-- | Implementation of the primitives relating to Cubical identity types.
module Agda.TypeChecking.Primitive.Cubical.Id
  ( -- * General elimination form
    primIdElim'
  -- * Introduction form
  , primConId'
  -- * Projection maps (primarily used internally)
  , primIdFace'
  , primIdPath'
  -- * Kan operations
  , doIdKanOp
  )
  where

import Control.Monad.Except

import Agda.Utils.Impossible (__IMPOSSIBLE__)
import Agda.Utils.Monad

import qualified Data.IntMap as IntMap
import Data.Traversable
import Data.Maybe

import Agda.TypeChecking.Monad.Builtin
import Agda.TypeChecking.Monad.Base
import Agda.TypeChecking.Monad.Env
import Agda.TypeChecking.Substitute (apply, sort, listS, applySubst)
import Agda.TypeChecking.Reduce (reduceB', reduce')
import Agda.TypeChecking.Names
  (runNamesT, runNames, cl, lam, ilam, open)

import Agda.Interaction.Options.Base (optCubical)

import Agda.Syntax.Common (Cubical(..), Arg(..), defaultArgInfo, hasQuantity0, defaultArg)

import Agda.TypeChecking.Primitive.Base
  ((-->), nPi', pPi', hPi', el, el', el's, (<@>), (<#>), (<..>), argN)

import Agda.Syntax.Internal
import Agda.TypeChecking.Monad.Debug (__IMPOSSIBLE_VERBOSE__)

import Agda.TypeChecking.Primitive.Cubical.Base

-- | Primitive elimination rule for the cubical identity types. Unlike
-- J, @idElim@ makes explicit the structure of Swan's identity types as
-- being pairs of a cofibration and a path. Moreover, it records that
-- the path is definitionally @refl@ under that cofibration.
primIdElim' :: TCM PrimitiveImpl
primIdElim' :: TCM PrimitiveImpl
primIdElim' = do
  -- The implementation here looks terrible but most of it is actually
  -- the type.
  Cubical -> String -> TCM ()
requireCubical Cubical
CErased String
""
  Type
t <- Names -> NamesT (TCMT IO) Type -> TCMT IO Type
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runNamesT [] (NamesT (TCMT IO) Type -> TCMT IO Type)
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$
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    -- For all cofibrations φ,
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      in String
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el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) (\ NamesT (TCMT IO) Term
y ->
      String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
nPi' String
"p" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primId NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
bA NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
x NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
p ->
      NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
c (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ NamesT (TCMT IO) Term
bC NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
p)

  -- Implementation starts here:
  Term
conid <- TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primConId
  Term
sin <- TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primSubIn
  Term
path <- TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primPath
  PrimitiveImpl -> TCM PrimitiveImpl
forall a. a -> TCMT IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (PrimitiveImpl -> TCM PrimitiveImpl)
-> PrimitiveImpl -> TCM PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ Type -> PrimFun -> PrimitiveImpl
PrimImpl Type
t (PrimFun -> PrimitiveImpl) -> PrimFun -> PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ QName
-> Arity
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
primFun QName
forall a. HasCallStack => a
__IMPOSSIBLE__ Arity
8 (([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
 -> PrimFun)
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
forall a b. (a -> b) -> a -> b
$ \case
    [Arg Term
a,Arg Term
c,Arg Term
bA,Arg Term
x,Arg Term
bC,Arg Term
f,Arg Term
y,Arg Term
p] -> do
      Blocked (Arg Term)
sp <- Arg Term -> ReduceM (Blocked (Arg Term))
forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
p
      Term -> Term -> Maybe (Arg Term, Arg Term)
cview <- ReduceM (Term -> Term -> Maybe (Arg Term, Arg Term))
forall (m :: * -> *).
HasBuiltins m =>
m (Term -> Term -> Maybe (Arg Term, Arg Term))
conidView'
      case Term -> Term -> Maybe (Arg Term, Arg Term)
cview (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
x) (Term -> Maybe (Arg Term, Arg Term))
-> Term -> Maybe (Arg Term, Arg Term)
forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
unArg (Arg Term -> Term) -> Arg Term -> Term
forall a b. (a -> b) -> a -> b
$ Blocked (Arg Term) -> Arg Term
forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
sp of
        -- Record that the right endpoint and the path definitionally
        -- agree with x φ holds. This is guaranteed internally by the
        -- typing rule for @conId@ but can't be recovered from
        -- @primIdPath@ and @primIdFace@ (see #2598)
        Just (Arg Term
phi, Arg Term
w) -> do
          let y' :: Term
y' = Term
sin Term -> [Arg Term] -> Term
forall t. Apply t => t -> [Arg Term] -> t
`apply` [Arg Term
a, Arg Term
bA, Arg Term
phi, Term -> Arg Term
forall e. e -> Arg e
argN (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
y)]
          let w' :: Term
w' = Term
sin Term -> [Arg Term] -> Term
forall t. Apply t => t -> [Arg Term] -> t
`apply` [Arg Term
a, Term -> Arg Term
forall e. e -> Arg e
argN (Term
path Term -> [Arg Term] -> Term
forall t. Apply t => t -> [Arg Term] -> t
`apply` [Arg Term
a, Arg Term
bA, Arg Term
x, Arg Term
y]), Arg Term
phi, Term -> Arg Term
forall e. e -> Arg e
argN (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
w)]
          Term -> ReduceM (Reduced MaybeReducedArgs Term)
forall a a'. a -> ReduceM (Reduced a' a)
redReturn (Term -> ReduceM (Reduced MaybeReducedArgs Term))
-> Term -> ReduceM (Reduced MaybeReducedArgs Term)
forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
f Term -> [Arg Term] -> Term
forall t. Apply t => t -> [Arg Term] -> t
`apply` [Arg Term
phi, Term -> Arg Term
forall e. e -> Arg e
defaultArg Term
y', Term -> Arg Term
forall e. e -> Arg e
defaultArg Term
w']
        Maybe (Arg Term, Arg Term)
_ -> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a. a -> ReduceM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Reduced MaybeReducedArgs Term
 -> ReduceM (Reduced MaybeReducedArgs Term))
-> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a b. (a -> b) -> a -> b
$ MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall no yes. no -> Reduced no yes
NoReduction (MaybeReducedArgs -> Reduced MaybeReducedArgs Term)
-> MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall a b. (a -> b) -> a -> b
$ (Arg Term -> MaybeReduced (Arg Term))
-> [Arg Term] -> MaybeReducedArgs
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> MaybeReduced (Arg Term)
forall a. a -> MaybeReduced a
notReduced [Arg Term
a,Arg Term
c,Arg Term
bA,Arg Term
x,Arg Term
bC,Arg Term
f,Arg Term
y] MaybeReducedArgs -> MaybeReducedArgs -> MaybeReducedArgs
forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sp]
    [Arg Term]
_ -> String -> ReduceM (Reduced MaybeReducedArgs Term)
forall (m :: * -> *) a.
(HasCallStack, MonadDebug m) =>
String -> m a
__IMPOSSIBLE_VERBOSE__ String
"implementation of primIdElim called with wrong arity"

-- | Introduction form for the cubical identity types.
primConId' :: TCM PrimitiveImpl
primConId' :: TCM PrimitiveImpl
primConId' = do
  Cubical -> String -> TCM ()
requireCubical Cubical
CErased String
""
  Type
t <- Names -> NamesT (TCMT IO) Type -> TCMT IO Type
forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] (NamesT (TCMT IO) Type -> TCMT IO Type)
-> NamesT (TCMT IO) Type -> TCMT IO Type
forall a b. (a -> b) -> a -> b
$
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"a" (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Functor m => m Term -> m Type
el (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevel) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
a ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"A" (Sort -> Type
sort (Sort -> Type) -> (Term -> Sort) -> Term -> Type
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort (Term -> Type) -> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
a) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
bA ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"x" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
x ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"y" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
y ->
    NamesT (TCMT IO) Type
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType -- Cofibration
    NamesT (TCMT IO) Type
-> NamesT (TCMT IO) Type -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primPath NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
bA NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
x NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y)
    NamesT (TCMT IO) Type
-> NamesT (TCMT IO) Type -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primId NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
bA NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
x NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y)

  -- Implementation note: conId, as the name implies, is a constructor.
  -- It's not represented as a constructor because users can't match on
  -- it (but we, internally, can: see createMissingConIdClause).

  PrimitiveImpl -> TCM PrimitiveImpl
forall a. a -> TCMT IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (PrimitiveImpl -> TCM PrimitiveImpl)
-> PrimitiveImpl -> TCM PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ Type -> PrimFun -> PrimitiveImpl
PrimImpl Type
t (PrimFun -> PrimitiveImpl) -> PrimFun -> PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ QName
-> Arity
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
primFun QName
forall a. HasCallStack => a
__IMPOSSIBLE__ Arity
6 (([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
 -> PrimFun)
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
forall a b. (a -> b) -> a -> b
$ \case
    [Arg Term
l,Arg Term
bA,Arg Term
x,Arg Term
y,Arg Term
phi,Arg Term
p] -> do
      Blocked (Arg Term)
sphi <- Arg Term -> ReduceM (Blocked (Arg Term))
forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
phi
      Term -> IntervalView
view <- ReduceM (Term -> IntervalView)
forall (m :: * -> *). HasBuiltins m => m (Term -> IntervalView)
intervalView'
      case Term -> IntervalView
view (Term -> IntervalView) -> Term -> IntervalView
forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
unArg (Arg Term -> Term) -> Arg Term -> Term
forall a b. (a -> b) -> a -> b
$ Blocked (Arg Term) -> Arg Term
forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
sphi of
        -- But even though it's a constructor, it does reduce, in some
        -- cases: If the cofibration is definitely true, then we return
        -- reflId.  TODO: Handle this in the conversion checker instead?
        IntervalView
IOne -> do
          Term
reflId <- String -> String -> ReduceM Term
forall (m :: * -> *). HasBuiltins m => String -> String -> m Term
getTerm String
builtinConId String
builtinReflId
          Term -> ReduceM (Reduced MaybeReducedArgs Term)
forall a a'. a -> ReduceM (Reduced a' a)
redReturn (Term -> ReduceM (Reduced MaybeReducedArgs Term))
-> Term -> ReduceM (Reduced MaybeReducedArgs Term)
forall a b. (a -> b) -> a -> b
$ Term
reflId
        IntervalView
_ -> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a. a -> ReduceM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Reduced MaybeReducedArgs Term
 -> ReduceM (Reduced MaybeReducedArgs Term))
-> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a b. (a -> b) -> a -> b
$ MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall no yes. no -> Reduced no yes
NoReduction (MaybeReducedArgs -> Reduced MaybeReducedArgs Term)
-> MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall a b. (a -> b) -> a -> b
$ (Arg Term -> MaybeReduced (Arg Term))
-> [Arg Term] -> MaybeReducedArgs
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> MaybeReduced (Arg Term)
forall a. a -> MaybeReduced a
notReduced [Arg Term
l,Arg Term
bA,Arg Term
x,Arg Term
y] MaybeReducedArgs -> MaybeReducedArgs -> MaybeReducedArgs
forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sphi, Arg Term -> MaybeReduced (Arg Term)
forall a. a -> MaybeReduced a
notReduced Arg Term
p]
    [Arg Term]
_ -> String -> ReduceM (Reduced MaybeReducedArgs Term)
forall (m :: * -> *) a.
(HasCallStack, MonadDebug m) =>
String -> m a
__IMPOSSIBLE_VERBOSE__ String
"implementation of primConId called with wrong arity"

-- | Extract the underlying cofibration from an inhabitant of the
-- cubical identity types.
--
-- TODO (Amy, 2022-08-17): Projecting a cofibration from a Kan type
-- violates the cubical phase distinction.
primIdFace' :: TCM PrimitiveImpl
primIdFace' :: TCM PrimitiveImpl
primIdFace' = do
  Cubical -> String -> TCM ()
requireCubical Cubical
CErased String
""
  Type
t <- Names -> NamesT (TCMT IO) Type -> TCMT IO Type
forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] (NamesT (TCMT IO) Type -> TCMT IO Type)
-> NamesT (TCMT IO) Type -> TCMT IO Type
forall a b. (a -> b) -> a -> b
$
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"a" (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Functor m => m Term -> m Type
el (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevel) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
a ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"A" (Sort -> Type
sort (Sort -> Type) -> (Term -> Sort) -> Term -> Type
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort (Term -> Type) -> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
a) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
bA ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"x" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
x ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"y" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
y ->
    NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a (TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primId NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
bA NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
x NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y)
    NamesT (TCMT IO) Type
-> NamesT (TCMT IO) Type -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> NamesT (TCMT IO) Type
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType

  PrimitiveImpl -> TCM PrimitiveImpl
forall a. a -> TCMT IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (PrimitiveImpl -> TCM PrimitiveImpl)
-> PrimitiveImpl -> TCM PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ Type -> PrimFun -> PrimitiveImpl
PrimImpl Type
t (PrimFun -> PrimitiveImpl) -> PrimFun -> PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ QName
-> Arity
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
primFun QName
forall a. HasCallStack => a
__IMPOSSIBLE__ Arity
5 (([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
 -> PrimFun)
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
forall a b. (a -> b) -> a -> b
$ \case
    [Arg Term
l,Arg Term
bA,Arg Term
x,Arg Term
y,Arg Term
t] -> do
      Blocked (Arg Term)
st <- Arg Term -> ReduceM (Blocked (Arg Term))
forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
t
      Maybe QName
mConId <- String -> ReduceM (Maybe QName)
forall (m :: * -> *). HasBuiltins m => String -> m (Maybe QName)
getName' String
builtinConId
      Term -> Term -> Maybe (Arg Term, Arg Term)
cview <- ReduceM (Term -> Term -> Maybe (Arg Term, Arg Term))
forall (m :: * -> *).
HasBuiltins m =>
m (Term -> Term -> Maybe (Arg Term, Arg Term))
conidView'
      case Term -> Term -> Maybe (Arg Term, Arg Term)
cview (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
x) (Term -> Maybe (Arg Term, Arg Term))
-> Term -> Maybe (Arg Term, Arg Term)
forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
unArg (Blocked (Arg Term) -> Arg Term
forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
st) of
        Just (Arg Term
phi, Arg Term
_) -> Term -> ReduceM (Reduced MaybeReducedArgs Term)
forall a a'. a -> ReduceM (Reduced a' a)
redReturn (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
phi)
        Maybe (Arg Term, Arg Term)
_ -> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a. a -> ReduceM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Reduced MaybeReducedArgs Term
 -> ReduceM (Reduced MaybeReducedArgs Term))
-> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a b. (a -> b) -> a -> b
$ MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall no yes. no -> Reduced no yes
NoReduction (MaybeReducedArgs -> Reduced MaybeReducedArgs Term)
-> MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall a b. (a -> b) -> a -> b
$ (Arg Term -> MaybeReduced (Arg Term))
-> [Arg Term] -> MaybeReducedArgs
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> MaybeReduced (Arg Term)
forall a. a -> MaybeReduced a
notReduced [Arg Term
l,Arg Term
bA,Arg Term
x,Arg Term
y] MaybeReducedArgs -> MaybeReducedArgs -> MaybeReducedArgs
forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
st]
    [Arg Term]
_ -> ReduceM (Reduced MaybeReducedArgs Term)
forall a. HasCallStack => a
__IMPOSSIBLE__

-- | Extract the underlying path from an inhabitant of the
-- cubical identity types.
primIdPath' :: TCM PrimitiveImpl
primIdPath' :: TCM PrimitiveImpl
primIdPath' = do
  Cubical -> String -> TCM ()
requireCubical Cubical
CErased String
""
  Type
t <- Names -> NamesT (TCMT IO) Type -> TCMT IO Type
forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] (NamesT (TCMT IO) Type -> TCMT IO Type)
-> NamesT (TCMT IO) Type -> TCMT IO Type
forall a b. (a -> b) -> a -> b
$
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"a" (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Functor m => m Term -> m Type
el (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevel) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
a ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"A" (Sort -> Type
sort (Sort -> Type) -> (Term -> Sort) -> Term -> Type
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort (Term -> Type) -> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
a) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
bA ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"x" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
x ->
    String
-> NamesT (TCMT IO) Type
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
String
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' String
"y" (NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
bA) ((NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
 -> NamesT (TCMT IO) Type)
-> (NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type)
-> NamesT (TCMT IO) Type
forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
y ->
    NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a (TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primId NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
bA NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
x NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y)
    NamesT (TCMT IO) Type
-> NamesT (TCMT IO) Type -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Type
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
a (TCMT IO Term -> NamesT (TCMT IO) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl TCMT IO Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primPath NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
a NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
bA NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
x NamesT (TCMT IO) Term
-> NamesT (TCMT IO) Term -> NamesT (TCMT IO) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
y)

  PrimitiveImpl -> TCM PrimitiveImpl
forall a. a -> TCMT IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (PrimitiveImpl -> TCM PrimitiveImpl)
-> PrimitiveImpl -> TCM PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ Type -> PrimFun -> PrimitiveImpl
PrimImpl Type
t (PrimFun -> PrimitiveImpl) -> PrimFun -> PrimitiveImpl
forall a b. (a -> b) -> a -> b
$ QName
-> Arity
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
primFun QName
forall a. HasCallStack => a
__IMPOSSIBLE__ Arity
5 (([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
 -> PrimFun)
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
forall a b. (a -> b) -> a -> b
$ \case
    [Arg Term
l,Arg Term
bA,Arg Term
x,Arg Term
y,Arg Term
t] -> do
      Blocked (Arg Term)
st <- Arg Term -> ReduceM (Blocked (Arg Term))
forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
t
      Maybe QName
mConId <- String -> ReduceM (Maybe QName)
forall (m :: * -> *). HasBuiltins m => String -> m (Maybe QName)
getName' String
builtinConId
      Term -> Term -> Maybe (Arg Term, Arg Term)
cview <- ReduceM (Term -> Term -> Maybe (Arg Term, Arg Term))
forall (m :: * -> *).
HasBuiltins m =>
m (Term -> Term -> Maybe (Arg Term, Arg Term))
conidView'
      case Term -> Term -> Maybe (Arg Term, Arg Term)
cview (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
x) (Term -> Maybe (Arg Term, Arg Term))
-> Term -> Maybe (Arg Term, Arg Term)
forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
unArg (Blocked (Arg Term) -> Arg Term
forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
st) of
        Just (Arg Term
_, Arg Term
w) -> Term -> ReduceM (Reduced MaybeReducedArgs Term)
forall a a'. a -> ReduceM (Reduced a' a)
redReturn (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
w)
        Maybe (Arg Term, Arg Term)
_ -> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a. a -> ReduceM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Reduced MaybeReducedArgs Term
 -> ReduceM (Reduced MaybeReducedArgs Term))
-> Reduced MaybeReducedArgs Term
-> ReduceM (Reduced MaybeReducedArgs Term)
forall a b. (a -> b) -> a -> b
$ MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall no yes. no -> Reduced no yes
NoReduction (MaybeReducedArgs -> Reduced MaybeReducedArgs Term)
-> MaybeReducedArgs -> Reduced MaybeReducedArgs Term
forall a b. (a -> b) -> a -> b
$ (Arg Term -> MaybeReduced (Arg Term))
-> [Arg Term] -> MaybeReducedArgs
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> MaybeReduced (Arg Term)
forall a. a -> MaybeReduced a
notReduced [Arg Term
l,Arg Term
bA,Arg Term
x,Arg Term
y] MaybeReducedArgs -> MaybeReducedArgs -> MaybeReducedArgs
forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
st]
    [Arg Term]
_ -> ReduceM (Reduced MaybeReducedArgs Term)
forall a. HasCallStack => a
__IMPOSSIBLE__

-- | Check that a term matches a given predicate on every consistent
-- substitution of interval variables which makes the given cofibration
-- hold.
onEveryFace
  :: Term -- ^ The cofibration @φ@
  -> Term -- ^ The term to test
  -> (Term -> Bool)
  -- ^ The predicate to test with.
  -> ReduceM Bool
onEveryFace :: Term -> Term -> (Term -> Bool) -> ReduceM Bool
onEveryFace Term
phi Term
u Term -> Bool
p = do
  IntervalView -> Term
unview <- ReduceM (IntervalView -> Term)
forall (m :: * -> *). HasBuiltins m => m (IntervalView -> Term)
intervalUnview'
  let boolToI :: Bool -> Term
boolToI Bool
b = if Bool
b then IntervalView -> Term
unview IntervalView
IOne else IntervalView -> Term
unview IntervalView
IZero
  [(IntMap Bool, [Term])]
as <- Term -> ReduceM [(IntMap Bool, [Term])]
forall (m :: * -> *).
HasBuiltins m =>
Term -> m [(IntMap Bool, [Term])]
decomposeInterval Term
phi
  [Bool]
bools <- [(IntMap Bool, [Term])]
-> ((IntMap Bool, [Term]) -> ReduceM Bool) -> ReduceM [Bool]
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
t a -> (a -> f b) -> f (t b)
for [(IntMap Bool, [Term])]
as (((IntMap Bool, [Term]) -> ReduceM Bool) -> ReduceM [Bool])
-> ((IntMap Bool, [Term]) -> ReduceM Bool) -> ReduceM [Bool]
forall a b. (a -> b) -> a -> b
$ \ (IntMap Bool
bs,[Term]
ts) -> do
    let u' :: Term
u' = [(Arity, Term)] -> Substitution' Term
forall a. EndoSubst a => [(Arity, a)] -> Substitution' a
listS (IntMap Term -> [(Arity, Term)]
forall a. IntMap a -> [(Arity, a)]
IntMap.toAscList (IntMap Term -> [(Arity, Term)]) -> IntMap Term -> [(Arity, Term)]
forall a b. (a -> b) -> a -> b
$ (Bool -> Term) -> IntMap Bool -> IntMap Term
forall a b. (a -> b) -> IntMap a -> IntMap b
IntMap.map Bool -> Term
boolToI IntMap Bool
bs) Substitution' (SubstArg Term) -> Term -> Term
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
`applySubst` Term
u
    Blocked Term
t <- Term -> ReduceM (Blocked Term)
reduce2Lam Term
u'
    Bool -> ReduceM Bool
forall a. a -> ReduceM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Bool -> ReduceM Bool) -> Bool -> ReduceM Bool
forall a b. (a -> b) -> a -> b
$! Term -> Bool
p (Term -> Bool) -> Term -> Bool
forall a b. (a -> b) -> a -> b
$ Blocked Term -> Term
forall t a. Blocked' t a -> a
ignoreBlocking Blocked Term
t
  Bool -> ReduceM Bool
forall a. a -> ReduceM a
forall (f :: * -> *) a. Applicative f => a -> f a
pure ([Bool] -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
and [Bool]
bools)

doIdKanOp
  :: KanOperation           -- ^ Are we composing or transporting?
  -> FamilyOrNot (Arg Term) -- ^ Level argument
  -> FamilyOrNot (Arg Term, Arg Term, Arg Term)
    -- ^ Domain, left and right endpoints of the identity type
  -> ReduceM (Maybe (Reduced t Term))
doIdKanOp :: forall t.
KanOperation
-> FamilyOrNot (Arg Term)
-> FamilyOrNot (Arg Term, Arg Term, Arg Term)
-> ReduceM (Maybe (Reduced t Term))
doIdKanOp KanOperation
kanOp FamilyOrNot (Arg Term)
l FamilyOrNot (Arg Term, Arg Term, Arg Term)
bA_x_y = do
  let getTermLocal :: String -> ReduceM Term
getTermLocal = String -> String -> ReduceM Term
forall (m :: * -> *). HasBuiltins m => String -> String -> m Term
getTerm (String -> String -> ReduceM Term)
-> String -> String -> ReduceM Term
forall a b. (a -> b) -> a -> b
$ KanOperation -> String
kanOpName KanOperation
kanOp String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
" for " String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
builtinId

  IntervalView -> Term
unview <- ReduceM (IntervalView -> Term)
forall (m :: * -> *). HasBuiltins m => m (IntervalView -> Term)
intervalUnview'
  Maybe QName
mConId <- String -> ReduceM (Maybe QName)
forall (m :: * -> *). HasBuiltins m => String -> m (Maybe QName)
getName' String
builtinConId
  Term -> Term -> Maybe (Arg Term, Arg Term)
cview <- ReduceM (Term -> Term -> Maybe (Arg Term, Arg Term))
forall (m :: * -> *).
HasBuiltins m =>
m (Term -> Term -> Maybe (Arg Term, Arg Term))
conidView'
  let isConId :: Term -> Bool
isConId Term
t = Maybe (Arg Term, Arg Term) -> Bool
forall a. Maybe a -> Bool
isJust (Maybe (Arg Term, Arg Term) -> Bool)
-> Maybe (Arg Term, Arg Term) -> Bool
forall a b. (a -> b) -> a -> b
$ Term -> Term -> Maybe (Arg Term, Arg Term)
cview Term
HasCallStack => Term
__DUMMY_TERM__ Term
t

  Blocked (Arg Term)
sa0 <- Arg Term -> ReduceM (Blocked (Arg Term))
forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' (KanOperation -> Arg Term
kanOpBase KanOperation
kanOp)
  -- TODO: wasteful to compute b even when cheaper checks might fail
  --
  -- Should we go forward with the Kan operation? This is the case when
  -- doing transport always, and when every face fo the partial element
  -- has reduced to @conid@ otherwise. Note that @conidView@ treats
  -- @reflId@ as though it were @conid i1 refl@.
  Bool
b <- case KanOperation
kanOp of
    TranspOp{}    -> Bool -> ReduceM Bool
forall a. a -> ReduceM a
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
True
    HCompOp Blocked (Arg Term)
_ Arg Term
u Arg Term
_ ->
      Term -> Term -> (Term -> Bool) -> ReduceM Bool
onEveryFace (Arg Term -> Term
forall e. Arg e -> e
unArg (Arg Term -> Term)
-> (KanOperation -> Arg Term) -> KanOperation -> Term
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Blocked (Arg Term) -> Arg Term
forall t a. Blocked' t a -> a
ignoreBlocking (Blocked (Arg Term) -> Arg Term)
-> (KanOperation -> Blocked (Arg Term)) -> KanOperation -> Arg Term
forall b c a. (b -> c) -> (a -> b) -> a -> c
. KanOperation -> Blocked (Arg Term)
kanOpCofib (KanOperation -> Term) -> KanOperation -> Term
forall a b. (a -> b) -> a -> b
$ KanOperation
kanOp) (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
u) Term -> Bool
isConId

  case Maybe QName
mConId of
    Just QName
conid | Term -> Bool
isConId (Arg Term -> Term
forall e. Arg e -> e
unArg (Arg Term -> Term)
-> (Blocked (Arg Term) -> Arg Term) -> Blocked (Arg Term) -> Term
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Blocked (Arg Term) -> Arg Term
forall t a. Blocked' t a -> a
ignoreBlocking (Blocked (Arg Term) -> Term) -> Blocked (Arg Term) -> Term
forall a b. (a -> b) -> a -> b
$ Blocked (Arg Term)
sa0), Bool
b -> (Reduced t Term -> Maybe (Reduced t Term)
forall a. a -> Maybe a
Just (Reduced t Term -> Maybe (Reduced t Term))
-> ReduceM (Reduced t Term) -> ReduceM (Maybe (Reduced t Term))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$>) (ReduceM (Reduced t Term) -> ReduceM (Maybe (Reduced t Term)))
-> (ReduceM Term -> ReduceM (Reduced t Term))
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forall a b. (a -> b) -> a -> b
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tHComp    <- String -> ReduceM Term
getTermLocal String
builtinHComp
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builtinTrans
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tIMin     <- String -> ReduceM Term
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"primDepIMin"
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idFace    <- String -> ReduceM Term
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idPath    <- String -> ReduceM Term
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tPathType <- String -> ReduceM Term
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builtinConId

      Names -> NamesT ReduceM Term -> ReduceM Term
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runNamesT [] (NamesT ReduceM Term -> ReduceM Term)
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io = Term -> NamesT ReduceM Term
forall a. a -> NamesT ReduceM a
forall (f :: * -> *) a. Applicative f => a -> f a
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forall a b. (a -> b) -> a -> b
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unview IntervalView
IOne
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pure Term
tConId

          eval :: KanOperation
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l NamesT ReduceM Term
bA NamesT ReduceM Term
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u0

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forall a b. (a -> b) -> a -> b
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forall a b. (a -> b) -> a -> b
$ KanOperation -> Blocked (Arg Term)
kanOpCofib KanOperation
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        -- Similarly to the fake line of levels above, fake lines of
        -- everything even when we're doing composition, for uniformity
        -- of eval.
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x, NamesT ReduceM Term
y] <- case FamilyOrNot (Arg Term, Arg Term, Arg Term)
bA_x_y of
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bA, Arg Term
x, Arg Term
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t a -> (a -> f b) -> f (t b)
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open (ArgInfo -> Abs Term -> Term
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defaultArgInfo (Abs Term -> Term) -> Abs Term -> Term
forall a b. (a -> b) -> a -> b
$ String -> Term -> Abs Term
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forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
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        -- The resulting path is constant when when
        --    @Σ φ λ o → -- primIdFace p i1 o@
        -- holds. That's why cofibrations have to be closed under Σ,
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pure Term
tIMin
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phi
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String -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
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p NamesT ReduceM Term
io NamesT ReduceM Term
o))

        -- Do the Kan operation for our faces in the Path type.
        Term
path <- KanOperation
-> NamesT ReduceM Term
-> NamesT ReduceM Term
-> NamesT ReduceM Term
-> NamesT ReduceM Term
-> NamesT ReduceM Term
-> NamesT ReduceM Term
eval KanOperation
kanOp NamesT ReduceM Term
l
          (String
-> (NamesT ReduceM Term -> NamesT ReduceM Term)
-> NamesT ReduceM Term
forall (m :: * -> *).
MonadFail m =>
String -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam String
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 -> NamesT ReduceM Term)
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forall a b. (a -> b) -> a -> b
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pure Term
tPathType NamesT ReduceM Term -> NamesT ReduceM Term -> NamesT ReduceM Term
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l NamesT ReduceM Term -> NamesT ReduceM Term -> NamesT ReduceM Term
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conId NamesT ReduceM Term -> NamesT ReduceM Term -> NamesT ReduceM Term
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