|||
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||| ⚠ **assumes the elim is already typechecked.** ⚠
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export covering
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computeElimType : (e : Elim d n) -> (0 ne : No (isRedexE defs e)) =>
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Either Error (Term d n)
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computeElimType (F x) = do
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let Just def = lookup x defs | Nothing => Left $ NotInScope x
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pure $ def.type
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computeElimType (B i) = pure $ ctx.tctx !! i
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computeElimType (f :@ s) {ne} = do
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-- can't use `expectPi` (or `expectEq` below) without making this
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-- mutual block from hell even worse lol
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Pi {arg, res, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
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| t => Left $ ExpectedPi ctx.names t
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pure $ sub1 res (s :# arg)
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computeElimType (CasePair {pair, ret, _}) = pure $ sub1 ret pair
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computeElimType (CaseEnum {tag, ret, _}) = pure $ sub1 ret tag
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computeElimType (CaseNat {nat, ret, _}) = pure $ sub1 ret nat
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computeElimType (CaseBox {box, ret, _}) = pure $ sub1 ret box
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computeElimType (f :% p) {ne} = do
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Eq {ty, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
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| t => Left $ ExpectedEq ctx.names t
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pure $ dsub1 ty p
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computeElimType (Coe {ty, q, _}) = pure $ dsub1 ty q
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computeElimType (Comp {ty, _}) = pure ty
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computeElimType (TypeCase {ret, _}) = pure ret
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computeElimType (_ :# ty) = pure ty
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parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
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||| for π.(x : A) → B, returns (A, B);
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||| for an elim returns a pair of type-cases that will reduce to that;
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||| for other intro forms error
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private covering
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tycasePi : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
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Either Error (Term (S d) n, ScopeTerm (S d) n)
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tycasePi (Pi {arg, res, _}) = pure (arg, res)
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tycasePi (E e) {tnf} = do
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ty <- computeElimType defs ctx e @{noOr2 tnf}
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let arg = E $ typeCase1 e ty KPi [< "Arg", "Ret"] (BVT 1)
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res' = typeCase1 e (Arr Zero arg ty) KPi [< "Arg", "Ret"] (BVT 0)
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res = SY [< "Arg"] $ E $ weakE 1 res' :@ BVT 0
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pure (arg, res)
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tycasePi t = Left $ ExpectedPi ctx.names t
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||| for (x : A) × B, returns (A, B);
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||| for an elim returns a pair of type-cases that will reduce to that;
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||| for other intro forms error
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private covering
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tycaseSig : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
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Either Error (Term (S d) n, ScopeTerm (S d) n)
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tycaseSig (Sig {fst, snd, _}) = pure (fst, snd)
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tycaseSig (E e) {tnf} = do
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ty <- computeElimType defs ctx e @{noOr2 tnf}
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let fst = E $ typeCase1 e ty KSig [< "Fst", "Snd"] (BVT 1)
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snd' = typeCase1 e (Arr Zero fst ty) KSig [< "Fst", "Snd"] (BVT 0)
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snd = SY [< "Fst"] $ E $ weakE 1 snd' :@ BVT 0
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pure (fst, snd)
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tycaseSig t = Left $ ExpectedSig ctx.names t
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||| for [π. A], returns A;
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||| for an elim returns a type-case that will reduce to that;
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||| for other intro forms error
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private covering
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tycaseBOX : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
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Either Error (Term (S d) n)
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tycaseBOX (BOX _ a) = pure a
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tycaseBOX (E e) {tnf} = do
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ty <- computeElimType defs ctx e @{noOr2 tnf}
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pure $ E $ typeCase1 e ty KBOX [< "Ty"] (BVT 0)
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tycaseBOX t = Left $ ExpectedBOX ctx.names t
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||| for Eq [i ⇒ A] l r, returns (A‹0/i›, A‹1/i›, A, l, r);
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||| for an elim returns five type-cases that will reduce to that;
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||| for other intro forms error
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private covering
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tycaseEq : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
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Either Error (Term (S d) n, Term (S d) n, DScopeTerm (S d) n,
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Term (S d) n, Term (S d) n)
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tycaseEq (Eq {ty, l, r}) = pure (ty.zero, ty.one, ty, l, r)
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tycaseEq (E e) {tnf} = do
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ty <- computeElimType defs ctx e @{noOr2 tnf}
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let names = [< "A0", "A1", "A", "L", "R"]
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a0 = E $ typeCase1 e ty KEq names (BVT 4)
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a1 = E $ typeCase1 e ty KEq names (BVT 3)
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a' = typeCase1 e (Eq0 ty a0 a1) KEq names (BVT 2)
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a = SY [< "i"] $ E $ dweakE 1 a' :% BV 0
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l = E $ typeCase1 e a0 KEq names (BVT 1)
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r = E $ typeCase1 e a1 KEq names (BVT 0)
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pure (a0, a1, a, l, r)
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tycaseEq t = Left $ ExpectedEq ctx.names t
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parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
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||| reduce a function application `Coe ty p q val :@ s`
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private covering
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piCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val, s : Term d n) ->
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Either Error (Subset (Elim d n) (No . isRedexE defs))
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piCoe sty@(S i ty) p q val s = do
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-- (coe [i ⇒ π.(x : A) → B] @p @q t) s ⇝
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-- coe [i ⇒ B[𝒔‹i›/x] @p @q ((t ∷ (π.(x : A) → B)‹p/i›) 𝒔‹p›)
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-- where 𝒔‹j› ≔ coe [i ⇒ A] @q @j s
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--
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-- type-case is used to expose A,B if the type is neutral
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let ctx1 = extendDimN i ctx
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Element ty tynf <- whnf defs ctx1 ty.term
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(arg, res) <- tycasePi defs ctx1 ty
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let s0 = Coe (SY i arg) q p s
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body = E $ (val :# (ty // one p)) :@ E s0
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s1 = Coe (SY i (arg // (BV 0 ::: shift 2))) (weakD 1 q) (BV 0)
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(s // shift 1)
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whnf defs ctx $ Coe (SY i $ sub1 res s1) p q body
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||| reduce a pair elimination `CasePair pi (Coe ty p q val) ret body`
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private covering
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sigCoe : (qty : Qty) ->
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(ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
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(ret : ScopeTerm d n) -> (body : ScopeTermN 2 d n) ->
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Either Error (Subset (Elim d n) (No . isRedexE defs))
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sigCoe qty sty@(S i ty) p q val ret body = do
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-- caseπ (coe [i ⇒ (x : A) × B] @p @q s) return z ⇒ C of { (a, b) ⇒ e }
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-- ⇝
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-- caseπ s ∷ ((x : A) × B)‹p/i› return z ⇒ C
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-- of { (a, b) ⇒
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-- e[(coe [i ⇒ A] @p @q a)/a,
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-- (coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i a)/x]] @p @q b)/b] }
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--
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-- type-case is used to expose A,B if the type is neutral
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let ctx1 = extendDimN i ctx
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Element ty tynf <- whnf defs ctx1 ty.term
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(tfst, tsnd) <- tycaseSig defs ctx1 ty
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let a' = Coe (SY i $ weakT 2 tfst) p q (BVT 1)
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tsnd' = tsnd.term //
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(Coe (SY i $ weakT 2 $ tfst // (BV 0 ::: shift 2))
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(weakD 1 p) (BV 0) (BVT 1) ::: shift 2)
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b' = Coe (SY i tsnd') p q (BVT 0)
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whnf defs ctx $ CasePair qty (val :# (ty // one p)) ret $
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SY body.names $ body.term // (a' ::: b' ::: shift 2)
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||| reduce a dimension application `Coe ty p q val :% r`
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private covering
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eqCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
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(r : Dim d) ->
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Either Error (Subset (Elim d n) (No . isRedexE defs))
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eqCoe sty@(S j ty) p q val r = do
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-- (coe [j ⇒ Eq [i ⇒ A] L R] @p @q eq) @r
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-- ⇝
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-- comp [j ⇒ A‹r/i›] @p @q (eq ∷ (Eq [i ⇒ A] L R)‹p/j›)
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-- { (r=0) j ⇒ L; (r=1) j ⇒ R }
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let ctx1 = extendDimN j ctx
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Element ty tynf <- whnf defs ctx1 ty.term
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(a0, a1, a, s, t) <- tycaseEq defs ctx1 ty
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let a' = SY j $ dsub1 a (weakD 1 r)
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val' = E $ (val :# (ty // one p)) :% r
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whnf defs ctx $ CompH a' p q val' r (SY j s) (SY j t)
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||| reduce a pair elimination `CaseBox pi (Coe ty p q val) ret body`
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private covering
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boxCoe : (qty : Qty) ->
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(ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
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(ret : ScopeTerm d n) -> (body : ScopeTerm d n) ->
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Either Error (Subset (Elim d n) (No . isRedexE defs))
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boxCoe qty sty@(S i ty) p q val ret body = do
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-- caseπ (coe [i ⇒ [ρ. A]] @p @q s) return z ⇒ C of { [a] ⇒ e }
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-- ⇝
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-- caseπ s ∷ [ρ. A]‹p/i› return z ⇒ C
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-- of { [a] ⇒ e[(coe [i ⇒ A] p q a)/a] }
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let ctx1 = extendDimN i ctx
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Element ty tynf <- whnf defs ctx1 ty.term
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ta <- tycaseBOX defs ctx1 ty
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let a' = Coe (SY i $ weakT 1 ta) p q $ BVT 0
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whnf defs ctx $ CaseBox qty (val :# (ty // one p)) ret $
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SY body.names $ body.term // (a' ::: shift 1)
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export covering
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Whnf Elim Reduce.isRedexE where
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whnf defs ctx (F x) with (lookupElim x defs) proof eq
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_ | Just y = whnf defs ctx y
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_ | Nothing = pure $ Element (F x) $ rewrite eq in Ah
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whnf _ _ (B i) = pure $ nred $ B i
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-- ((λ x ⇒ t) ∷ (π.x : A) → B) s ⇝ t[s∷A/x] ∷ B[s∷A/x]
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whnf defs ctx (f :@ s) = do
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Element f fnf <- whnf defs ctx f
|
||
case nchoose $ isLamHead f of
|
||
Left _ => case f of
|
||
Lam body :# Pi {arg, res, _} =>
|
||
let s = s :# arg in
|
||
whnf defs ctx $ sub1 body s :# sub1 res s
|
||
Coe ty p q val => piCoe defs ctx ty p q val s
|
||
Right nlh => pure $ Element (f :@ s) $ fnf `orNo` nlh
|
||
|
||
-- case (s, t) ∷ (x : A) × B return p ⇒ C of { (a, b) ⇒ u } ⇝
|
||
-- u[s∷A/a, t∷B[s∷A/x]] ∷ C[(s, t)∷((x : A) × B)/p]
|
||
whnf defs ctx (CasePair pi pair ret body) = do
|
||
Element pair pairnf <- whnf defs ctx pair
|
||
case nchoose $ isPairHead pair of
|
||
Left _ => case pair of
|
||
Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} =>
|
||
let fst = fst :# tfst
|
||
snd = snd :# sub1 tsnd fst
|
||
in
|
||
whnf defs ctx $ subN body [< fst, snd] :# sub1 ret pair
|
||
Coe ty p q val => do
|
||
sigCoe defs ctx pi ty p q val ret body
|
||
Right np =>
|
||
pure $ Element (CasePair pi pair ret body) $ pairnf `orNo` np
|
||
|
||
-- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝
|
||
-- u ∷ C['a∷{a,…}/p]
|
||
whnf defs ctx (CaseEnum pi tag ret arms) = do
|
||
Element tag tagnf <- whnf defs ctx tag
|
||
case nchoose $ isTagHead tag of
|
||
Left t => case tag of
|
||
Tag t :# Enum ts =>
|
||
let ty = sub1 ret tag in
|
||
case lookup t arms of
|
||
Just arm => whnf defs ctx $ arm :# ty
|
||
Nothing => Left $ MissingEnumArm t (keys arms)
|
||
Coe ty p q val =>
|
||
-- there is nowhere an equality can be hiding inside an Enum
|
||
whnf defs ctx $ CaseEnum pi (val :# dsub1 ty q) ret arms
|
||
Right nt =>
|
||
pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` nt
|
||
|
||
-- case zero ∷ ℕ return p ⇒ C of { zero ⇒ u; … } ⇝
|
||
-- u ∷ C[zero∷ℕ/p]
|
||
--
|
||
-- case succ n ∷ ℕ return p ⇒ C of { succ n', π.ih ⇒ u; … } ⇝
|
||
-- u[n∷ℕ/n', (case n ∷ ℕ ⋯)/ih] ∷ C[succ n ∷ ℕ/p]
|
||
whnf defs ctx (CaseNat pi piIH nat ret zer suc) = do
|
||
Element nat natnf <- whnf defs ctx nat
|
||
case nchoose $ isNatHead nat of
|
||
Left _ =>
|
||
let ty = sub1 ret nat in
|
||
case nat of
|
||
Zero :# Nat => whnf defs ctx (zer :# ty)
|
||
Succ n :# Nat =>
|
||
let nn = n :# Nat
|
||
tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc]
|
||
in
|
||
whnf defs ctx $ tm :# ty
|
||
Coe ty p q val =>
|
||
-- same deal as Enum
|
||
whnf defs ctx $ CaseNat pi piIH (val :# dsub1 ty q) ret zer suc
|
||
Right nn =>
|
||
pure $ Element (CaseNat pi piIH nat ret zer suc) $ natnf `orNo` nn
|
||
|
||
-- case [t] ∷ [π.A] return p ⇒ C of { [x] ⇒ u } ⇝
|
||
-- u[t∷A/x] ∷ C[[t] ∷ [π.A]/p]
|
||
whnf defs ctx (CaseBox pi box ret body) = do
|
||
Element box boxnf <- whnf defs ctx box
|
||
case nchoose $ isBoxHead box of
|
||
Left _ => case box of
|
||
Box val :# BOX q bty =>
|
||
let ty = sub1 ret box in
|
||
whnf defs ctx $ sub1 body (val :# bty) :# ty
|
||
Coe ty p q val =>
|
||
boxCoe defs ctx pi ty p q val ret body
|
||
Right nb =>
|
||
pure $ Element (CaseBox pi box ret body) $ boxnf `orNo` nb
|
||
|
||
-- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @0 ⇝ t ∷ A‹0/𝑗›
|
||
-- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @1 ⇝ u ∷ A‹1/𝑗›
|
||
-- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗›
|
||
-- (if 𝑘 is a variable)
|
||
whnf defs ctx (f :% p) = do
|
||
Element f fnf <- whnf defs ctx f
|
||
case nchoose $ isDLamHead f of
|
||
Left _ => case f of
|
||
DLam body :# Eq {ty = ty, l, r, _} =>
|
||
let body = endsOr l r (dsub1 body p) p in
|
||
whnf defs ctx $ body :# dsub1 ty p
|
||
Coe ty p' q' val =>
|
||
eqCoe defs ctx ty p' q' val p
|
||
Right ndlh => case p of
|
||
K e => do
|
||
Eq {l, r, ty, _} <- whnf0 defs ctx =<< computeElimType defs ctx f
|
||
| ty => Left $ ExpectedEq ctx.names ty
|
||
whnf defs ctx $ ends (l :# ty.zero) (r :# ty.one) e
|
||
B _ => pure $ Element (f :% p) $ fnf `orNo` ndlh `orNo` Ah
|
||
|
||
-- e ∷ A ⇝ e
|
||
whnf defs ctx (s :# a) = do
|
||
Element s snf <- whnf defs ctx s
|
||
case nchoose $ isE s of
|
||
Left _ => let E e = s in pure $ Element e $ noOr2 snf
|
||
Right ne => do
|
||
Element a anf <- whnf defs ctx a
|
||
pure $ Element (s :# a) $ ne `orNo` snf `orNo` anf
|
||
|
||
whnf defs ctx (Coe (S _ (N ty)) _ _ val) =
|
||
whnf defs ctx $ val :# ty
|
||
whnf defs ctx (Coe (S [< i] ty) p q val) = do
|
||
Element ty tynf <- whnf defs (extendDim i ctx) ty.term
|
||
Element val valnf <- whnf defs ctx val
|
||
pushCoe defs ctx i ty p q val
|
||
|
||
whnf defs ctx (Comp ty p q val r zero one) =
|
||
-- comp [A] @p @p s { ⋯ } ⇝ s ∷ A
|
||
if p == q then whnf defs ctx $ val :# ty else
|
||
case nchoose (isK r) of
|
||
-- comp [A] @p @q s { (0=0) j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
|
||
-- comp [A] @p @q s { (1=1) j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
|
||
Left y => case r of
|
||
K Zero => whnf defs ctx $ dsub1 zero q :# ty
|
||
K One => whnf defs ctx $ dsub1 one q :# ty
|
||
Right nk => do
|
||
Element ty tynf <- whnf defs ctx ty
|
||
pure $ Element (Comp ty p q val r zero one) $ tynf `orNo` nk
|
||
-- [todo] anything other than just the boundaries??
|
||
|
||
whnf defs ctx (TypeCase ty ret arms def) = do
|
||
Element ty tynf <- whnf defs ctx ty
|
||
Element ret retnf <- whnf defs ctx ret
|
||
case nchoose $ isAnnTyCon ty of
|
||
Left y => let ty :# TYPE u = ty in
|
||
reduceTypeCase defs ctx ty u ret arms def
|
||
Right nt => pure $ Element (TypeCase ty ret arms def) $
|
||
tynf `orNo` retnf `orNo` nt
|
||
|
||
whnf defs ctx (CloE el th) = whnf defs ctx $ pushSubstsWith' id th el
|
||
whnf defs ctx (DCloE el th) = whnf defs ctx $ pushSubstsWith' th id el
|
||
|
||
export covering
|
||
Whnf Term Reduce.isRedexT where
|
||
whnf _ _ t@(TYPE {}) = pure $ nred t
|
||
whnf _ _ t@(Pi {}) = pure $ nred t
|
||
whnf _ _ t@(Lam {}) = pure $ nred t
|
||
whnf _ _ t@(Sig {}) = pure $ nred t
|
||
whnf _ _ t@(Pair {}) = pure $ nred t
|
||
whnf _ _ t@(Enum {}) = pure $ nred t
|
||
whnf _ _ t@(Tag {}) = pure $ nred t
|
||
whnf _ _ t@(Eq {}) = pure $ nred t
|
||
whnf _ _ t@(DLam {}) = pure $ nred t
|
||
whnf _ _ Nat = pure $ nred Nat
|
||
whnf _ _ Zero = pure $ nred Zero
|
||
whnf _ _ t@(Succ {}) = pure $ nred t
|
||
whnf _ _ t@(BOX {}) = pure $ nred t
|
||
whnf _ _ t@(Box {}) = pure $ nred t
|
||
|
||
-- s ∷ A ⇝ s (in term context)
|
||
whnf defs ctx (E e) = do
|
||
Element e enf <- whnf defs ctx e
|
||
case nchoose $ isAnn e of
|
||
Left _ => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf
|
||
Right na => pure $ Element (E e) $ na `orNo` enf
|
||
|
||
whnf defs ctx (CloT tm th) = whnf defs ctx $ pushSubstsWith' id th tm
|
||
whnf defs ctx (DCloT tm th) = whnf defs ctx $ pushSubstsWith' th id tm
|
||
|
||
||| reduce a type-case applied to a type constructor
|
||
private covering
|
||
reduceTypeCase : {d, n : Nat} -> (defs : Definitions) -> WhnfContext d n ->
|
||
(ty : Term d n) -> (u : Universe) -> (ret : Term d n) ->
|
||
(arms : TypeCaseArms d n) -> (def : Term d n) ->
|
||
(0 _ : So (isTyCon ty)) =>
|
||
Either Error (Subset (Elim d n) (No . isRedexE defs))
|
||
reduceTypeCase defs ctx ty u ret arms def = case ty of
|
||
-- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
|
||
TYPE _ =>
|
||
whnf defs ctx $ tycaseRhsDef0 def KTYPE arms :# ret
|
||
|
||
-- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
|
||
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
|
||
Pi _ arg res =>
|
||
let arg = arg :# TYPE u
|
||
res = Lam res :# Arr Zero (TYPE u) (TYPE u)
|
||
in
|
||
whnf defs ctx $ subN (tycaseRhsDef def KPi arms) [< arg, res] :# ret
|
||
|
||
-- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
|
||
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
|
||
Sig fst snd =>
|
||
let fst = fst :# TYPE u
|
||
snd = Lam snd :# Arr Zero (TYPE u) (TYPE u)
|
||
in
|
||
whnf defs ctx $ subN (tycaseRhsDef def KSig arms) [< fst, snd] :# ret
|
||
|
||
-- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q
|
||
Enum _ =>
|
||
whnf defs ctx $ tycaseRhsDef0 def KEnum arms :# ret
|
||
|
||
-- (type-case Eq [i ⇒ A] L R ∷ ★ᵢ return Q
|
||
-- of { Eq a₀ a₁ a l r ⇒ s; ⋯ }) ⇝
|
||
-- s[(A‹0/i› ∷ ★ᵢ)/a₀, (A‹1/i› ∷ ★ᵢ)/a₁,
|
||
-- ((δ i ⇒ A) ∷ Eq [★ᵢ] A‹0/i› A‹1/i›)/a,
|
||
-- (L ∷ A‹0/i›)/l, (R ∷ A‹1/i›)/r] ∷ Q
|
||
Eq a l r =>
|
||
let a0 = a.zero; a1 = a.one in
|
||
whnf defs ctx $
|
||
subN (tycaseRhsDef def KEq arms)
|
||
[< a0 :# TYPE u, a1 :# TYPE u,
|
||
DLam a :# Eq0 (TYPE u) a0 a1, l :# a0, r :# a1]
|
||
:# ret
|
||
|
||
-- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q
|
||
Nat =>
|
||
whnf defs ctx $ tycaseRhsDef0 def KNat arms :# ret
|
||
|
||
-- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
|
||
BOX _ s =>
|
||
whnf defs ctx $ sub1 (tycaseRhsDef def KBOX arms) (s :# TYPE u) :# ret
|
||
|
||
||| pushes a coercion inside a whnf-ed term
|
||
private covering
|
||
pushCoe : {n, d : Nat} -> (defs : Definitions) -> WhnfContext d n ->
|
||
BaseName ->
|
||
(ty : Term (S d) n) -> (0 tynf : No (isRedexT defs ty)) =>
|
||
Dim d -> Dim d ->
|
||
(s : Term d n) -> (0 snf : No (isRedexT defs s)) =>
|
||
Either Error (NonRedex Elim d n defs)
|
||
pushCoe defs ctx i ty p q s =
|
||
if p == q then whnf defs ctx $ s :# (ty // one q) else
|
||
case s of
|
||
-- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
|
||
TYPE {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
Pi {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
Sig {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
Enum {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
Eq {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
Nat => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
BOX {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
|
||
|
||
-- just η expand it. then whnf for (:@) will handle it later
|
||
-- this is how @xtt does it
|
||
Lam body => do
|
||
let body' = Coe (SY [< i] ty) p q (Lam body)
|
||
term' = Lam (SY [< "y"] $ E $ weakE 1 body' :@ BVT 0)
|
||
type' = ty // one q
|
||
whnf defs ctx $ term' :# type'
|
||
|
||
{-
|
||
-- maybe:
|
||
-- (coe [i ⇒ π.(x : A) → B] @p @q (λ x ⇒ s)) ⇝
|
||
-- (λ x ⇒ coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @q @i x)/x]] @p @q s)
|
||
-- ∷ (π.(x: A‹q/i›) → B‹q/i›)
|
||
Lam body => do
|
||
let Pi {qty, arg, res} = ty
|
||
| _ => Left $ ?err
|
||
let arg' = SY [< "j"] $ weakT 1 $ arg // (BV 0 ::: shift 2)
|
||
res' = SY [< i] $ res.term //
|
||
(Coe arg' (weakD 1 q) (BV 0) (BVT 0) ::: shift 1)
|
||
body = SY body.names $ E $ Coe res' p q body.term
|
||
pure $ Element (Lam body :# Pi qty (arg // one q) (res // one q)) Ah
|
||
-}
|
||
|
||
-- (coe [i ⇒ (x : A) × B] @p @q (s, t)) ⇝
|
||
-- (coe [i ⇒ A] @p @q s,
|
||
-- coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i s)/x]] @p @q t)
|
||
-- ∷ (x : A‹q/i›) × B‹q/i›
|
||
--
|
||
-- can't use η here because... it doesn't exist
|
||
Pair fst snd => do
|
||
let Sig {fst = tfst, snd = tsnd} = ty
|
||
| _ => Left $ ExpectedSig (extendDim i ctx.names) ty
|
||
let fst' = E $ Coe (SY [< i] tfst) p q fst
|
||
tfst' = SY [< "j"] $ tfst `CanDSubst.(//)` (BV 0 ::: shift 2)
|
||
tsnd' = SY [< i] $ sub1 tsnd $
|
||
Coe tfst' (weakD 1 p) (BV 0) $ dweakT 1 fst
|
||
snd' = E $ Coe tsnd' p q snd
|
||
pure $
|
||
Element (Pair fst' snd' :# Sig (tfst // one q) (tsnd // one q)) Ah
|
||
|
||
-- η expand like λ
|
||
DLam body => do
|
||
let body' = Coe (SY [< i] ty) p q (DLam body)
|
||
term' = DLam (SY [< "j"] $ E $ dweakE 1 body' :% BV 0)
|
||
type' = ty // one q
|
||
whnf defs ctx $ term' :# type'
|
||
|
||
-- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯})
|
||
Tag tag => do
|
||
let Enum ts = ty
|
||
| _ => Left $ ExpectedEnum (extendDim i ctx.names) ty
|
||
pure $ Element (Tag tag :# Enum ts) Ah
|
||
|
||
-- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ)
|
||
Zero => pure $ Element (Zero :# Nat) Ah
|
||
Succ t => pure $ Element (Succ t :# Nat) Ah
|
||
|
||
-- (coe [i ⇒ [π.A]] @p @q [s]) ⇝
|
||
-- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›]
|
||
Box val => do
|
||
let BOX {qty, ty = a} = ty
|
||
| _ => Left $ ExpectedBOX (extendDim i ctx.names) ty
|
||
let a = SY [< i] a
|
||
pure $ Element (Box (E $ Coe a p q s) :# BOX qty (dsub1 a q)) Ah
|
||
|
||
E e => pure $ Element (Coe (SY [< i] ty) p q (E e)) (snf `orNo` Ah)
|
||
where
|
||
unwrapTYPE : Term (S d) n -> Either Error Universe
|
||
unwrapTYPE (TYPE u) = pure u
|
||
unwrapTYPE ty = Left $ ExpectedTYPE (extendDim i ctx.names) ty
|