{-# OPTIONS_GHC -Wunused-imports #-}

{-# LANGUAGE NondecreasingIndentation #-}

module Agda.TypeChecking.Primitive.Cubical.HCompU
  ( doHCompUKanOp
  , prim_glueU'
  , prim_unglueU'
  )
  where

import Control.Monad

import Agda.Syntax.Common
  ( Cubical(..), Arg(..)
  , ProjOrigin(..)
  )
import Agda.Syntax.Internal

import Agda.TypeChecking.Monad.Base
import Agda.TypeChecking.Monad.Builtin
import Agda.TypeChecking.Monad.Pure

import Agda.TypeChecking.Names
  ( runNamesT, runNames, cl, lam, open, ilam )
import Agda.TypeChecking.Primitive.Base
  ( (-->), nPi', pPi', hPi', el, el', el's, (<@>), (<@@>), (<#>), argN, (<..>)
  , SigmaKit(..), getSigmaKit
  )
import Agda.TypeChecking.Primitive.Cubical.Glue
import Agda.TypeChecking.Primitive.Cubical.Base
import Agda.TypeChecking.Reduce
  ( reduceB', reduceB )
import Agda.TypeChecking.Substitute
  ( absBody, apply, sort, subst, applyE )

import Agda.Utils.Functor
import Agda.Utils.Maybe
import Agda.Utils.Monad

import Agda.Utils.Impossible (__IMPOSSIBLE__)

-- | Perform the Kan operations for an @hcomp {A = Type} {φ} u u0@ type.
doHCompUKanOp
  :: forall m. PureTCM m
  => KanOperation
  -> FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term)
  -> TermPosition
  -> m (Maybe Term)

-- TODO (Amy, 2022-08-17): This is literally the same algorithm as
-- doGlueKanOp, but specialised for using transport as the equivalence.
-- Can we deduplicate them?
doHCompUKanOp :: forall (m :: * -> *).
PureTCM m =>
KanOperation
-> FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term)
-> TermPosition
-> m (Maybe Term)
doHCompUKanOp (HCompOp Blocked (Arg Term)
psi Arg Term
u Arg Term
u0) (IsNot (Arg Term
la, Arg Term
phi, Arg Term
bT, Arg Term
bA)) TermPosition
tpos = do
  let getTermLocal :: IsBuiltin a => a -> m Term
      getTermLocal :: forall a. IsBuiltin a => a -> m Term
getTermLocal = forall (m :: * -> *) a.
(HasBuiltins m, IsBuiltin a) =>
[Char] -> a -> m Term
getTerm forall a b. (a -> b) -> a -> b
$ forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtinHComp forall a. [a] -> [a] -> [a]
++ [Char]
" for " forall a. [a] -> [a] -> [a]
++ forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtinHComp forall a. [a] -> [a] -> [a]
++ [Char]
" of Set"
  Term
io       <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinIOne
  Term
iz       <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinIZero
  Term
tHComp   <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinHComp
  Term
tTransp  <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinTrans
  Term
tglue    <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtin_glueU
  Term
tunglue  <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtin_unglueU
  Term
tLSuc    <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinLevelSuc
  Term
tSubIn   <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinSubIn
  Term
tItIsOne <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinItIsOne
  forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] forall a b. (a -> b) -> a -> b
$ do
    [NamesT m Term
psi, NamesT m Term
u, NamesT m Term
u0] <- forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM (forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall e. Arg e -> e
unArg) [forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
psi, Arg Term
u, Arg Term
u0]
    [NamesT m Term
la, NamesT m Term
phi, NamesT m Term
bT, NamesT m Term
bA] <- forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM (forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall e. Arg e -> e
unArg) [Arg Term
la, Arg Term
phi, Arg Term
bT, Arg Term
bA]

    forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM (forall (m :: * -> *). PureTCM m => TermPosition -> m Term -> m Bool
headStop TermPosition
tpos NamesT m Term
phi) (forall (m :: * -> *) a. Monad m => a -> m a
return forall a. Maybe a
Nothing) forall a b. (a -> b) -> a -> b
$ forall a. a -> Maybe a
Just forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> do

    let
      transp :: NamesT m Term
-> (NamesT m Term -> NamesT m Term)
-> NamesT m Term
-> NamesT m Term
transp NamesT m Term
la NamesT m Term -> NamesT m Term
bA NamesT m Term
a0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tTransp forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (forall a b. a -> b -> a
const NamesT m Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" NamesT m Term -> NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
iz forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
a0
      tf :: NamesT m Term -> NamesT m Term -> NamesT m Term
tf NamesT m Term
i NamesT m Term
o = forall (m :: * -> *).
(HasBuiltins m, HasConstInfo m) =>
NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
hfill NamesT m Term
la (NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o) NamesT m Term
psi NamesT m Term
u NamesT m Term
u0 NamesT m Term
i

      bAS :: NamesT m Term
bAS = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tSubIn forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tLSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT m Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
bA
      unglue :: NamesT m Term -> NamesT m Term
unglue NamesT m Term
g = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tunglue forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
bAS forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
g

      a1 :: NamesT m Term
a1 = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tHComp forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imax NamesT m Term
psi NamesT m Term
phi)
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (\NamesT m Term
i -> forall (m :: * -> *).
HasBuiltins m =>
NamesT m Term
-> NamesT m Term
-> [(NamesT m Term, NamesT m Term)]
-> NamesT m Term
combineSys NamesT m Term
la NamesT m Term
bA
            [ (NamesT m Term
psi, forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" (\NamesT m Term
o -> NamesT m Term -> NamesT m Term
unglue (NamesT m Term
u forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o)))
            , (NamesT m Term
phi, forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" (\ NamesT m Term
o -> NamesT m Term
-> (NamesT m Term -> NamesT m Term)
-> NamesT m Term
-> NamesT m Term
transp NamesT m Term
la (\NamesT m Term
i -> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (forall (m :: * -> *). HasBuiltins m => m Term -> m Term
ineg NamesT m Term
i) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o) (NamesT m Term -> NamesT m Term -> NamesT m Term
tf NamesT m Term
i NamesT m Term
o)))
            ])
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term -> NamesT m Term
unglue NamesT m Term
u0

      t1 :: NamesT m Term -> NamesT m Term
t1 = NamesT m Term -> NamesT m Term -> NamesT m Term
tf (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io)

    -- pure tglue <#> la <#> phi <#> bT <#> bAS <@> (ilam "o" $ \ o -> t1 o) <@> a1
    case TermPosition
tpos of
      TermPosition
Eliminated -> NamesT m Term
a1
      TermPosition
Head       -> NamesT m Term -> NamesT m Term
t1 (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tItIsOne)


doHCompUKanOp (TranspOp Blocked (Arg Term)
psi Arg Term
u0) (IsFam (Arg Term
la, Arg Term
phi, Arg Term
bT, Arg Term
bA)) TermPosition
tpos = do
  let
    localUse :: [Char]
localUse = forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtinTrans forall a. [a] -> [a] -> [a]
++ [Char]
" for " forall a. [a] -> [a] -> [a]
++ forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtinHComp forall a. [a] -> [a] -> [a]
++ [Char]
" of Set"
    getTermLocal :: IsBuiltin a => a -> m Term
    getTermLocal :: forall a. IsBuiltin a => a -> m Term
getTermLocal = forall (m :: * -> *) a.
(HasBuiltins m, IsBuiltin a) =>
[Char] -> a -> m Term
getTerm [Char]
localUse
  Term
tPOr <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinPOr
  Term
tIMax <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinIMax
  Term
tIMin <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinIMin
  Term
tINeg <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinINeg
  Term
tHComp <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinHComp
  Term
tTrans <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinTrans
  Term
tTranspProof <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinTranspProof
  Term
tSubIn <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinSubIn
  Term
tForall  <- forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtinFaceForall
  Term
io      <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinIOne
  Term
iz      <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinIZero
  Term
tLSuc   <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinLevelSuc
  Term
tPath   <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinPath
  Term
tItIsOne   <- forall a. IsBuiltin a => a -> m Term
getTermLocal BuiltinId
builtinItIsOne
  SigmaKit
kit <- forall a. a -> Maybe a -> a
fromMaybe forall a. HasCallStack => a
__IMPOSSIBLE__ forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (m :: * -> *).
(HasBuiltins m, HasConstInfo m) =>
m (Maybe SigmaKit)
getSigmaKit
  forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] forall a b. (a -> b) -> a -> b
$ do
    -- Helper definitions we'll use:
    NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
gcomp <- forall (m :: * -> *).
HasBuiltins m =>
[Char]
-> NamesT
     m
     (NamesT m Term
      -> NamesT m Term
      -> NamesT m Term
      -> NamesT m Term
      -> NamesT m Term
      -> NamesT m Term)
mkGComp [Char]
localUse

    let
      transp :: NamesT m Term
-> (NamesT m Term -> NamesT m Term)
-> NamesT m Term
-> NamesT m Term
transp NamesT m Term
la NamesT m Term -> NamesT m Term
bA NamesT m Term
a0 = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tTrans forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (forall a b. a -> b -> a
const NamesT m Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" NamesT m Term -> NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
iz forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
a0
      transpFill :: NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
transpFill NamesT m Term
la NamesT m Term
bA NamesT m Term
phi NamesT m Term
u0 NamesT m Term
i = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tTrans
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"j" (\ NamesT m Term
j -> NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imin NamesT m Term
i NamesT m Term
j)
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"j" (\ NamesT m Term
j -> NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imin NamesT m Term
i NamesT m Term
j)
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imax NamesT m Term
phi (forall (m :: * -> *). HasBuiltins m => m Term -> m Term
ineg NamesT m Term
i))
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
u0

    [NamesT m Term
psi, NamesT m Term
u0] <- forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM (forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall e. Arg e -> e
unArg) [forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
psi, Arg Term
u0]
    NamesT m Term -> NamesT m Term -> NamesT m Term
glue1 <- do
      Term
tglue             <- forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall a b. (a -> b) -> a -> b
$ forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtin_glueU
      [NamesT m Term
la, NamesT m Term
phi, NamesT m Term
bT, NamesT m Term
bA] <- forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM (forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall e. Arg e -> e
unArg forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Subst a => Int -> SubstArg a -> a -> a
subst Int
0 Term
io) forall a b. (a -> b) -> a -> b
$ [Arg Term
la, Arg Term
phi, Arg Term
bT, Arg Term
bA]
      let bAS :: NamesT m Term
bAS = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tSubIn forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tLSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT m Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
bA
      NamesT m Term
g <- (forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<<) forall a b. (a -> b) -> a -> b
$ forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tglue forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term
bAS
      forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ \ NamesT m Term
t NamesT m Term
a -> NamesT m Term
g forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
a

    [NamesT m Term
la, NamesT m Term
phi, NamesT m Term
bT, NamesT m Term
bA] <- forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM (\Arg Term
a -> forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Names -> NamesT Fail a -> a
runNames [] forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (forall a b. a -> b -> a
const (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ forall e. Arg e -> e
unArg Arg Term
a))) [Arg Term
la, Arg Term
phi, Arg Term
bT, Arg Term
bA]

    -- Andreas, 2022-03-25, issue #5838.
    -- Port the fix of @unglueTranspGlue@ and @doGlueKanOp DoTransp@
    -- also to @doHCompUKanOp DoTransp@, as suggested by Tom Jack and Anders Mörtberg.
    -- We define @unglue_u0 i@ that is first used with @i@ and then with @i0@.
    -- The original code used it only with @i0@.
    Term
tunglue <- forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall a b. (a -> b) -> a -> b
$ forall a. IsBuiltin a => a -> m Term
getTermLocal PrimitiveId
builtin_unglueU
    let
      bAS :: NamesT m Term -> NamesT m Term
bAS NamesT m Term
i = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tSubIn
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tLSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i)) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i)) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i)
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i)
      unglue_u0 :: NamesT m Term -> NamesT m Term
unglue_u0 NamesT m Term
i = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tunglue
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i)
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT m Term -> NamesT m Term
bAS NamesT m Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
u0

    forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM (forall (m :: * -> *). PureTCM m => TermPosition -> m Term -> m Bool
headStop TermPosition
tpos (NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io)) (forall (m :: * -> *) a. Monad m => a -> m a
return forall a. Maybe a
Nothing) forall a b. (a -> b) -> a -> b
$ forall a. a -> Maybe a
Just forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> do

    let
      tf :: NamesT m Term -> NamesT m Term -> NamesT m Term
tf NamesT m Term
i NamesT m Term
o = NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
transpFill NamesT m Term
la (forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" forall a b. (a -> b) -> a -> b
$ \ NamesT m Term
i -> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o) NamesT m Term
psi NamesT m Term
u0 NamesT m Term
i
      t1 :: NamesT m Term -> NamesT m Term
t1 NamesT m Term
o   = NamesT m Term -> NamesT m Term -> NamesT m Term
tf (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) NamesT m Term
o

      -- compute "forall. phi"
      forallphi :: NamesT m Term
forallphi = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tForall forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
phi

      -- a1 with gcomp
      a1 :: NamesT m Term
a1 = NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
-> NamesT m Term
gcomp NamesT m Term
la NamesT m Term
bA (forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imax NamesT m Term
psi NamesT m Term
forallphi)
        (forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" forall a b. (a -> b) -> a -> b
$ \ NamesT m Term
i -> forall (m :: * -> *).
HasBuiltins m =>
NamesT m Term
-> NamesT m Term
-> [(NamesT m Term, NamesT m Term)]
-> NamesT m Term
combineSys (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i) (NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i)
          [ (NamesT m Term
psi,       forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" forall a b. (a -> b) -> a -> b
$ \NamesT m Term
_ -> NamesT m Term -> NamesT m Term
unglue_u0 NamesT m Term
i)
          , (NamesT m Term
forallphi, forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" (\NamesT m Term
o -> NamesT m Term
-> (NamesT m Term -> NamesT m Term)
-> NamesT m Term
-> NamesT m Term
transp (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i) (\NamesT m Term
j -> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term
ineg NamesT m Term
j forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o) (NamesT m Term -> NamesT m Term -> NamesT m Term
tf NamesT m Term
i NamesT m Term
o)))
          ])
          (NamesT m Term -> NamesT m Term
unglue_u0 (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
iz))

      w :: NamesT m Term -> NamesT m Term -> NamesT m Term
w NamesT m Term
i NamesT m Term
o = forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"x" forall a b. (a -> b) -> a -> b
$ NamesT m Term
-> (NamesT m Term -> NamesT m Term)
-> NamesT m Term
-> NamesT m Term
transp (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i) (\NamesT m Term
j -> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term
ineg NamesT m Term
j forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o)

      pt :: NamesT m Term -> NamesT m Term
pt NamesT m Term
o = -- o : [ φ 1 ]
        forall (m :: * -> *).
HasBuiltins m =>
NamesT m Term
-> NamesT m Term
-> [(NamesT m Term, NamesT m Term)]
-> NamesT m Term
combineSys (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) (NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o)
          [ (NamesT m Term
psi       , forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" forall a b. (a -> b) -> a -> b
$ \NamesT m Term
_ -> NamesT m Term
u0)
          , (NamesT m Term
forallphi , forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" forall a b. (a -> b) -> a -> b
$ \NamesT m Term
o -> NamesT m Term -> NamesT m Term
t1 NamesT m Term
o)
          ]

      -- "ghcomp" is implemented in the proof of tTranspProof
      -- (see src/data/lib/prim/Agda/Builtin/Cubical/HCompU.agda)
      t1'alpha :: NamesT m Term -> NamesT m Term
t1'alpha NamesT m Term
o = -- o : [ φ 1 ]
         forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tTranspProof
          forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (\NamesT m Term
i -> NamesT m Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term
ineg NamesT m Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT m Term
o)
          forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imax NamesT m Term
psi NamesT m Term
forallphi
          forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term -> NamesT m Term
pt NamesT m Term
o
          forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tSubIn forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imax NamesT m Term
psi NamesT m Term
forallphi
                forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
a1)

      -- TODO: optimize?
      t1' :: NamesT m Term -> NamesT m Term
t1' NamesT m Term
o   = NamesT m Term -> NamesT m Term
t1'alpha NamesT m Term
o forall (m :: * -> *) a b. Functor m => m a -> (a -> b) -> m b
<&> (forall t. Apply t => t -> Elims -> t
`applyE` [forall a. ProjOrigin -> QName -> Elim' a
Proj ProjOrigin
ProjSystem (SigmaKit -> QName
sigmaFst SigmaKit
kit)])
      alpha :: NamesT m Term -> NamesT m Term
alpha NamesT m Term
o = NamesT m Term -> NamesT m Term
t1'alpha NamesT m Term
o forall (m :: * -> *) a b. Functor m => m a -> (a -> b) -> m b
<&> (forall t. Apply t => t -> Elims -> t
`applyE` [forall a. ProjOrigin -> QName -> Elim' a
Proj ProjOrigin
ProjSystem (SigmaKit -> QName
sigmaSnd SigmaKit
kit)])
      a1' :: NamesT m Term
a1' = forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tHComp forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io)
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> forall (m :: * -> *). HasBuiltins m => m Term -> m Term -> m Term
imax (NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) NamesT m Term
psi
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"j" (\NamesT m Term
j -> forall (m :: * -> *).
HasBuiltins m =>
NamesT m Term
-> NamesT m Term
-> [(NamesT m Term, NamesT m Term)]
-> NamesT m Term
combineSys (NamesT m Term
la forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) (NamesT m Term
bA forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io)
          [ (NamesT m Term
phi forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io, forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" forall a b. (a -> b) -> a -> b
$ \NamesT m Term
o -> NamesT m Term -> NamesT m Term
alpha NamesT m Term
o forall (m :: * -> *).
Applicative m =>
m Term -> (m Term, m Term, m Term) -> m Term
<@@> (NamesT m Term -> NamesT m Term -> NamesT m Term
w (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
io) NamesT m Term
o forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term -> NamesT m Term
t1' NamesT m Term
o, NamesT m Term
a1, NamesT m Term
j))
          , (NamesT m Term
psi,             forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
ilam [Char]
"o" forall a b. (a -> b) -> a -> b
$ \NamesT m Term
o -> NamesT m Term
a1)
          ])
        forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT m Term
a1

    -- glue1 (ilam "o" t1') a1'
    case TermPosition
tpos of
      TermPosition
Eliminated -> NamesT m Term
a1'
      TermPosition
Head       -> NamesT m Term -> NamesT m Term
t1' (forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tItIsOne)
doHCompUKanOp KanOperation
_ FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term)
_ TermPosition
_ = forall a. HasCallStack => a
__IMPOSSIBLE__

-- | The implementation of 'prim_glueU', the introduction form for
-- @hcomp@ types.
prim_glueU' :: TCM PrimitiveImpl
prim_glueU' :: TCM PrimitiveImpl
prim_glueU' = do
-- TODO (Amy, 2022-08-17): Same thing about duplicated code with Glue
-- applies here.
  Cubical -> [Char] -> TCM ()
requireCubical Cubical
CErased [Char]
""
  Type
t <- forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] forall a b. (a -> b) -> a -> b
$
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"la" (forall (m :: * -> *). Functor m => m Term -> m Type
el forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevel) (\ NamesT (TCMT IO) Term
la ->
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"φ" forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
φ ->
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"T" (forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
nPi' [Char]
"i" forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
_ -> forall (m :: * -> *).
(MonadAddContext m, HasBuiltins m, MonadDebug m) =>
[Char]
-> NamesT m Term
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
pPi' [Char]
"o" NamesT (TCMT IO) Term
φ forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
o -> Sort -> Type
sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
t ->
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"A" (forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el's (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primSub forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
φ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primIZero)) forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
a -> do
       let bA :: NamesT (TCMT IO) Term
bA = (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primSubOut forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
φ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primIZero) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
a)
       forall (m :: * -> *).
(MonadAddContext m, HasBuiltins m, MonadDebug m) =>
[Char]
-> NamesT m Term
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
pPi' [Char]
"o" NamesT (TCMT IO) Term
φ (\ NamesT (TCMT IO) Term
o -> forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
la (NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primIOne forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> NamesT (TCMT IO) Term
o))
         forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> (forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
la NamesT (TCMT IO) Term
bA)
         forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
la (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primHComp forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
φ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
bA))
  Term -> IntervalView
view <- forall (m :: * -> *). HasBuiltins m => m (Term -> IntervalView)
intervalView'
  Term
one <- forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primItIsOne
  forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Type -> PrimFun -> PrimitiveImpl
PrimImpl Type
t forall a b. (a -> b) -> a -> b
$ QName
-> Int
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
primFun forall a. HasCallStack => a
__IMPOSSIBLE__ Int
6 forall a b. (a -> b) -> a -> b
$ \[Arg Term]
ts ->
    case [Arg Term]
ts of
      [Arg Term
la,Arg Term
phi,Arg Term
bT,Arg Term
bA,Arg Term
t,Arg Term
a] -> do
       Blocked (Arg Term)
sphi <- forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
phi
       case Term -> IntervalView
view forall a b. (a -> b) -> a -> b
$ forall e. Arg e -> e
unArg forall a b. (a -> b) -> a -> b
$ forall t a. Blocked' t a -> a
ignoreBlocking forall a b. (a -> b) -> a -> b
$ Blocked (Arg Term)
sphi of
         IntervalView
IOne -> forall a a'. a -> ReduceM (Reduced a' a)
redReturn forall a b. (a -> b) -> a -> b
$ forall e. Arg e -> e
unArg Arg Term
t forall t. Apply t => t -> [Arg Term] -> t
`apply` [forall e. e -> Arg e
argN Term
one]
         IntervalView
_    -> forall (m :: * -> *) a. Monad m => a -> m a
return (forall no yes. no -> Reduced no yes
NoReduction forall a b. (a -> b) -> a -> b
$ forall a b. (a -> b) -> [a] -> [b]
map forall a. a -> MaybeReduced a
notReduced [Arg Term
la] forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sphi] forall a. [a] -> [a] -> [a]
++ forall a b. (a -> b) -> [a] -> [b]
map forall a. a -> MaybeReduced a
notReduced [Arg Term
bT,Arg Term
bA,Arg Term
t,Arg Term
a])
      [Arg Term]
_ -> forall a. HasCallStack => a
__IMPOSSIBLE__

-- | The implementation of 'prim_unglueU', the elimination form for
-- @hcomp@ types.
prim_unglueU' :: TCM PrimitiveImpl
prim_unglueU' :: TCM PrimitiveImpl
prim_unglueU' = do
-- TODO (Amy, 2022-08-17): Same thing about duplicated code with Glue
-- applies here.
  Cubical -> [Char] -> TCM ()
requireCubical Cubical
CErased [Char]
""
  Type
t <- forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] forall a b. (a -> b) -> a -> b
$
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"la" (forall (m :: * -> *). Functor m => m Term -> m Type
el forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevel) (\ NamesT (TCMT IO) Term
la ->
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"φ" forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
φ ->
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"T" (forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
nPi' [Char]
"i" forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
_ -> forall (m :: * -> *).
(MonadAddContext m, HasBuiltins m, MonadDebug m) =>
[Char]
-> NamesT m Term
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
pPi' [Char]
"o" NamesT (TCMT IO) Term
φ forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
o -> Sort -> Type
sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
t ->
       forall (m :: * -> *).
(MonadFail m, MonadAddContext m, MonadDebug m) =>
[Char]
-> NamesT m Type
-> (NamesT m Term -> NamesT m Type)
-> NamesT m Type
hPi' [Char]
"A" (forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el's (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primSub forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
φ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> (NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primIZero)) forall a b. (a -> b) -> a -> b
$ \ NamesT (TCMT IO) Term
a -> do
       let bA :: NamesT (TCMT IO) Term
bA = (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primSubOut forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
φ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primIZero) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
a)
       forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
la (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primHComp forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primLevelSuc forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> (Sort -> Term
Sort forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Sort
tmSort forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (TCMT IO) Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> NamesT (TCMT IO) Term
φ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
t forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (TCMT IO) Term
bA)
         forall (m :: * -> *). Applicative m => m Type -> m Type -> m Type
--> forall (m :: * -> *). Applicative m => m Term -> m Term -> m Type
el' NamesT (TCMT IO) Term
la NamesT (TCMT IO) Term
bA)

  Term -> IntervalView
view <- forall (m :: * -> *). HasBuiltins m => m (Term -> IntervalView)
intervalView'
  Term
one <- forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primItIsOne
  Maybe QName
mglueU <- forall (m :: * -> *).
HasBuiltins m =>
PrimitiveId -> m (Maybe QName)
getPrimitiveName' PrimitiveId
builtin_glueU
  Maybe QName
mtransp <- forall (m :: * -> *).
HasBuiltins m =>
PrimitiveId -> m (Maybe QName)
getPrimitiveName' PrimitiveId
builtinTrans
  Maybe QName
mHCompU <- forall (m :: * -> *).
HasBuiltins m =>
PrimitiveId -> m (Maybe QName)
getPrimitiveName' PrimitiveId
builtinHComp
  let mhcomp :: Maybe QName
mhcomp = Maybe QName
mHCompU

  forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Type -> PrimFun -> PrimitiveImpl
PrimImpl Type
t forall a b. (a -> b) -> a -> b
$ QName
-> Int
-> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term))
-> PrimFun
primFun forall a. HasCallStack => a
__IMPOSSIBLE__ Int
5 forall a b. (a -> b) -> a -> b
$ \case
    [Arg Term
la,Arg Term
phi,Arg Term
bT,Arg Term
bA,Arg Term
b] -> do
      Blocked (Arg Term)
sphi <- forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
phi
      case Term -> IntervalView
view forall a b. (a -> b) -> a -> b
$ forall e. Arg e -> e
unArg forall a b. (a -> b) -> a -> b
$ forall t a. Blocked' t a -> a
ignoreBlocking forall a b. (a -> b) -> a -> b
$ Blocked (Arg Term)
sphi of
        -- Case where the hcomp has reduced away: Transport backwards
        -- along the partial element we've glued.
        IntervalView
IOne -> do
          Term
tTransp <- forall (m :: * -> *) a.
(HasBuiltins m, IsBuiltin a) =>
[Char] -> a -> m Term
getTerm (forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtin_unglueU) PrimitiveId
builtinTrans
          Term
iNeg    <- forall (m :: * -> *) a.
(HasBuiltins m, IsBuiltin a) =>
[Char] -> a -> m Term
getTerm (forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtin_unglueU) PrimitiveId
builtinINeg
          Term
iZ      <- forall (m :: * -> *) a.
(HasBuiltins m, IsBuiltin a) =>
[Char] -> a -> m Term
getTerm (forall a. IsBuiltin a => a -> [Char]
getBuiltinId PrimitiveId
builtin_unglueU) BuiltinId
builtinIZero
          forall a a'. a -> ReduceM (Reduced a' a)
redReturn forall (m :: * -> *) b c a.
Monad m =>
(b -> m c) -> (a -> m b) -> a -> m c
<=< forall (m :: * -> *) a. Names -> NamesT m a -> m a
runNamesT [] forall a b. (a -> b) -> a -> b
$ do
            [NamesT ReduceM Term
la,NamesT ReduceM Term
bT,NamesT ReduceM Term
b] <- forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM (forall (m :: * -> *) a.
(MonadFail m, Subst a) =>
a -> NamesT m (NamesT m a)
open forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall e. Arg e -> e
unArg) [Arg Term
la,Arg Term
bT,Arg Term
b]
            forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
tTransp forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<#> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (\ NamesT ReduceM Term
_ -> NamesT ReduceM Term
la) forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *).
MonadFail m =>
[Char] -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam [Char]
"i" (\ NamesT ReduceM Term
i -> NamesT ReduceM Term
bT forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (m :: * -> *). HasBuiltins m => m Term -> m Term
ineg NamesT ReduceM Term
i forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<..> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
one)
              forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> forall (f :: * -> *) a. Applicative f => a -> f a
pure Term
iZ forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT ReduceM Term
b

        -- Otherwise, we're dealing with a proper glu- didn't I already
        -- make this joke? Oh, yeah, in prim_unglue, right.
        IntervalView
_ -> do
          Blocked (Arg Term)
sb <- forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' Arg Term
b
          let fallback :: Blocked (Arg Term) -> ReduceM (Reduced MaybeReducedArgs Term)
fallback Blocked (Arg Term)
sbA = forall (m :: * -> *) a. Monad m => a -> m a
return (forall no yes. no -> Reduced no yes
NoReduction forall a b. (a -> b) -> a -> b
$ forall a b. (a -> b) -> [a] -> [b]
map forall a. a -> MaybeReduced a
notReduced [Arg Term
la] forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sphi] forall a. [a] -> [a] -> [a]
++ forall a b. (a -> b) -> [a] -> [b]
map forall a. a -> MaybeReduced a
notReduced [Arg Term
bT,Arg Term
bA] forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sb])
          case forall e. Arg e -> e
unArg forall a b. (a -> b) -> a -> b
$ forall t a. Blocked' t a -> a
ignoreBlocking forall a b. (a -> b) -> a -> b
$ Blocked (Arg Term)
sb of
            -- Project:
            Def QName
q Elims
es | Just [Arg Term
_,Arg Term
_,Arg Term
_,Arg Term
_,Arg Term
_, Arg Term
a] <- forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es, forall a. a -> Maybe a
Just QName
q forall a. Eq a => a -> a -> Bool
== Maybe QName
mglueU -> forall a a'. a -> ReduceM (Reduced a' a)
redReturn forall a b. (a -> b) -> a -> b
$ forall e. Arg e -> e
unArg Arg Term
a

            -- Transport:
            Def QName
q [Apply Arg Term
l, Apply Arg Term
bA, Apply Arg Term
r, Apply Arg Term
u0] | forall a. a -> Maybe a
Just QName
q forall a. Eq a => a -> a -> Bool
== Maybe QName
mtransp -> do
              Blocked (Arg Term)
sbA <- forall a (m :: * -> *).
(Reduce a, MonadReduce m) =>
a -> m (Blocked a)
reduceB Arg Term
bA
              case forall e. Arg e -> e
unArg forall a b. (a -> b) -> a -> b
$ forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
sbA of
                Lam ArgInfo
_ Abs Term
t -> do
                  Blocked Term
st <- forall t. Reduce t => t -> ReduceM (Blocked t)
reduceB' (forall a. Subst a => Abs a -> a
absBody Abs Term
t)
                  case forall t a. Blocked' t a -> a
ignoreBlocking Blocked Term
st of
                    Def QName
h Elims
es | Just [Arg Term
la,Arg Term
_,Arg Term
phi,Arg Term
bT,Arg Term
bA] <- forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es, forall a. a -> Maybe a
Just QName
h forall a. Eq a => a -> a -> Bool
== Maybe QName
mHCompU -> do
                      forall a a'. a -> ReduceM (Reduced a' a)
redReturn forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Maybe a -> a
fromMaybe forall a. HasCallStack => a
__IMPOSSIBLE__ forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<<
                        forall (m :: * -> *).
PureTCM m =>
KanOperation
-> FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term)
-> TermPosition
-> m (Maybe Term)
doHCompUKanOp (Blocked (Arg Term) -> Arg Term -> KanOperation
TranspOp (forall a t. a -> Blocked' t a
notBlocked Arg Term
r) Arg Term
u0) (forall a. a -> FamilyOrNot a
IsFam (Arg Term
la,Arg Term
phi,Arg Term
bT,Arg Term
bA)) TermPosition
Eliminated
                    Term
_ -> Blocked (Arg Term) -> ReduceM (Reduced MaybeReducedArgs Term)
fallback (Blocked Term
st forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> Blocked (Arg Term)
sbA)
                Term
_  -> Blocked (Arg Term) -> ReduceM (Reduced MaybeReducedArgs Term)
fallback Blocked (Arg Term)
sbA

            -- Compose:
            Def QName
q [Apply Arg Term
l,Apply Arg Term
bA,Apply Arg Term
r,Apply Arg Term
u,Apply Arg Term
u0] | forall a. a -> Maybe a
Just QName
q forall a. Eq a => a -> a -> Bool
== Maybe QName
mhcomp -> do
              Blocked (Arg Term)
sbA <- forall a (m :: * -> *).
(Reduce a, MonadReduce m) =>
a -> m (Blocked a)
reduceB Arg Term
bA
              case forall e. Arg e -> e
unArg forall a b. (a -> b) -> a -> b
$ forall t a. Blocked' t a -> a
ignoreBlocking Blocked (Arg Term)
sbA of
                Def QName
h Elims
es | Just [Arg Term
la,Arg Term
_,Arg Term
phi,Arg Term
bT,Arg Term
bA] <- forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es, forall a. a -> Maybe a
Just QName
h forall a. Eq a => a -> a -> Bool
== Maybe QName
mHCompU -> do
                  forall a a'. a -> ReduceM (Reduced a' a)
redReturn forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Maybe a -> a
fromMaybe forall a. HasCallStack => a
__IMPOSSIBLE__ forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<<
                    forall (m :: * -> *).
PureTCM m =>
KanOperation
-> FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term)
-> TermPosition
-> m (Maybe Term)
doHCompUKanOp (Blocked (Arg Term) -> Arg Term -> Arg Term -> KanOperation
HCompOp (forall a t. a -> Blocked' t a
notBlocked Arg Term
r) Arg Term
u Arg Term
u0) (forall a. a -> FamilyOrNot a
IsNot (Arg Term
la,Arg Term
phi,Arg Term
bT,Arg Term
bA)) TermPosition
Eliminated
                Term
_ -> Blocked (Arg Term) -> ReduceM (Reduced MaybeReducedArgs Term)
fallback Blocked (Arg Term)
sbA
            Term
_ -> forall (m :: * -> *) a. Monad m => a -> m a
return (forall no yes. no -> Reduced no yes
NoReduction forall a b. (a -> b) -> a -> b
$ forall a b. (a -> b) -> [a] -> [b]
map forall a. a -> MaybeReduced a
notReduced [Arg Term
la] forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sphi] forall a. [a] -> [a] -> [a]
++ forall a b. (a -> b) -> [a] -> [b]
map forall a. a -> MaybeReduced a
notReduced [Arg Term
bT,Arg Term
bA] forall a. [a] -> [a] -> [a]
++ [Blocked (Arg Term) -> MaybeReduced (Arg Term)
reduced Blocked (Arg Term)
sb])

    [Arg Term]
_ -> forall a. HasCallStack => a
__IMPOSSIBLE__