751 lines
29 KiB
Idris
751 lines
29 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.Displace
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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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import Control.Eff
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%default total
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public export
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Whnf : List (Type -> Type)
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Whnf = [NameGen, Except Error]
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export
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runWhnfWith : NameSuf -> Eff Whnf a -> (Either Error a, NameSuf)
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runWhnfWith suf act = extract $ runStateAt GEN suf $ runExcept act
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export
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runWhnf : Eff Whnf a -> Either Error a
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runWhnf = fst . runWhnfWith 0
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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 CanWhnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm
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where
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whnf : {d, n : Nat} -> (defs : Definitions) ->
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(ctx : WhnfContext d n) ->
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tm d n -> Eff Whnf (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} -> CanWhnf tm isRedex =>
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(defs : Definitions) -> WhnfContext d n -> tm d n -> Eff Whnf (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} -> CanWhnf 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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CanWhnf 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 _ : CanWhnf tm isRedex) =>
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(t : tm d n) -> (0 nr : NotRedex defs t) => 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 (Ann (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 (Ann (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 (Ann (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 (Ann (Tag {}) (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 (Ann (Zero {}) (Nat {}) _) = True
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isNatHead (Ann (Succ {}) (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 (Ann (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 (Ann {}) = 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 (Ann 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 (App {fun, _}) =
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isRedexE defs fun || isLamHead fun
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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 (DApp {fun, arg, _}) =
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isRedexE defs fun || isDLamHead fun || isK arg
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isRedexE defs (Ann {tm, ty, _}) =
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isE tm || isRedexT defs tm || isRedexT defs ty
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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 -> Loc ->
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ScopeTermN s d n -> ScopeTermN s d n
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coeScoped ty p q loc (S names (Y body)) =
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S names $ Y $ E $ Coe (weakDS s ty) p q body loc
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coeScoped ty p q loc (S names (N body)) =
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S names $ N $ E $ Coe ty p q body loc
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export covering
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CanWhnf Term Reduce.isRedexT
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export covering
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CanWhnf Elim Reduce.isRedexE
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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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Eff Whnf (Term d n)
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computeElimType (F {x, u, loc}) = do
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let Just def = lookup x defs | Nothing => throw $ NotInScope loc x
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pure $ displace u def.type
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computeElimType (B {i, _}) = pure $ ctx.tctx !! i
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computeElimType (App {fun = f, arg = s, loc}) {ne} = do
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Pi {arg, res, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
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| t => throw $ ExpectedPi loc ctx.names t
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pure $ sub1 res $ Ann s arg loc
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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 (DApp {fun = f, arg = p, loc}) {ne} = do
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Eq {ty, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
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| t => throw $ ExpectedEq loc ctx.names t
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pure $ dsub1 ty p
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computeElimType (Ann {ty, _}) = pure ty
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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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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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Eff Whnf (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 loc = e.loc
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narg = mnb "Arg"; nret = mnb "Ret"
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arg = E $ typeCase1Y e ty KPi [< !narg, !nret] (BVT 1 loc) loc
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res' = typeCase1Y e (Arr Zero arg ty loc) KPi [< !narg, !nret]
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(BVT 0 loc) loc
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res = SY [< !narg] $ E $ App (weakE 1 res') (BVT 0 loc) loc
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pure (arg, res)
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tycasePi t = throw $ ExpectedPi t.loc 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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Eff Whnf (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 loc = e.loc
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nfst = mnb "Fst"; nsnd = mnb "Snd"
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fst = E $ typeCase1Y e ty KSig [< !nfst, !nsnd] (BVT 1 loc) loc
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snd' = typeCase1Y e (Arr Zero fst ty loc) KSig [< !nfst, !nsnd]
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(BVT 0 loc) loc
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snd = SY [< !nfst] $ E $ App (weakE 1 snd') (BVT 0 loc) loc
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pure (fst, snd)
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tycaseSig t = throw $ ExpectedSig t.loc 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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Eff Whnf (Term (S d) n)
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tycaseBOX (BOX {ty, _}) = pure ty
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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 $ typeCase1Y e ty KBOX [< !(mnb "Ty")] (BVT 0 e.loc) e.loc
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tycaseBOX t = throw $ ExpectedBOX t.loc 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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Eff Whnf (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 loc = e.loc
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names = traverse' (\x => mnb x) [< "A0", "A1", "A", "L", "R"]
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a0 = E $ typeCase1Y e ty KEq !names (BVT 4 loc) loc
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a1 = E $ typeCase1Y e ty KEq !names (BVT 3 loc) loc
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a' = typeCase1Y e (Eq0 ty a0 a1 loc) KEq !names (BVT 2 loc) loc
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a = SY [< !(mnb "i")] $ E $ DApp (dweakE 1 a') (B VZ loc) loc
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l = E $ typeCase1Y e a0 KEq !names (BVT 1 loc) loc
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r = E $ typeCase1Y e a1 KEq !names (BVT 0 loc) loc
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pure (a0, a1, a, l, r)
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tycaseEq t = throw $ ExpectedEq t.loc ctx.names t
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-- new block because the functions below might pass a different ctx
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-- into the ones above
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parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
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||| reduce a function application `App (Coe ty p q val) s loc`
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private covering
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piCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
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(val, s : Term d n) -> Loc ->
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Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
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piCoe sty@(S [< i] ty) p q val s loc = 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 = extendDim 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 = CoeT i arg q p s s.loc
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body = E $ App (Ann val (ty // one p) val.loc) (E s0) loc
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s1 = CoeT i (arg // (BV 0 i.loc ::: shift 2)) (weakD 1 q) (BV 0 i.loc)
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(s // shift 1) s.loc
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whnf defs ctx $ CoeT i (sub1 res s1) p q body loc
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||| reduce a pair elimination `CasePair pi (Coe ty p q val) ret body loc`
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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) -> Loc ->
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Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
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sigCoe qty sty@(S [< i] ty) p q val ret body loc = 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 = extendDim 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 [< x, y] = body.names
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a' = CoeT i (weakT 2 tfst) p q (BVT 1 noLoc) x.loc
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tsnd' = tsnd.term //
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(CoeT i (weakT 2 $ tfst // (B VZ noLoc ::: shift 2))
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(weakD 1 p) (B VZ noLoc) (BVT 1 noLoc) y.loc ::: shift 2)
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b' = CoeT i tsnd' p q (BVT 0 noLoc) y.loc
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whnf defs ctx $ CasePair qty (Ann val (ty // one p) val.loc) ret
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(ST body.names $ body.term // (a' ::: b' ::: shift 2)) loc
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||| reduce a dimension application `DApp (Coe ty p q val) r loc`
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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) -> Loc ->
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Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
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eqCoe sty@(S [< j] ty) p q val r loc = 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; 1 j ⇒ R }
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let ctx1 = extendDim 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' = dsub1 a (weakD 1 r)
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val' = E $ DApp (Ann val (ty // one p) val.loc) r loc
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whnf defs ctx $ CompH j a' p q val' r j s j t loc
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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) ->
|
||
(ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
|
||
(ret : ScopeTerm d n) -> (body : ScopeTerm d n) -> Loc ->
|
||
Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
|
||
boxCoe qty sty@(S [< i] ty) p q val ret body loc = do
|
||
-- caseπ (coe [i ⇒ [ρ. A]] @p @q s) return z ⇒ C of { [a] ⇒ e }
|
||
-- ⇝
|
||
-- caseπ s ∷ [ρ. A]‹p/i› return z ⇒ C
|
||
-- of { [a] ⇒ e[(coe [i ⇒ A] p q a)/a] }
|
||
let ctx1 = extendDim i ctx
|
||
Element ty tynf <- whnf defs ctx1 ty.term
|
||
ta <- tycaseBOX defs ctx1 ty
|
||
let a' = CoeT i (weakT 1 ta) p q (BVT 0 noLoc) body.name.loc
|
||
whnf defs ctx $ CaseBox qty (Ann val (ty // one p) val.loc) ret
|
||
(ST body.names $ body.term // (a' ::: shift 1)) loc
|
||
|
||
|
||
||| 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)) => Loc ->
|
||
Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
|
||
reduceTypeCase defs ctx ty u ret arms def loc = case ty of
|
||
-- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
|
||
TYPE {} =>
|
||
whnf defs ctx $ Ann (tycaseRhsDef0 def KTYPE arms) ret loc
|
||
|
||
-- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
|
||
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
|
||
Pi {arg, res, loc = piLoc, _} =>
|
||
let arg' = Ann arg (TYPE u noLoc) arg.loc
|
||
res' = Ann (Lam res res.loc)
|
||
(Arr Zero arg (TYPE u noLoc) arg.loc) res.loc
|
||
in
|
||
whnf defs ctx $
|
||
Ann (subN (tycaseRhsDef def KPi arms) [< arg', res']) ret loc
|
||
|
||
-- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
|
||
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
|
||
Sig {fst, snd, loc = sigLoc, _} =>
|
||
let fst' = Ann fst (TYPE u noLoc) fst.loc
|
||
snd' = Ann (Lam snd snd.loc)
|
||
(Arr Zero fst (TYPE u noLoc) fst.loc) snd.loc
|
||
in
|
||
whnf defs ctx $
|
||
Ann (subN (tycaseRhsDef def KSig arms) [< fst', snd']) ret loc
|
||
|
||
-- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q
|
||
Enum {} =>
|
||
whnf defs ctx $ Ann (tycaseRhsDef0 def KEnum arms) ret loc
|
||
|
||
-- (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 {ty = a, l, r, loc = eqLoc, _} =>
|
||
let a0 = a.zero; a1 = a.one in
|
||
whnf defs ctx $ Ann
|
||
(subN (tycaseRhsDef def KEq arms)
|
||
[< Ann a0 (TYPE u noLoc) a.loc, Ann a1 (TYPE u noLoc) a.loc,
|
||
Ann (DLam a a.loc) (Eq0 (TYPE u noLoc) a0 a1 a.loc) a.loc,
|
||
Ann l a0 l.loc, Ann r a1 r.loc])
|
||
ret loc
|
||
|
||
-- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q
|
||
Nat {} =>
|
||
whnf defs ctx $ Ann (tycaseRhsDef0 def KNat arms) ret loc
|
||
|
||
-- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
|
||
BOX {ty = a, loc = boxLoc, _} =>
|
||
whnf defs ctx $ Ann
|
||
(sub1 (tycaseRhsDef def KBOX arms) (Ann a (TYPE u noLoc) a.loc))
|
||
ret loc
|
||
|
||
|
||
||| pushes a coercion inside a whnf-ed term
|
||
private covering
|
||
pushCoe : {d, n : Nat} -> (defs : Definitions) -> WhnfContext d n ->
|
||
BindName ->
|
||
(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)) => Loc ->
|
||
Eff Whnf (NonRedex Elim d n defs)
|
||
pushCoe defs ctx i ty p q s loc =
|
||
if p == q then whnf defs ctx $ Ann s (ty // one q) loc else
|
||
case s of
|
||
-- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
|
||
TYPE {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
Pi {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
Sig {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
Enum {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
Eq {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
Nat {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
BOX {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
|
||
|
||
-- just η expand it. then whnf for App will handle it later
|
||
-- this is how @xtt does it
|
||
--
|
||
-- (coe [i ⇒ A] @p @q (λ x ⇒ s)) ⇝
|
||
-- (λ y ⇒ (coe [i ⇒ A] @p @q (λ x ⇒ s)) y) ∷ A‹q/i› ⇝ ⋯
|
||
lam@(Lam {body, _}) => do
|
||
let lam' = CoeT i ty p q lam loc
|
||
term' = LamY !(fresh body.name)
|
||
(E $ App (weakE 1 lam') (BVT 0 noLoc) loc) loc
|
||
type' = ty // one q
|
||
whnf defs ctx $ Ann term' type' loc
|
||
|
||
-- (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, loc = pairLoc} => do
|
||
let Sig {fst = tfst, snd = tsnd, loc = sigLoc} = ty
|
||
| _ => throw $ ExpectedSig ty.loc (extendDim i ctx.names) ty
|
||
let fst' = E $ CoeT i tfst p q fst fst.loc
|
||
tfst' = tfst // (B VZ noLoc ::: shift 2)
|
||
tsnd' = sub1 tsnd $
|
||
CoeT !(fresh i) tfst' (weakD 1 p) (B VZ noLoc)
|
||
(dweakT 1 fst) fst.loc
|
||
snd' = E $ CoeT i tsnd' p q snd snd.loc
|
||
pure $
|
||
Element (Ann (Pair fst' snd' pairLoc)
|
||
(Sig (tfst // one q) (tsnd // one q) sigLoc) loc) Ah
|
||
|
||
-- η expand, like for Lam
|
||
--
|
||
-- (coe [i ⇒ A] @p @q (δ j ⇒ s)) ⇝
|
||
-- (δ k ⇒ (coe [i ⇒ A] @p @q (δ j ⇒ s)) @k) ∷ A‹q/i› ⇝ ⋯
|
||
dlam@(DLam {body, _}) => do
|
||
let dlam' = CoeT i ty p q dlam loc
|
||
term' = DLamY !(mnb "j")
|
||
(E $ DApp (dweakE 1 dlam') (B VZ noLoc) loc) loc
|
||
type' = ty // one q
|
||
whnf defs ctx $ Ann term' type' loc
|
||
|
||
-- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯})
|
||
Tag {tag, loc = tagLoc} => do
|
||
let Enum {cases, loc = enumLoc} = ty
|
||
| _ => throw $ ExpectedEnum ty.loc (extendDim i ctx.names) ty
|
||
pure $ Element (Ann (Tag tag tagLoc) (Enum cases enumLoc) loc) Ah
|
||
|
||
-- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ)
|
||
Zero {loc = zeroLoc} => do
|
||
pure $ Element (Ann (Zero zeroLoc) (Nat ty.loc) loc) Ah
|
||
Succ {p = pred, loc = succLoc} => do
|
||
pure $ Element (Ann (Succ pred succLoc) (Nat ty.loc) loc) Ah
|
||
|
||
-- (coe [i ⇒ [π.A]] @p @q [s]) ⇝
|
||
-- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›]
|
||
Box {val, loc = boxLoc} => do
|
||
let BOX {qty, ty = a, loc = tyLoc} = ty
|
||
| _ => throw $ ExpectedBOX ty.loc (extendDim i ctx.names) ty
|
||
pure $ Element
|
||
(Ann (Box (E $ CoeT i a p q val val.loc) boxLoc)
|
||
(BOX qty (a // one q) tyLoc) loc)
|
||
Ah
|
||
|
||
E e => pure $ Element (CoeT i ty p q (E e) e.loc) (snf `orNo` Ah)
|
||
where
|
||
unwrapTYPE : Term (S d) n -> Eff Whnf Universe
|
||
unwrapTYPE (TYPE {l, _}) = pure l
|
||
unwrapTYPE ty = throw $ ExpectedTYPE ty.loc (extendDim i ctx.names) ty
|
||
|
||
|
||
export covering
|
||
CanWhnf Elim Reduce.isRedexE where
|
||
whnf defs ctx (F x u loc) with (lookupElim x defs) proof eq
|
||
_ | Just y = whnf defs ctx $ setLoc loc $ displace u y
|
||
_ | Nothing = pure $ Element (F x u loc) $ rewrite eq in Ah
|
||
|
||
whnf _ _ (B i loc) = pure $ nred $ B i loc
|
||
|
||
-- ((λ x ⇒ t) ∷ (π.x : A) → B) s ⇝ t[s∷A/x] ∷ B[s∷A/x]
|
||
whnf defs ctx (App f s appLoc) = do
|
||
Element f fnf <- whnf defs ctx f
|
||
case nchoose $ isLamHead f of
|
||
Left _ => case f of
|
||
Ann (Lam {body, _}) (Pi {arg, res, _}) floc =>
|
||
let s = Ann s arg s.loc in
|
||
whnf defs ctx $ Ann (sub1 body s) (sub1 res s) appLoc
|
||
Coe ty p q val _ => piCoe defs ctx ty p q val s appLoc
|
||
Right nlh => pure $ Element (App f s appLoc) $ 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 caseLoc) = do
|
||
Element pair pairnf <- whnf defs ctx pair
|
||
case nchoose $ isPairHead pair of
|
||
Left _ => case pair of
|
||
Ann (Pair {fst, snd, _}) (Sig {fst = tfst, snd = tsnd, _}) pairLoc =>
|
||
let fst = Ann fst tfst fst.loc
|
||
snd = Ann snd (sub1 tsnd fst) snd.loc
|
||
in
|
||
whnf defs ctx $ Ann (subN body [< fst, snd]) (sub1 ret pair) caseLoc
|
||
Coe ty p q val _ => do
|
||
sigCoe defs ctx pi ty p q val ret body caseLoc
|
||
Right np =>
|
||
pure $ Element (CasePair pi pair ret body caseLoc) $ 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 caseLoc) = do
|
||
Element tag tagnf <- whnf defs ctx tag
|
||
case nchoose $ isTagHead tag of
|
||
Left _ => case tag of
|
||
Ann (Tag t _) (Enum ts _) _ =>
|
||
let ty = sub1 ret tag in
|
||
case lookup t arms of
|
||
Just arm => whnf defs ctx $ Ann arm ty arm.loc
|
||
Nothing => throw $ MissingEnumArm caseLoc t (keys arms)
|
||
Coe ty p q val _ =>
|
||
-- there is nowhere an equality can be hiding inside an enum type
|
||
whnf defs ctx $
|
||
CaseEnum pi (Ann val (dsub1 ty q) val.loc) ret arms caseLoc
|
||
Right nt =>
|
||
pure $ Element (CaseEnum pi tag ret arms caseLoc) $ 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 caseLoc) = do
|
||
Element nat natnf <- whnf defs ctx nat
|
||
case nchoose $ isNatHead nat of
|
||
Left _ =>
|
||
let ty = sub1 ret nat in
|
||
case nat of
|
||
Ann (Zero _) (Nat _) _ =>
|
||
whnf defs ctx $ Ann zer ty zer.loc
|
||
Ann (Succ n succLoc) (Nat natLoc) _ =>
|
||
let nn = Ann n (Nat natLoc) succLoc
|
||
tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc caseLoc]
|
||
in
|
||
whnf defs ctx $ Ann tm ty caseLoc
|
||
Coe ty p q val _ =>
|
||
-- same deal as Enum
|
||
whnf defs ctx $
|
||
CaseNat pi piIH (Ann val (dsub1 ty q) val.loc) ret zer suc caseLoc
|
||
Right nn => pure $
|
||
Element (CaseNat pi piIH nat ret zer suc caseLoc) $ 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 caseLoc) = do
|
||
Element box boxnf <- whnf defs ctx box
|
||
case nchoose $ isBoxHead box of
|
||
Left _ => case box of
|
||
Ann (Box val boxLoc) (BOX q bty tyLoc) _ =>
|
||
let ty = sub1 ret box in
|
||
whnf defs ctx $ Ann (sub1 body (Ann val bty val.loc)) ty caseLoc
|
||
Coe ty p q val _ =>
|
||
boxCoe defs ctx pi ty p q val ret body caseLoc
|
||
Right nb =>
|
||
pure $ Element (CaseBox pi box ret body caseLoc) $ boxnf `orNo` nb
|
||
|
||
-- e : Eq (𝑗 ⇒ A) t u ⊢ e @0 ⇝ t ∷ A‹0/𝑗›
|
||
-- e : Eq (𝑗 ⇒ A) t u ⊢ e @1 ⇝ u ∷ A‹1/𝑗›
|
||
--
|
||
-- ((δ 𝑖 ⇒ s) ∷ Eq (𝑗 ⇒ A) t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗›
|
||
whnf defs ctx (DApp f p appLoc) = do
|
||
Element f fnf <- whnf defs ctx f
|
||
case nchoose $ isDLamHead f of
|
||
Left _ => case f of
|
||
Ann (DLam {body, _}) (Eq {ty, l, r, _}) _ =>
|
||
whnf defs ctx $
|
||
Ann (endsOr (setLoc appLoc l) (setLoc appLoc r) (dsub1 body p) p)
|
||
(dsub1 ty p) appLoc
|
||
Coe ty p' q' val _ =>
|
||
eqCoe defs ctx ty p' q' val p appLoc
|
||
Right ndlh => case p of
|
||
K e _ => do
|
||
Eq {l, r, ty, _} <- whnf0 defs ctx =<< computeElimType defs ctx f
|
||
| ty => throw $ ExpectedEq ty.loc ctx.names ty
|
||
whnf defs ctx $
|
||
ends (Ann (setLoc appLoc l) ty.zero appLoc)
|
||
(Ann (setLoc appLoc r) ty.one appLoc) e
|
||
B {} => pure $ Element (DApp f p appLoc) $ fnf `orNo` ndlh `orNo` Ah
|
||
|
||
-- e ∷ A ⇝ e
|
||
whnf defs ctx (Ann s a annLoc) = 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 (Ann s a annLoc) $ ne `orNo` snf `orNo` anf
|
||
|
||
whnf defs ctx (Coe (S _ (N ty)) _ _ val coeLoc) =
|
||
whnf defs ctx $ Ann val ty coeLoc
|
||
whnf defs ctx (Coe (S [< i] ty) p q val coeLoc) = 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 coeLoc
|
||
|
||
whnf defs ctx (Comp ty p q val r zero one compLoc) =
|
||
-- comp [A] @p @p s { ⋯ } ⇝ s ∷ A
|
||
if p == q then whnf defs ctx $ Ann val ty compLoc 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 $ Ann (dsub1 zero q) ty compLoc
|
||
K One _ => whnf defs ctx $ Ann (dsub1 one q) ty compLoc
|
||
Right nk => do
|
||
Element ty tynf <- whnf defs ctx ty
|
||
pure $ Element (Comp ty p q val r zero one compLoc) $ tynf `orNo` nk
|
||
|
||
whnf defs ctx (TypeCase ty ret arms def tcLoc) = do
|
||
Element ty tynf <- whnf defs ctx ty
|
||
Element ret retnf <- whnf defs ctx ret
|
||
case nchoose $ isAnnTyCon ty of
|
||
Left y =>
|
||
let Ann ty (TYPE u _) _ = ty in
|
||
reduceTypeCase defs ctx ty u ret arms def tcLoc
|
||
Right nt => pure $
|
||
Element (TypeCase ty ret arms def tcLoc) (tynf `orNo` retnf `orNo` nt)
|
||
|
||
whnf defs ctx (CloE (Sub el th)) = whnf defs ctx $ pushSubstsWith' id th el
|
||
whnf defs ctx (DCloE (Sub el th)) = whnf defs ctx $ pushSubstsWith' th id el
|
||
|
||
export covering
|
||
CanWhnf 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 _ _ t@(Nat {}) = pure $ nred t
|
||
whnf _ _ t@(Zero {}) = pure $ nred t
|
||
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 Ann {tm, _} = e in pure $ Element tm $ noOr1 $ noOr2 enf
|
||
Right na => pure $ Element (E e) $ na `orNo` enf
|
||
|
||
whnf defs ctx (CloT (Sub tm th)) = whnf defs ctx $ pushSubstsWith' id th tm
|
||
whnf defs ctx (DCloT (Sub tm th)) = whnf defs ctx $ pushSubstsWith' th id tm
|