Agda-2.9.0: src/full/Agda/Termination/TermCheck.hs
{-# LANGUAGE ImplicitParams #-}
{-# LANGUAGE NondecreasingIndentation #-}
{- Checking for Structural recursion
Authors: Andreas Abel, Nils Anders Danielsson, Ulf Norell,
Karl Mehltretter and others
Created: 2007-05-28
Source : TypeCheck.Rules.Decl
-}
module Agda.Termination.TermCheck
( termDecl
, termMutual
, Result
) where
import Prelude hiding ( null, zip, zipWith )
import Control.Applicative ( liftA2 )
import Control.Monad ( (<=<), filterM, forM, forM_, zipWithM )
import Data.Foldable (toList)
import qualified Data.IntMap.Strict as IntMap
import qualified Data.List as List
import qualified Data.Map.Strict as Map
import Data.Monoid hiding ((<>))
import Data.Set (Set)
import qualified Data.Set as Set
import qualified Agda.Syntax.Abstract as A
import Agda.Syntax.Internal as I
import Agda.Syntax.Internal.Pattern as I
import Agda.Syntax.Internal.Generic
import qualified Agda.Syntax.Info as Info
import Agda.Syntax.Position
import Agda.Syntax.Common
import Agda.Syntax.Translation.InternalToAbstract (NamedClause(..))
import Agda.Termination.CutOff
import Agda.Termination.Monad
import Agda.Termination.CallGraph hiding (toList)
import Agda.Termination.CallGraph qualified as CallGraph
import Agda.Termination.CallMatrix hiding (toList)
import Agda.Termination.Order as Order
import Agda.Termination.SparseMatrix qualified as Matrix
import Agda.Termination.Termination (Terminates(..), GuardednessHelps(..), idempotentEndos, terminatesFilter, terminationCounterexample)
import Agda.Termination.RecCheck
import Agda.TypeChecking.Datatypes
import Agda.TypeChecking.Functions
import Agda.TypeChecking.Monad
import Agda.TypeChecking.Pretty
import Agda.TypeChecking.Forcing
import Agda.TypeChecking.Records -- (isRecordConstructor, isInductiveRecord)
import Agda.TypeChecking.Reduce (reduce, normalise, instantiate, instantiateFull, appDefE0)
import Agda.TypeChecking.SizedTypes
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Telescope
import qualified Agda.Benchmarking as Benchmark
import Agda.TypeChecking.Monad.Benchmark (billTo, billPureTo)
import Agda.Interaction.Options
import Agda.Utils.Either
import Agda.Utils.Function
import Agda.Utils.Functor
import Agda.Utils.List
import Agda.Utils.ListInf ( pattern (:<) )
import Agda.Utils.ListInf qualified as ListInf
import Agda.Utils.Maybe
import Agda.Utils.Monad -- (mapM', forM', ifM, or2M, and2M)
import Agda.Utils.Null
import Agda.Syntax.Common.Pretty (prettyShow)
import Agda.Utils.Singleton
import Agda.Utils.Size
-- import Agda.Utils.SmallSet (SmallSet)
import qualified Agda.Utils.SmallSet as SmallSet
import qualified Agda.Utils.VarSet as VarSet
import Agda.Utils.Zip
import Agda.Utils.Impossible
-- | Call graph with call info for composed calls.
type Calls = CallGraph CallPath
-- | The result of termination checking a module.
-- Must be a 'Monoid' and have 'Singleton'.
type Result = [TerminationError]
-- | Entry point: Termination check a single declaration.
--
-- Precondition: 'envMutualBlock' must be set correctly.
termDecl :: A.Declaration -> TCM Result
termDecl d = inTopContext $ termDecl' d
-- | Termination check a single declaration
-- (without necessarily ignoring @abstract@).
termDecl' :: A.Declaration -> TCM Result
termDecl' = \case
A.Axiom {} -> return mempty
A.Field {} -> return mempty
A.Primitive {} -> return mempty
A.Mutual _ ds -> termMutual $ getNames ds
A.Section _ _ _ _ ds -> foldMap termDecl' ds
-- section structure can be ignored as we are termination checking
-- definitions lifted to the top-level
A.Apply {} -> return mempty
A.Import {} -> return mempty
A.Pragma {} -> return mempty
A.Open {} -> return mempty
A.PatternSynDef {} -> return mempty
A.UnfoldingDecl{} -> return mempty
A.Generalize {} -> return mempty
-- open, pattern synonym and generalize defs are just artifacts from the concrete syntax
A.ScopedDecl scope ds -> {- withScope_ scope $ -} foldMap termDecl' ds
-- scope is irrelevant as we are termination checking Syntax.Internal
A.RecSig{} -> return mempty
A.RecDef _ x _ _ _ _ _ _ ds -> termMutual [x] <> foldMap termDecl' ds
-- Andreas, 2022-10-23, issue #5823
-- Also check record types for termination.
-- They are unfolded during construction of unique inhabitants of eta-records.
-- These should all be wrapped in mutual blocks:
A.FunDef{} -> __IMPOSSIBLE__
A.DataSig{} -> __IMPOSSIBLE__
A.DataDef{} -> __IMPOSSIBLE__
A.UnquoteDecl{} -> __IMPOSSIBLE__
A.UnquoteDef{} -> __IMPOSSIBLE__
A.UnquoteData{} -> __IMPOSSIBLE__
where
-- The mutual names mentioned in the abstract syntax
-- for symbols that need to be termination-checked.
getNames :: Foldable t => t A.Declaration -> [QName]
getNames = foldMap getName
getName (A.FunDef i x cs) = [x]
getName (A.RecDef _ x _ _ _ _ _ _ ds) = x : getNames ds
getName (A.Mutual _ ds) = getNames ds
getName (A.Section _ _ _ _ ds) = getNames ds
getName (A.ScopedDecl _ ds) = getNames ds
getName (A.UnquoteDecl _ _ xs _) = xs
getName (A.UnquoteDef _ xs _) = xs
getName _ = []
-- | Entry point: Termination check the current mutual block.
termMutual
:: [QName]
-- ^ The function names defined in this block on top-level.
-- (For error-reporting only.)
-> TCM Result
termMutual names0 = ifNotM (optTerminationCheck <$> pragmaOptions) (return mempty) $ {-else-}
inTopContext $ do
-- Get set of mutually defined names from the TCM.
-- This includes local and auxiliary functions introduced
-- during type-checking.
mid <- fromMaybe __IMPOSSIBLE__ <$> viewTC eMutualBlock
mutualBlock <- lookupMutualBlock mid
let allNames = Set.filter (not . isAbsurdLambdaName) $
mutualNames mutualBlock
names = if null names0 then allNames else Set.fromList names0
i = mutualInfo mutualBlock
-- We set the range to avoid panics when printing error messages.
setCurrentRange i $ do
-- The following debug statement is part of a test case for Issue
-- #3590.
reportSLn "term.mutual.id" 40 $
"Termination checking mutual block " ++ prettyShow mid
reportSLn "term.mutual" 10 $ "Termination checking " ++ prettyShow allNames
-- NO_TERMINATION_CHECK
if (Info.mutualTerminationCheck i `elem` [ NoTerminationCheck, Terminating ]) then do
reportSLn "term.warn.yes" 10 $ "Skipping termination check for " ++ prettyShow names
forM_ allNames $ \ q -> setTerminates q $ Just True -- considered terminating!
return mempty
-- NON_TERMINATING
else if (Info.mutualTerminationCheck i == NonTerminating) then do
reportSLn "term.warn.yes" 10 $ "Considering as non-terminating: " ++ prettyShow names
forM_ allNames $ \ q -> setTerminates q $ Just False
return mempty
else do
sccs <- do
-- Andreas, 2016-10-01 issue #2231
-- Recursivity checker has to see through abstract definitions!
ignoreAbstractMode $ do
billTo [Benchmark.Termination, Benchmark.RecCheck] $ recursive allNames
-- -- Andreas, 2017-03-24, use positivity info to skip non-recursive functions
-- skip = ignoreAbstractMode $ forallM allNames $ \ x -> do
-- null <$> getMutual x
-- PROBLEMS with test/Succeed/AbstractCoinduction.agda
-- Trivially terminating (non-recursive)?
when (null sccs) $
reportSLn "term.warn.yes" 10 $ "Trivially terminating: " ++ prettyShow names
-- Actual termination checking needed: go through SCCs.
concat <$> do
forM sccs $ \ allNames -> do
-- Andreas, 2025-05-31, AIM XL, re issue #7906:
-- Clear previous information about termination to avoid loops in the termination checker.
forM_ allNames $ \ q -> setTerminates q Nothing
-- Set the mutual names in the termination environment.
let namesSCC = Set.filter (`Set.member` allNames) names
let setNames e = e
{ terMutual = allNames
, terUserNames = namesSCC
}
-- Pre-compute the copattern projection lists and assign node ids, per issue #8596.
(projectedNameToNode, nodeToName, nameToProjections, projectedNameToMaskArgs) <- buildNodeAndProjectionMaps allNames
let runTerm cont = runTerDefault $ do
cutoff <- terGetCutOff
reportSLn "term.top" 10 $ "Termination checking " ++ prettyShow namesSCC ++
" with cutoff=" ++ show cutoff ++ "..."
terSetProjectedNameToNode projectedNameToNode $
terSetNodeToName nodeToName $
terSetNameToProjections nameToProjections $
terSetProjectedNameToMaskArgs projectedNameToMaskArgs $
terLocal setNames cont
-- New check currently only makes a difference for copatterns and record types.
-- Since it is slow, only invoke it if
-- any of the definitions uses copatterns or is a record type.
ifM (existsM allNames $ \ q -> usesCopatterns q `or2M` (isJust <$> isRecord q))
-- Then: New check, one after another.
(runTerm $ forM' allNames $ termFunction)
-- Else: Old check, all at once.
(runTerm $ termMutual')
-- | Run the termination checker.
runTerminationCheck ::
Maybe QName
-> TerM Calls
-> TerM (Terminates CallPath)
runTerminationCheck mname collect = do
-- Use full precision when extracting calls
let ?cutoff = DontCutOff
calls <- collect
nodeToName <- terGetNodeToName
let filt :: Node -> Bool
filt = case mname of
Nothing -> const True
Just f -> \ n -> IntMap.lookup n nodeToName == Just f
useGuardedness <- liftTCM guardednessOption
maxcutoff <- terGetCutOff
-- Iteratively increase cutoff up to its maximal value.
let
loop :: CutOff
-> Maybe (GuardednessHelps, CallPath)
-> TerM (Terminates CallPath)
loop cutoff currentResult = do
let ?cutoff = cutoff
reportCalls cutoff filt calls
r <- billToTerGraph $ terminatesFilter useGuardedness filt calls
case r of
Terminates -> return Terminates
TerminatesNot gh cinfo -> do
let result = bestResult currentResult (gh, cinfo)
if cutoff >= maxcutoff then return $ uncurry TerminatesNot result
else loop (cutoff + 1) (Just result)
loop 0 Nothing
where
bestResult :: Maybe (GuardednessHelps, CallPath) -> (GuardednessHelps, CallPath) -> (GuardednessHelps, CallPath)
bestResult Nothing r = r
bestResult (Just (GuardednessHelpsNot, _)) r@(GuardednessHelpsYes, _) = r
bestResult (Just r0) _ = r0
-- | @termMutual'@ checks all names of the current mutual block,
-- henceforth called @allNames@, for termination.
--
-- @allNames@ is taken from 'Internal' syntax, it contains also
-- the definitions created by the type checker (e.g., with-functions).
termMutual' :: TerM Result
termMutual' = do
-- collect all recursive calls in the block
allNames <- terGetMutual
let collect :: TerM Calls
collect = forM' allNames termDef
r <- runTerminationCheck Nothing collect
-- @names@ is taken from the 'Abstract' syntax, so it contains only
-- the names the user has declared. This is for error reporting.
names <- terGetUserNames
case r of
TerminatesNot guardednessHelps calls -> do
mapM_ (`setTerminates` Just False) allNames
return $ singleton $ terminationError names calls guardednessHelps
Terminates -> do
liftTCM $ reportSLn "term.warn.yes" 2 $
prettyShow (names) ++ " does termination check"
mapM_ (`setTerminates` Just True) allNames
return mempty
-- | Smart constructor for 'TerminationError'.
-- Removes 'termErrFunctions' that are not mentioned in 'termErrCalls'.
terminationError :: Set QName -> CallPath -> GuardednessHelps -> TerminationError
terminationError names calls guardednessHelps = TerminationError names' calls' guardednessHelps
where
calls' = callInfos calls
mentioned = map' callInfoTarget calls'
names' = filter (hasElem mentioned) $ toList names
billToTerGraph :: a -> TerM a
billToTerGraph a = liftTCM $ billPureTo [Benchmark.Termination, Benchmark.Graph] a
-- | @reportCalls@ for debug printing.
--
-- Replays the call graph completion for debugging.
reportCalls :: CutOff -> (Node -> Bool) -> Calls -> TerM ()
reportCalls cutoff filt calls = do
useGuardedness <- liftTCM guardednessOption
let ?cutoff = cutoff
-- We work in TCM exclusively.
liftTCM $ do
reportS "term.lex" 20
[ "Termination depth: " ++ show cutoff
, "Calls: " ++ prettyShow calls
]
-- Print the whole completion phase.
verboseS "term.matrices" 40 $ do
let header s = unlines
[ replicate n '='
, replicate k '=' ++ s ++ replicate k' '='
, replicate n '='
]
where n = 70
r = n - length s
k = r `div` 2
k' = r - k
let report s cs = reportSDoc "term.matrices" 40 $ vcat
[ text $ header s
, nest 2 $ prettyTCM cs
]
cs0 = calls
step cs = do
let (new, cs') = completionStep cs0 cs
report " New call matrices " new
case terminationCounterexample useGuardedness filt new of
Terminates | not (null new) -> return $ Right cs'
_ -> return $ Left ()
-- return $ if null new then Left () else Right cs'
report (" Initial call matrices (cutoff: " ++ show cutoff ++ ") ") cs0
trampolineM step cs0
-- Print the result of completion.
let calls' = CallGraph.complete calls
idems = idempotentEndos calls'
-- TODO
-- reportSDoc "term.behaviours" 20 $ vcat
-- [ text $ "Recursion behaviours (" ++ no ++ "dot patterns):"
-- , nest 2 $ return $ Term.prettyBehaviour calls'
-- ]
reportSDoc "term.matrices" 30 $ vcat
[ text $ "Idempotent call matrices:\n"
, nest 2 $ vcat $ punctuate "\n" $ map' prettyTCM idems
]
-- reportSDoc "term.matrices" 30 $ vcat
-- [ text $ "Other call matrices (" ++ no ++ "dot patterns):"
-- , nest 2 $ pretty $ CallGraph.fromList others
-- ]
return ()
-- | @termFunction name@ checks @name@ for termination.
-- If it passes the termination check it is marked as "terminates" in the signature.
termFunction :: QName -> TerM Result
termFunction name = inConcreteOrAbstractMode name $ \ def -> do
-- Retrieve the target type of the function to check.
-- #4256: Don't use typeOfConst (which instantiates type with module params), since termination
-- checking is running in the empty context, but with the current module unchanged.
target <- case theDef def of
-- We are termination-checking a record (calls to record will not be guarding):
Record{} -> return TargetRecord
-- We are termination-checking a definition:
_ -> typeEndsInDef (defType def) <&> \case
Just d -> TargetDef d
Nothing -> TargetOther
reportTarget target
terSetTarget target $ do
-- Collect the recursive calls in the block which (transitively)
-- involve @name@,
-- taking the target of @name@ into account for computing guardedness.
let
collect :: TerM Calls
collect = -- strengthenLoopDiagonals <$> do -- bad heuristics, see https://github.com/agda/agda/pull/8184#issuecomment-3487147737
(`trampolineM` (Set.singleton name, mempty, mempty)) $ \ (todo, done, calls) -> do
if null todo then return $ Left calls else do
-- Extract calls originating from functions in @todo@.
new <- forM' todo termDef
-- call-graph nodes correspond to @(name, [projection])@ pairs, so we
-- need to do a step of processing to translate node numbers into the
-- corresponding function name (see #8596).
nodeToName <- terGetNodeToName
let newNames = Set.fromList
[ q | n <- Set.toList (CallGraph.targetNodes new)
, Just q <- [IntMap.lookup n nodeToName]
]
-- Mark those functions as processed and add the calls to the result.
let done' = done `mappend` todo
calls' = new `mappend` calls
-- Compute the new todo list:
todo' = newNames Set.\\ done'
-- Jump the trampoline.
return $ Right (todo', done', calls')
r <- runTerminationCheck (Just name) collect
names <- terGetUserNames
case r of
TerminatesNot guardednessHelps callpaths -> do
let calls = callInfos callpaths
-- Mark as non-terminating.
setTerminates name $ Just False
-- Functions must be terminating, records types need not...
case theDef def of
-- Records need not terminate, so we just put the error on the debug log.
Record{} -> do
reportSDoc "term.warn.no" 10 $ vcat $
hsep [ "Record type", prettyTCM name, "does not termination check.", "Problematic calls:" ] :
map' (nest 2 . prettyTCM) (List.sortOn getRange calls)
mempty
-- Functions must terminate, so we report the error.
_ -> do
let err = TerminationError [name | name `elem` names] calls guardednessHelps
return $ singleton err
Terminates -> do
reportSLn "term.warn.yes" 2 $
prettyShow name ++ " does termination check"
setTerminates name $ Just True
return mempty
where
reportTarget :: MonadDebug m => Target -> m ()
reportTarget tgt = reportSLn "term.target" 20 $ (" " ++) $
case tgt of
TargetRecord -> "termination checking a record type"
TargetDef q -> unwords [ "target type ends in", prettyShow q ]
TargetOther -> "target type not recognized"
-- | To process the target type.
typeEndsInDef :: MonadTCM tcm => Type -> tcm (Maybe QName)
typeEndsInDef t = liftTCM $ do
TelV _ core <- telViewPath t
case unEl core of
Def d vs -> return $ Just d
_ -> return Nothing
-- | Termination check a definition by pattern matching.
--
-- TODO: Refactor!
-- As this function may be called twice,
-- once disregarding dot patterns,
-- the second time regarding dot patterns,
-- it is better if we separated bare call extraction
-- from computing the change in structural order.
-- Only the latter depends on the choice whether we
-- consider dot patterns or not.
termDef :: QName -> TerM Calls
termDef name = terSetCurrent name $ inConcreteOrAbstractMode name \ def -> do
-- strengthenLoopDiagonals <$> do -- bad heuristics, see https://github.com/agda/agda/pull/8184#issuecomment-3487147737
-- Skip calls to record types unless we are checking a record type in the first place.
let isRecord_ = case theDef def of { Record{} -> True; _ -> False }
let notTargetRecord = terGetTarget <&> \case
TargetRecord -> False
_ -> True
ifM (pure isRecord_ `and2M` notTargetRecord) mempty {-else-} $ do
-- Retrieve definition
let t = defType def
liftTCM $ reportSDoc "term.def.fun" 5 $
sep [ "termination checking type of" <+> prettyTCM name
, nest 2 $ ":" <+> prettyTCM t
]
termType t `mappend` do
liftTCM $ reportSDoc "term.def.fun" 5 $
sep [ "termination checking body of" <+> prettyTCM name
, nest 2 $ ":" <+> prettyTCM t
]
-- If --without-K, we disregard all arguments (and result)
-- which are not of data or record type.
withoutKEnabled <- liftTCM withoutKOption
applyWhen withoutKEnabled (setResultMask t) $ do
-- If the result should be disregarded, set all calls to unguarded.
applyWhenM terGetMaskResult terUnguarded $ do
case theDef def of
Function{ funClauses = cls } -> forM' cls $ \ cl -> do
if hasDefP (namedClausePats cl) -- generated hcomp clause, should be safe.
-- TODO find proper strategy.
then return empty
else termClause cl
-- @record R pars : Set where field tel@
-- is treated like function @R pars = tel@.
Record{ recPars, recTel } -> termRecTel recPars recTel
_ -> return empty
-- | Extract "calls" to the field types from a record constructor telescope.
-- Does not extract from the parameters, but treats these as the "pattern variables"
-- (the lhs of the "function").
termRecTel :: Nat -> Telescope -> TerM Calls
termRecTel npars tel = do
-- Set up the record parameters like function parameters.
let (pars, fields) = splitAt' npars $ telToList tel
addContext pars $ do
ps <- mkPats npars
terSetPatterns ps $ terSetSizeDepth pars $ do
-- Treat the record fields like the body of a function.
extract $ telFromList fields
where
-- create n variable patterns
mkPats n = map' mkPat <$> getContextVars
mkPat (i, x) = notMasked $ VarP defaultPatternInfo $ DBPatVar (prettyShow x) i
-- | Collect calls in type signature @f : (x1:A1)...(xn:An) -> B@.
-- It is treated as if there were the additional function clauses.
-- @@
-- f = A1
-- f x1 = A2
-- f x1 x2 = A3
-- ...
-- f x1 ... xn = B
-- @@
termType :: Type -> TerM Calls
termType = return mempty
-- termType = loop 0 -- Andreas, 2019-04-10 deactivate for backwards-compatibility in 2.6.0 #1556
where
loop n t = do
ps <- mkPats n
reportSDoc "term.type" 60 $ vcat
[ text $ "termType " ++ show n ++ " with " ++ show (length ps) ++ " patterns"
, nest 2 $ "looking at type " <+> prettyTCM t
]
tel <- getContextTelescope -- Andreas, 2018-11-15, issue #3394, forgotten initialization of terSizeDepth
terSetPatterns ps $ terSetSizeDepth tel $ do
ifNotPiType t {-then-} extract {-else-} $ \ dom absB -> do
extract dom `mappend` underAbstractionAbs dom absB (loop $! n + 1)
-- create n variable patterns
mkPats n = map' mkPat <$> getContextVars
mkPat (i, x) = notMasked $ VarP defaultPatternInfo $ DBPatVar (prettyShow x) i
-- | Mask the result for termination checking according to type of function.
-- (Masking for arguments is handled per-clause in 'termClause'.)
setResultMask :: Type -> TerM a -> TerM a
setResultMask t cont = do
d <- liftTCM $ do
TelV tel core <- telViewPath t
d <- addContext tel $ isNothing <.> isDataOrRecord . unEl $ core
when d $
reportSLn "term.mask" 20 $ "result type is not data or record type, ignoring guardedness for --without-K"
return d
terSetMaskResult d cont
-- | Precompute the argument masks for a @(name, [projection])@ pair. Strips
-- and classifies the leading Π-arguments (which occupy the argument-pattern
-- slots reached before the next projection), then follows the next projection
-- in @path@ into its field type and recurses.
argumentMasksForPath :: Type -> [QName] -> TCM (ListInf.ListInf Bool)
argumentMasksForPath t path = do
TelV tel core <- telViewPath t
ds <- checkArgumentTypes tel
case path of
[] -> return (ListInf.pad ds True)
(d : path') -> addContext tel $ reduce core >>= getDefType d >>= \case
Just projTy -> reduce projTy >>= \case
El _ (Pi dom b) -> underAbstraction dom b $ \ft -> do
-- Projection patterns occupy one slot in the clause pattern list, but
-- should always be considered unmasked. Hence the @False@:
rest <- argumentMasksForPath ft path'
return $ ListInf.append ds (False :< rest)
_ -> return (ListInf.pad ds True)
Nothing -> return (ListInf.pad ds True)
where
checkArgumentTypes :: Telescope -> TCM [Bool]
checkArgumentTypes EmptyTel = return []
checkArgumentTypes (ExtendTel dom atel) = do
TelV tel2 t <- telViewPath $ unDom dom
d <- addContext tel2 $
(isNothing <$> isDataOrRecord (unEl t)) `or2M` (isJust <$> isSizeType t)
when d $
reportSDoc "term.mask" 20 $ do
"argument type "
<+> prettyTCM t
<+> " is not data or record type, ignoring structural descent for --without-K"
underAbstraction dom atel $ \tel -> (d:) <$> checkArgumentTypes tel
-- | Is the current target type among the given ones?
targetElem :: [QName] -> TerM Bool
targetElem ds = terGetTarget <&> \case
TargetDef d -> d `elem` ds
TargetRecord -> False
TargetOther -> False
-- | Convert a term (from a dot pattern) to a pattern for the purposes of the termination checker.
--
-- @SIZESUC@ is treated as a constructor.
class TermToPattern a b where
termToPattern :: a -> TerM b
-- UNUSED default instances (Andreas, 2026-08-29):
-- default termToPattern :: (TermToPattern a' b', Traversable f, a ~ f a', b ~ f b') => a -> TerM b
-- termToPattern = traverse termToPattern
-- instance TermToPattern a b => TermToPattern [a] [b] where
-- instance TermToPattern a b => TermToPattern (Arg a) (Arg b) where
-- instance TermToPattern a b => TermToPattern (Named c a) (Named c b) where
instance TermToPattern Term DeBruijnPattern where
termToPattern t = do
t <- constructorForm =<< reduce t
let
-- Andrea: 22/04/2020.
-- With cubical we will always have a clause where the dot
-- patterns are instead replaced with a variable, so they
-- cannot be relied on for termination.
-- See issue #4606 for a counterexample involving HITs.
--
-- Without the presence of HITs I conjecture that dot patterns
-- could be turned into actual splits, because no-confusion
-- would make the other cases impossible, so I do not disable
-- this for --without-K entirely.
--
-- Szumi, 2025-03-11:
-- Instead of completely turning off dot-pattern termination for cubical,
-- it should be enough to only ignore constructors of HITs in dot patterns.
-- This way, the issues #5953 and #4725 are also avoided.
ifNotConsOfHIT :: ConHead -> TerM DeBruijnPattern -> TerM DeBruijnPattern
ifNotConsOfHIT c = ifM (consOfHIT (conName c)) fallback
-- Andreas, 2025-11-20, issue #8212
-- Reduce constructor to their original form
-- as this also happens in the call arguments.
fallback :: TerM DeBruijnPattern
fallback = dotP <$> do reduceCon t
case t of
-- Constructors.
Con c _ args -> ifNotConsOfHIT c $
ConP c noConPatternInfo . map' (fmap unnamed) <$> mapM argToPattern (mustAllApplyElims args)
Def s [Apply arg] -> do
suc <- terGetSizeSuc
if Just s == suc then ConP (ConHead s IsData Inductive NotHIT []) noConPatternInfo . singleton . fmap unnamed <$> argToPattern arg
else fallback
-- Leaves.
-- Any (not coinductively) projected variable becomes a variable pattern.
Var i es -> case mapM isProjElim es of
Just oxs -> foldMap (All <.> isProjectionButNotCoinductive . snd) oxs >>= \case
All True -> varP . (`DBPatVar` i) . prettyShow <$> nameOfBV i
_ -> fallback
_ -> fallback
Lit l -> return $ litP l
Dummy s _ -> __IMPOSSIBLE_VERBOSE__ (show s)
Def{} -> fallback
Lam{} -> fallback
Pi{} -> fallback
Sort{} -> fallback
Level{} -> fallback
MetaV{} -> fallback
-- Andreas, 2026-08-27, going under DontCare causes issue #8699.
-- See test/Fail/Issue8699Prop.
DontCare{} -> fallback
-- | Convert an argument into a pattern, but don't descent into irrelevant (sub)terms.
-- (See issue #8699).
argToPattern :: Arg Term -> TerM (Arg DeBruijnPattern)
argToPattern arg
-- Andreas, 2026-08-29: irrelevant parts of dot patterns do not provide evidence for termination
-- since their specific form is not forced (by matches on other patterns) but arbitrary.
| isIrrelevant arg = return $ fmap dotP arg
| otherwise = traverse termToPattern arg
-- | Masks all non-data/record type patterns if --without-K.
-- See issue #1023.
maskNonDataArgs :: [DeBruijnPattern] -> TerM [Masked DeBruijnPattern]
maskNonDataArgs ps = zipWith mask ps <$> terGetMaskArgs
where
mask p@ProjP{} _ = Masked False p
mask p d = Masked d p
-- | Drop elements of the list which correspond to arguments forced by
-- the constructor with the given QName.
mapForcedArguments :: QName -> [a] -> (IsForced -> a -> Maybe b) -> TerM [b]
mapForcedArguments c xs k = do
forcedArgs <- getForcedArgs c
let go xs (p:ps) = do
let (f, xs') = nextIsForced xs
case k f p of
Just b -> b:go xs' ps
Nothing -> go xs' ps
go _ [] = []
pure $ go forcedArgs xs
-- | Extract recursive calls from one clause.
termClause :: Clause -> TerM Calls
termClause clause = do
Clause{ clauseTel = tel, namedClausePats = ps, clauseBody = body } <- snd <$> etaExpandClause clause
liftTCM $ reportSDoc "term.check.clause" 25 $ vcat
[ "termClause"
, nest 2 $ "tel =" <+> prettyTCM tel
, nest 2 $ "ps =" <+> do addContext tel $ prettyTCMPatternList ps
]
maskArgs <- do
f <- terGetCurrent
path <- liftTCM $ mapM getOriginalProjection $
mapMaybe (fmap (headAmbQ . snd) . isProjP . namedArg) ps
modeMasks <- terGetProjectedNameToMaskArgs
case Map.lookup (f, path) modeMasks of
Just m -> return m
Nothing -> terGetMaskArgs -- --with-K: map is empty; fallback is "mask nothing"
terSetMaskArgs maskArgs $ forM' body $ \ v -> addContext tel $ do
-- TODO: combine the following two traversals, avoid full normalisation.
-- Parse dot patterns as patterns as far as possible.
ps <- postTraversePatternM parseDotP ps
-- Blank out coconstructors.
ps <- preTraversePatternM stripCoCon ps
-- Mask non-data arguments.
mdbpats <- maskNonDataArgs $ map' namedArg ps
terSetPatterns mdbpats $ do
terSetSizeDepth tel $ do
reportBody v
extract v
where
parseDotP :: DeBruijnPattern -> TerM DeBruijnPattern
parseDotP = \case
DotP o t -> termToPattern t
p -> return p
stripCoCon :: DeBruijnPattern -> TerM DeBruijnPattern
stripCoCon = \case
ConP (ConHead c _ CoInductive _ _) _ _ -> return unusedVar
p -> return p
reportBody :: Term -> TerM ()
reportBody v = verboseS "term.check.clause" 6 $ do
f <- terGetCurrent
pats <- terGetPatterns
liftTCM $ reportSDoc "term.check.clause" 6 $ do
sep [ text ("termination checking clause of")
<+> prettyTCM f
, nest 2 $ "lhs:" <+> sep (map' prettyTCM pats)
, nest 2 $ "rhs:" <+> prettyTCM v
]
-- | Extract recursive calls from expressions.
class ExtractCalls a where
extract :: a -> TerM Calls
instance ExtractCalls a => ExtractCalls (Abs a) where
extract (NoAbs _ a) = extract a
extract (Abs x a) = addContext x $ terRaise $ extract a
instance ExtractCalls a => ExtractCalls (Arg a) where
extract = extract . unArg
instance ExtractCalls a => ExtractCalls (Dom a) where
extract = extract . unDom
instance ExtractCalls a => ExtractCalls (Elim' a) where
extract Proj{} = return empty
extract (Apply a) = extract $ unArg a
extract (IApply x y a) = extract (x,(y,a)) -- TODO Andrea: conservative
instance ExtractCalls a => ExtractCalls [a] where
extract = mapM' extract
instance (ExtractCalls a, ExtractCalls b) => ExtractCalls (a,b) where
extract (a, b) = CallGraph.union <$> extract a <*> extract b
instance (ExtractCalls a, ExtractCalls b, ExtractCalls c) => ExtractCalls (a,b,c) where
extract (a, b, c) = extract (a, (b, c))
-- | Sorts can contain arbitrary terms of type @Level@,
-- so look for recursive calls also in sorts.
-- Ideally, 'Sort' would not be its own datatype but just
-- a subgrammar of 'Term', then we would not need this boilerplate.
instance ExtractCalls Sort where
extract s = do
liftTCM $ do
reportSDoc "term.sort" 20 $
"extracting calls from sort" <+> prettyTCM s
reportSDoc "term.sort" 50 $
text ("s = " ++ show s)
case s of
Inf _ _ -> return empty
SizeUniv -> return empty
LockUniv -> return empty
LevelUniv -> return empty
IntervalUniv -> return empty
Univ _ t -> terUnguarded $ extract t -- no guarded levels
-- We ignore calls in the blocked dependency check (these will vanish
-- after the 'PiSort' reduces)
PiSort _c a s1 s2 -> extract (a, s1, s2)
FunSort s1 s2 -> extract (s1, s2)
UnivSort s -> extract s
MetaS x es -> return empty
DefS d es -> return empty
DummyS{} -> return empty
-- | Extract recursive calls from a type.
instance ExtractCalls Type where
extract (El s t) = extract (s, t)
instance ExtractCalls a => ExtractCalls (Tele a) where
extract = \case
EmptyTel -> mempty
ExtendTel a tel -> extract a <> extract tel
-- | Extract recursive calls from a constructor application.
constructor
:: QName
-- ^ Constructor name.
-> Induction
-- ^ Should the constructor be treated as inductive or coinductive?
-> [(Arg Term, Bool)]
-- ^ All the arguments,
-- and for every argument a boolean which is 'True' iff the
-- argument should be viewed as preserving guardedness.
-> TerM Calls
constructor c ind args = do
cutoff <- terGetCutOff
let ?cutoff = cutoff
forM' args $ \ (arg, preserves) -> do
let g' = case (preserves, ind) of
(True, Inductive) -> id
(True, CoInductive) -> (Order.lt .*.)
(False, _) -> const Order.unknown
terModifyGuarded g' $ extract arg
-- | Handles function applications @g es@.
function :: QName -> Elims -> TerM Calls
function g es0 = do
f <- terGetCurrent
names <- terGetMutual
guarded <- terGetGuarded
-- let gArgs = Def g es0
liftTCM $ reportSDoc "term.function" 30 $
"termination checking function call " <+> prettyTCM (Def g es0)
-- First, look for calls in the arguments of the call gArgs.
-- If the function is a projection but not for a coinductive record,
-- then preserve guardedness for its principal argument.
isProj <- isProjectionButNotCoinductive g
let unguards = ListInf.repeat Order.unknown
let guards = applyWhen isProj (guarded :<) unguards
-- Collect calls in the arguments of this call.
let args = map' unArg $ argsFromElims es0
calls <- forM' (zip guards args) $ \ (guard, a) -> do
terSetGuarded guard $ extract a
-- Then, consider call gArgs itself.
liftTCM $ reportSDoc "term.found.call" 20 $
sep [ "found call from" <+> prettyTCM f
, nest 2 $ "to" <+> prettyTCM g
]
-- insert this call into the call list
case Set.lookupIndex g names of
-- call leads outside the mutual block and can be ignored
Nothing -> return calls
-- call is to one of the mutally recursive functions/record
Just{} -> do
cutoff <- terGetCutOff
let ?cutoff = cutoff
-- Andreas, 2017-02-14, issue #2458:
-- If we have inlined with-functions, we could be illtyped,
-- hence, do not reduce anything.
-- Andreas, 2017-06-20 issue #2613:
-- We still need to reduce constructors, even when with-inlining happened.
es <- -- ifM terGetHaveInlinedWith (return es0) {-else-} $
liftTCM $ forM es0 $
-- 2017-09-09, re issue #2732
-- The eta-contraction that was here does not seem necessary to make structural order
-- comparison not having to worry about eta.
-- Maybe we thought an eta redex could come from a meta instantiation.
-- However, eta-contraction is already performed by instantiateFull.
-- See test/Succeed/Issue2732-termination.agda.
traverse reduceCon <=< instantiateFull
-- 2017-05-16, issue #2403: Argument normalization is too expensive,
-- even if we only expand non-recursive functions.
-- Argument normalization TURNED OFF.
-- liftTCM $ billTo [Benchmark.Termination, Benchmark.Reduce] $ do
-- -- Andreas, 2017-01-13, issue #2403, normalize arguments for the structural ordering.
-- -- Andreas, 2017-03-25, issue #2495, restrict this to non-recursive functions
-- -- otherwise, the termination checking may run forever.
-- reportSLn "term.reduce" 90 $ "normalizing call arguments"
-- modifyAllowedReductions (List.\\ [UnconfirmedReductions,RecursiveReductions]) $
-- forM es0 $ \ e -> do
-- reportSDoc "term.reduce" 95 $ "normalizing " <+> prettyTCM e
-- etaContract =<< normalise e
-- Compute the call matrix.
-- Andreas, 2014-03-26 only 6% of termination time for library test
-- spent on call matrix generation
(nrows, ncols, matrix) <- billTo [Benchmark.Termination, Benchmark.Compare] $
compareArgs es
-- Andreas, 2022-03-21, #5823:
-- If we are "calling" a record type we are guarded unless the origin
-- of the termination analysis is itself a record.
-- This is because we usually do not "unfold" record types into their
-- field telescope. We only do so when trying to construct the
-- unique inhabitant of record type (singleton analysis).
-- In the latter case, a call to a record type is not guarding.
guarded' <- isRecord g >>= \case
Just{} -> terGetTarget >>= \case
TargetRecord
-> return guarded
_ -> return (guarded .*. Order.lt)
-- guarding when we call a record and not termination checking a record
Nothing
-- only a delayed definition can be guarded
| Order.decreasing guarded
-> return Order.le
| otherwise
-> return guarded
liftTCM $ reportSLn "term.guardedness" 20 $
"composing with guardedness " ++ prettyShow guarded ++
" counting as " ++ prettyShow guarded'
let matrix' = composeGuardedness guarded' matrix
-- Andreas, 2013-04-26 FORBIDDINGLY expensive!
-- This PrettyTCM QName cost 50% of the termination time for std-lib!!
-- gPretty <-liftTCM $ billTo [Benchmark.Termination, Benchmark.Level] $
-- render <$> prettyTCM g
-- Andreas, 2013-05-19 as pointed out by Andrea Vezzosi,
-- printing the call eagerly is forbiddingly expensive.
-- So we build a closure such that we can print the call
-- whenever we really need to.
-- This saves 30s (12%) on the std-lib!
-- Andreas, 2015-01-21 Issue 1410: Go to the module where g is defined
-- otherwise its free variables with be prepended to the call
-- in the error message.
doc <- liftTCM $ withCurrentModule (qnameModule g) $ buildClosure $
Def g $ List.dropWhileEnd ((Inserted ==) . getOrigin) es0
-- Andreas, 2018-07-22, issue #3136
-- Dropping only inserted arguments at the end, since
-- dropping arguments in the middle might make the printer crash.
-- Def g $ filter ((/= Inserted) . getOrigin) es0
-- Andreas, 2017-01-05, issue #2376
-- Remove arguments inserted by etaExpandClause.
-- Issue #8596: stratify the call-graph nodes by copattern projection
-- list. The source node is the caller's (name, [projection]) tuple;
-- the target fans out to every real callee mode this call can reach
-- (those whose projection path is prefix-comparable to the call's).
srcNode <- projNode f =<< clauseProjPath
tgtNodes <- callTargetNodes g es0
let cm = makeCM ncols nrows matrix'
info = CallPath { callPathStart = f, callPathSteps = singleton $
CallInfo
{ callInfoTarget = g
, callInfoCall = doc
}}
verboseS "term.kept.call" 5 $ do
pats <- terGetPatterns
reportSDoc "term.kept.call" 5 $ vcat
[ "kept call from" <+> text (prettyShow f) <+> hsep (map' prettyTCM pats)
, nest 2 $ "to" <+> text (prettyShow g) <+>
hsep (map' (parens . prettyTCM) args)
, nest 2 $ "call matrix (with guardedness): "
, nest 2 $ pretty cm
]
return $ List.foldl' (\ cs t -> CallGraph.insert srcNode t cm info cs) calls tgtNodes
-- | The canonical leading copattern projection path of the clause currently
-- being checked.
clauseProjPath :: TerM [QName]
clauseProjPath = do
pats <- terGetPatterns
mapM getOriginalProjection $
mapMaybe (fmap (headAmbQ . snd) . isProjP . getMasked) pats
-- | Look up the call-graph node for a @(function, projection path)@ pair.
-- The pair must have been registered by 'buildNodeAndProjectionMaps'.
projNode :: QName -> [QName] -> TerM Node
projNode f path = fromMaybe __IMPOSSIBLE__ . Map.lookup (f, path) <$> terGetProjectedNameToNode
-- | Pre-compute the copattern-mode node maps for a mutual SCC.
--
-- For each function in the SCC we collect the canonical leading copattern
-- projection path of every clause, deduplicate, and assign a fresh 'Node'
-- integer to each @(function, [projection])@ pair. The resulting maps
-- are stored in 'TerEnv' before call extraction begins. The reverse map
-- is split into an @IntMap QName@ and a @Map QName [[QName]]@ because
-- 'termFunction' walks per-function, and thus only needs the names.
buildNodeAndProjectionMaps
:: Set QName
-> TCM ( Map.Map (QName, [QName]) Node
, IntMap.IntMap QName
, Map.Map QName [[QName]]
, Map.Map (QName, [QName]) (ListInf.ListInf Bool)
)
buildNodeAndProjectionMaps allNames = do
withoutK <- withoutKOption
pairs <- forM (Set.toList allNames) $ \ g -> do
def <- ignoreAbstractMode (getConstInfo g)
ms <- forM (defClauses def) $ \ cl ->
mapM getOriginalProjection $
mapMaybe (fmap (headAmbQ . snd) . isProjP . namedArg) $ namedClausePats cl
return (g, defType def, List.nub ms)
let projectionsOf (g, _, ps) = if null ps then [(g, [])] else map (g,) ps
allProjectionLists = concatMap projectionsOf pairs
projectedNameToNode = Map.fromList $ zip allProjectionLists [0..]
nodeToName = IntMap.fromList $ zip [0..] $ map fst allProjectionLists
nameToProjections = Map.fromList [ (g, if null ms then [[]] else ms) | (g, _, ms) <- pairs ]
projectedNameToMaskArgs <- if withoutK
then do
let typeOf = Map.fromList [ (g, t) | (g, t, _) <- pairs ]
Map.fromList <$> forM allProjectionLists (\ (g, path) ->
-- Andreas, 2026-08-21, issue #8674:
-- Compute the masks in the abstract/opaque mode of @g@,
-- otherwise abstract data types are invisible here (they look like axioms)
-- and their arguments get masked, destroying structural descent.
((g, path),) <$> inConcreteOrAbstractMode g \ _def ->
argumentMasksForPath (typeOf Map.! g) path)
else return Map.empty
return (projectedNameToNode, nodeToName, nameToProjections, projectedNameToMaskArgs)
-- | Two projection paths are comparable if one is a prefix of the other.
comparableProjPath :: [QName] -> [QName] -> Bool
comparableProjPath xs ys = xs `List.isPrefixOf` ys || ys `List.isPrefixOf` xs
-- | The callee nodes that a recursive call should connect to. It is not as easy
-- as just looking up the node corresponding to a name, because in the case of
-- definitions by copatterns, a call to @x .foo@ also counts as routing through
-- @x .foo .bar@, for the purpose of termination checking. So the call must be
-- "fanned out" to every callee with a comparable projection list.
callTargetNodes :: QName -> Elims -> TerM [Node]
callTargetNodes g es = do
givenProjList <- mapM getOriginalProjection [ d | Proj _ d <- es ]
knownProjLists <- Map.findWithDefault [[]] g <$> terGetNameToProjections
let comparable = filter (comparableProjPath givenProjList) knownProjLists
leaves
| null comparable = knownProjLists -- incomparable: conservatively connect to all
| otherwise = comparable
unless (leaves == [givenProjList]) $
reportSLn "term.copattern.modes" 30 $ unwords
[ "call to", prettyShow g
, "at projection path", show (map prettyShow givenProjList)
, "connects to modes", show (map (map prettyShow) leaves)
]
mapM (projNode g) leaves
-- We have to reduce constructors in case they're reexported.
-- Andreas, Issue 1530: constructors have to be reduced deep inside terms,
-- thus, we need to use traverseTermM.
reduceCon :: MonadTCM tcm => Term -> tcm Term
reduceCon = liftTCM . traverseTermM \case
Con c ci vs -> (`applyE` vs) <$> reduce (Con c ci []) -- make sure we don't reduce the arguments
t -> return t
-- | Try to get rid of a function call targeting the current SCC
-- using a non-recursive clause.
--
-- This can help copattern definitions of dependent records.
tryReduceNonRecursiveClause
:: QName -- ^ Function
-> Elims -- ^ Arguments
-> (Term -> TerM Calls) -- ^ Continue here if we managed to reduce.
-> TerM Calls -- ^ Otherwise, continue here.
-> TerM Calls
tryReduceNonRecursiveClause g es continue fallback = do
-- Andreas, 2020-02-06, re: issue #906
let v0 = Def g es
reportSDoc "term.reduce" 40 $ "Trying to reduce away call: " <+> prettyTCM v0
-- First, make sure the function is in the current SCC.
ifM (notElem g <$> terGetMutual) fallback {-else-} $ do
reportSLn "term.reduce" 40 $ "This call is in the current SCC!"
def <- getConstInfo g
-- -- Then, collect its clauses.
-- cls <- defClauses <$> getConstInfo g
-- reportSLn "term.reduce" 40 $ unwords [ "Function has", show (length cls), "clauses"]
-- reportSDoc "term.reduce" 80 $ vcat $ map (prettyTCM . NamedClause g True) cls
-- reportSLn "term.reduce" 80 . ("allowed reductions = " ++) . show . SmallSet.elems
-- =<< asksTC envAllowedReductions
-- Finally, try to reduce with the non-recursive clauses (and no rewrite rules).
r <- liftTCM $
modifyAllowedReductions (SmallSet.delete UnconfirmedReductions) $
runReduceM $ appDefE0 g def v0 [] (map' notReduced es)
case r of
NoReduction{} -> fallback
YesReduction _ v -> do
reportSDoc "term.reduce" 30 $ vcat
[ "Termination checker: Successfully reduced away call:"
, nest 2 $ prettyTCM v0
]
verboseS "term.reduce" 5 $ tick "termination-checker-reduced-nonrecursive-call"
continue v
-- | Extract recursive calls from a term.
instance ExtractCalls Term where
extract t = do
reportSDoc "term.check.term" 50 $ do
"looking for calls in" <+> prettyTCM t
-- Instantiate top-level MetaVar.
instantiate t >>= \case
-- Constructed value.
Con ConHead{conName = c, conDataRecord = dataOrRec} _ es -> do
let args = mustAllApplyElims es
-- A constructor preserves the guardedness of all its arguments.
-- Andreas, 2022-09-19, issue #6108:
-- A higher constructor does not. So check if there is an @IApply@ amoung @es@.
let noIApply = all isProperApplyElim es
let argsg = map' (,noIApply) args
-- If we encounter a coinductive record constructor
-- in a type mutual with the current target
-- then we count it as guarding.
let inductive = return Inductive -- not guarding, but preserving
coinductive = return CoInductive -- guarding
-- ♯ is guarding
ind <- ifM ((Just c ==) <$> terGetSharp) coinductive $ {-else-} do
-- data constructors are not guarding
if dataOrRec == IsData then inductive else do
-- abstract constructors are not guarding
caseMaybeM (isRecordConstructor c) inductive $ \ (q, def) -> do
reportSLn "term.check.term" 50 $ "constructor " ++ prettyShow c ++ " has record type " ++ prettyShow q
-- inductive record constructors are not guarding
if _recInduction def /= Just CoInductive then inductive else do
-- coinductive constructors unrelated to the mutually
-- constructed inhabitants of coinductive types are not guarding
ifM (targetElem . fromMaybe __IMPOSSIBLE__ $ _recMutual def)
{-then-} coinductive
{-else-} inductive
constructor c ind argsg
-- Function, data, or record type.
Def g es -> tryReduceNonRecursiveClause g es extract $ function g es
-- Abstraction. Preserves guardedness.
Lam h b -> extract b
-- Neutral term. Destroys guardedness.
Var i es -> terUnguarded $ extract es
-- Dependent function space.
Pi a (Abs x b) ->
CallGraph.union <$>
extract a <*> do
a <- maskSizeLt a -- OR: just do not add a to the context!
addContext (x, a) $ terRaise $ extract b
-- Non-dependent function space.
Pi a (NoAbs _ b) ->
CallGraph.union <$> extract a <*> extract b
-- Literal.
Lit l -> return empty
-- Sort.
Sort s -> extract s
-- Unsolved metas are not considered termination problems, there
-- will be a warning for them anyway.
MetaV x args -> return empty
-- Erased and not-yet-erased proof.
DontCare t -> extract t
-- Level.
Level l -> -- billTo [Benchmark.Termination, Benchmark.Level] $ do
-- Andreas, 2014-03-26 Benchmark discontinued, < 0.3% spent on levels.
extract l
-- Dummy.
Dummy{} -> return empty
-- | Extract recursive calls from level expressions.
instance ExtractCalls Level where
extract (Max n as) = extract as
instance ExtractCalls PlusLevel where
extract (Plus n l) = extract l
-- | Rewrite type @tel -> Size< u@ to @tel -> Size@.
maskSizeLt :: MonadTCM tcm => Dom Type -> tcm (Dom Type)
maskSizeLt !dom = liftTCM $ do
let a = unDom dom
(msize, msizelt) <- getBuiltinSize
case (msize, msizelt) of
(_ , Nothing) -> return dom
(Nothing, _) -> __IMPOSSIBLE__
(Just size, Just sizelt) -> do
TelV tel c <- telView a
case a of
El s (Def d [v]) | d == sizelt -> return $
abstract tel (El s $ Def size []) <$ dom
_ -> return dom
{- | @compareArgs es@
Compare the list of de Bruijn patterns (=parameters) @pats@
with a list of arguments @es@ and create a call maxtrix
with |es| rows and |pats| columns.
The guardedness is the number of projection patterns in @pats@
minus the number of projections in @es@.
-}
compareArgs :: [Elim] -> TerM (Int, Int, [[Order]])
compareArgs es = do
pats <- terGetPatterns
liftTCM $ reportSDoc "term.compareArgs" 90 $ vcat
[ text $ "comparing " ++ show (length es) ++ " args to " ++ show (length pats) ++ " patterns"
]
-- apats <- annotatePatsWithUseSizeLt pats
-- reportSDoc "term.compare" 20 $
-- "annotated patterns = " <+> sep (map prettyTCM apats)
-- matrix <- forM es $ \ e -> forM apats $ \ (b, p) -> terSetUseSizeLt b $ compareElim e p
matrix <- withUsableVars pats $ forM es $ \ e -> forM pats $ \ p -> compareElim e p
-- Count the number of coinductive projection(pattern)s in caller and callee.
-- Only recursive coinductive projections are eligible (Issue 1209).
projsCaller <- length <$> do
filterM (isCoinductiveProjection True) $ mapMaybe (fmap (headAmbQ . snd) . isProjP . getMasked) pats
projsCallee <- length <$> do
filterM (isCoinductiveProjection True) $ mapMaybe (fmap snd . isProjElim) es
cutoff <- terGetCutOff
let ?cutoff = cutoff
let guardedness = decr True $ projsCaller - projsCallee
liftTCM $ reportSDoc "term.guardedness" 30 $ sep
[ "compareArgs:"
, nest 2 $ text $ "projsCaller = " ++ prettyShow projsCaller
, nest 2 $ text $ "projsCallee = " ++ prettyShow projsCallee
, nest 2 $ text $ "guardedness of call: " ++ prettyShow guardedness
]
return $ addGuardedness guardedness (size es, size pats, matrix)
-- | Traverse patterns from left to right.
-- When we come to a projection pattern,
-- switch usage of SIZELT constraints:
-- on, if coinductive,
-- off, if inductive.
--
-- UNUSED
--annotatePatsWithUseSizeLt :: [DeBruijnPattern] -> TerM [(Bool,DeBruijnPattern)]
--annotatePatsWithUseSizeLt = loop where
-- loop [] = return []
-- loop (p@(ProjP _ q) : pats) = ((False,p) :) <$> do projUseSizeLt q $ loop pats
-- loop (p : pats) = (\ b ps -> (b,p) : ps) <$> terGetUseSizeLt <*> loop pats
-- | @compareElim e dbpat@
compareElim :: Elim -> Masked DeBruijnPattern -> TerM Order
compareElim e p = do
liftTCM $ do
reportSDoc "term.compare" 30 $ sep
[ "compareElim"
, nest 2 $ "e = " <> prettyTCM e
, nest 2 $ "p = " <> prettyTCM p
]
reportSDoc "term.compare" 50 $ sep
[ nest 2 $ text $ "e = " ++ show e
, nest 2 $ text $ "p = " ++ show p
]
case (e, getMasked p) of
(Proj _ d, ProjP _ d') -> do
d <- getOriginalProjection d
d' <- getOriginalProjection d'
o <- compareProj d d'
reportSDoc "term.compare" 30 $ sep
[ text $ "comparing callee projection " ++ prettyShow d
, text $ "against caller projection " ++ prettyShow d'
, text $ "yields order " ++ prettyShow o
]
return o
(Proj{}, _) -> return Order.unknown
(Apply{}, ProjP{}) -> return Order.unknown
(Apply arg, _) -> compareTerm (unArg arg) p
-- TODO Andrea: making sense?
(IApply{}, ProjP{}) -> return Order.unknown
(IApply _ _ arg, _) -> compareTerm arg p
-- | In dependent records, the types of later fields may depend on the
-- values of earlier fields. Thus when defining an inhabitant of a
-- dependent record type such as Σ by copattern matching,
-- a recursive call eliminated by an earlier projection (proj₁) might
-- occur in the definition at a later projection (proj₂).
-- Thus, earlier projections are considered "smaller" when
-- comparing copattern spines. This is an ok approximation
-- of the actual dependency order.
-- See issues 906, 942.
compareProj :: MonadTCM tcm => QName -> QName -> tcm Order
compareProj d d'
| d == d' = return Order.le
| otherwise = liftTCM $ do
-- different projections
mr <- getRecordOfField d
mr' <- getRecordOfField d'
case (mr, mr') of
(Just r, Just r') | r == r' -> do
-- of same record
def <- theDef <$> getConstInfo r
case def of
Record{ recFields = fs } -> do
fs <- return $ map' unDom fs
case (List.find (d ==) fs, List.find (d' ==) fs) of
(Just i, Just i')
-- earlier field is smaller
| i < i' -> return Order.lt
| i == i' -> do
__IMPOSSIBLE__
| otherwise -> return Order.unknown
_ -> __IMPOSSIBLE__
_ -> __IMPOSSIBLE__
_ -> return Order.unknown
-- | 'makeCM' turns the result of 'compareArgs' into a proper call matrix
makeCM :: Int -> Int -> [[Order]] -> CallMatrix
makeCM ncols nrows matrix = CallMatrix $
Matrix.fromLists (Matrix.Size nrows ncols) matrix
-- | 'addGuardedness' adds guardedness flag in the upper left corner
-- (0,0).
addGuardedness :: Order -> (Int, Int, [[Order]]) -> (Int, Int, [[Order]])
addGuardedness o (nrows, ncols, m) =
(nrows + 1, ncols + 1,
(o : replicate ncols Order.unknown) : map' (Order.unknown :) m)
-- | Compose something with the upper-left corner of a call matrix
composeGuardedness :: (?cutoff :: CutOff) => Order -> [[Order]] -> [[Order]]
composeGuardedness o ((corner : row) : rows) = ((o .*. corner) : row) : rows
composeGuardedness _ _ = __IMPOSSIBLE__
-- | Stripping off a record constructor is not counted as decrease, in
-- contrast to a data constructor.
-- A record constructor increases/decreases by 0, a data constructor by 1.
offsetFromConstructor :: HasConstInfo tcm => QName -> tcm Int
offsetFromConstructor c =
ifM (isEtaOrCoinductiveRecordConstructor c) (return 0) (return 1)
compareTerm :: Term -> Masked DeBruijnPattern -> TerM Order
compareTerm t p = do
-- reportSDoc "term.compare" 25 $
-- " comparing term " <+> prettyTCM t <+>
-- " to pattern " <+> prettyTCM p
o <- compareTerm' t =<< traverse reduceConPattern p
liftTCM $ reportSDoc "term.compare" 25 $
" comparing term " <+> prettyTCM t <+>
" to pattern " <+> prettyTCM p <+>
text (" results in " ++ prettyShow o)
return o
-- | Normalize outermost constructor name in a pattern.
{-# SPECIALIZE reduceConPattern :: DeBruijnPattern -> TerM DeBruijnPattern #-}
reduceConPattern :: MonadTCM tcm => DeBruijnPattern -> tcm DeBruijnPattern
reduceConPattern = \case
ConP c i ps -> fromRightM (\ err -> return c) (liftTCM $ getConForm $ conName c) <&> \ c' ->
ConP c' i ps
p -> return p
-- | @compareTerm' t dbpat@
--
-- Precondition: 'reduceConPattern' has been applied to the pattern.
compareTerm' :: Term -> Masked DeBruijnPattern -> TerM Order
compareTerm' v mp@(Masked m p) = do
suc <- terGetSizeSuc
cutoff <- terGetCutOff
let ?cutoff = cutoff
-- v <- liftTCM (instantiate v) -- call extraction already instantiates metas in call arguments
let fallback = return $ subTerm v p
case (v, p) of
-- Andreas, 2013-11-20 do not drop projections,
-- in any case not coinductive ones!:
-- Andreas, 2025-11-05 we may drop all eliminations that are not coinductive projections.
(Var i es, _) -> foldMap (All <.> elimNotCoinductive) es >>= \case
All True -> compareVar i mp
_ -> fallback
(DontCare t, _) ->
compareTerm' t mp
-- Andreas, 2014-09-22, issue 1281:
-- For metas, termination checking should be optimistic.
-- If there is any instance of the meta making termination
-- checking succeed, then we should not fail.
-- Thus, we assume the meta will be instantiated with the
-- deepest variable in @p@.
-- For sized types, the depth is maximally
-- the number of SIZELT hypotheses one can have in a context.
(MetaV{}, p) -> Order.decr True . max (if m then 0 else patternDepth p) . pred <$>
terAsks _terSizeDepth
-- Successor on both sides cancel each other.
-- We ignore the mask for sizes.
(Def s [Apply t], ConP s' _ [p]) | s == conName s' && Just s == suc ->
compareTerm' (unArg t) . notMasked =<< reduceConPattern (namedArg p)
-- Register also size increase.
(Def s [Apply t], p) | Just s == suc ->
-- Andreas, 2012-10-19 do not cut off here
increase 1 <$> compareTerm' (unArg t) mp
-- In all cases that do not concern sizes,
-- we cannot continue if pattern is masked.
_ | m -> return Order.unknown
(Lit l, LitP _ l')
| l == l' -> return Order.le
| otherwise -> return Order.unknown
(Lit l, _) -> do
v <- liftTCM $ constructorForm v
case v of
Lit{} -> return Order.unknown
v -> compareTerm' v mp
-- Andreas, 2011-04-19 give subterm priority over matrix order
(Con{}, ConP c _ ps) | any (isSubTerm v . namedArg) ps ->
decr True <$> offsetFromConstructor (conName c)
(Con c _ es, ConP c' _ ps) | conName c == conName c'->
let ts = mustAllApplyElims es in
compareConArgs ts ps
(Con _ _ [], _) -> return Order.le
-- new case for counting constructors / projections
-- register also increase
(Con c _ es, _) -> do
let ts = mustAllApplyElims es
increase <$> offsetFromConstructor (conName c)
<*> (infimum <$> mapM (\ t -> compareTerm' (unArg t) mp) ts)
_ -> fallback
-- | @subTerm@ computes a size difference (Order)
subTerm :: (?cutoff :: CutOff) => Term -> DeBruijnPattern -> Order
subTerm t p = if equal t p then Order.le else properSubTerm t p
where
equal (Con c _ es) (ConP c' _ ps) =
let ts = mustAllApplyElims es in
and $ (conName c == conName c')
: (length ts == length ps)
: zipWith' (\ t p -> equal (unArg t) (namedArg p)) ts ps
equal (Var i []) (VarP _ x) = i == dbPatVarIndex x
equal (Lit l) (LitP _ l') = l == l'
-- Terms.
-- Checking for identity here is very fragile.
-- However, we cannot do much more, as we are not allowed to normalize t.
-- (It might diverge, and we are just in the process of termination checking.)
equal t (DotP _ t') = t == t'
equal _ _ = False
properSubTerm t (ConP _ _ ps) =
setUsability True $ decrease 1 $ supremum $ map' (subTerm t . namedArg) ps
properSubTerm _ _ = Order.unknown
isSubTerm :: (?cutoff :: CutOff) => Term -> DeBruijnPattern -> Bool
isSubTerm t p = nonIncreasing $ subTerm t p
compareConArgs :: Args -> [NamedArg DeBruijnPattern] -> TerM Order
compareConArgs ts ps = do
cutoff <- terGetCutOff
let ?cutoff = cutoff
case compare (length ts) (length ps) of
-- We may assume |ps| >= |ts|, otherwise c ps would be of functional type
-- which is impossible.
GT -> __IMPOSSIBLE__
-- Andreas, 2022-08-31, issue #6059: doing anything smarter than
-- @unknown@ here can lead to non-termination.
LT -> return Order.unknown
EQ -> List.foldl' (Order..*.) Order.le <$>
zipWithM compareTerm' (map' unArg ts) (map' (notMasked . namedArg) ps)
-- corresponds to taking the size, not the height
-- allows examples like (x, y) < (Succ x, y)
{- version which does an "order matrix"
-- Andreas, 2013-02-18 disabled because it is unclear
-- how to scale idempotency test to matrix-shaped orders (need thinking/researcH)
-- Trigges issue 787.
(_,_) -> do -- build "call matrix"
m <- mapM (\t -> mapM (compareTerm' suc (unArg t)) ps) ts
let m2 = makeCM (length ps) (length ts) m
return $ Order.orderMat (Order.mat m2)
-}
{- version which takes height
-- if null ts then Order.Le
-- else Order.infimum (zipWith compareTerm' (map' unArg ts) ps)
-}
compareVar :: Nat -> Masked DeBruijnPattern -> TerM Order
compareVar i (Masked m p) = do
suc <- terGetSizeSuc
cutoff <- terGetCutOff
let ?cutoff = cutoff
let no = return Order.unknown
case p of
ProjP{} -> no
IApplyP _ _ _ x -> compareVarVar i (Masked m x)
LitP{} -> no
DotP{} -> no
VarP _ x -> compareVarVar i (Masked m x)
ConP s _ [p] | Just (conName s) == suc ->
setUsability True . decrease 1 <$> compareVar i (notMasked $ namedArg p)
ConP c pi ps -> if m then no else setUsability True <$> do
let
dropit Forced _ = Nothing
dropit NotForced x = Just x
ps <- ifM (optForcedArgumentRecursion <$> pragmaOptions)
{- then -} (pure ps)
{- else -} (mapForcedArguments (conName c) ps dropit)
decrease <$> offsetFromConstructor (conName c)
<*> (Order.supremum <$> mapM (compareVar i . notMasked . namedArg) ps)
DefP _ c ps -> if m then no else setUsability True <$> do
decrease <$> offsetFromConstructor c
<*> (Order.supremum <$> mapM (compareVar i . notMasked . namedArg) ps)
-- This should be fine for c == hcomp
-- | Compare two variables.
--
-- The first variable comes from a term, the second from a pattern.
compareVarVar :: Nat -> Masked DBPatVar -> TerM Order
compareVarVar i (Masked m x@(DBPatVar _ j))
| i == j = if not m then return Order.le else liftTCM $
-- If j is a size, we ignore the mask.
ifM (isJust <$> do isSizeType =<< reduce =<< typeOfBV j)
{- then -} (return Order.le)
{- else -} (return Order.unknown)
| otherwise = do
-- record usability of variable
u <- (i `VarSet.member`) <$> terGetUsableVars
-- Andreas, 2017-07-26, issue #2331.
-- The usability logic is refuted by bounded size quantification in terms.
-- Thus, it is switched off (the infrastructure remains in place for now).
if not u then return Order.unknown else do
-- Only if usable:
res <- isBounded i
case res of
BoundedNo -> return Order.unknown
BoundedLt v -> setUsability u . decrease 1 <$> compareTerm' v (Masked m $ varP x)