Agda.Termination.Monad

The monad for the termination checker.

The termination monad TerM is an extension of the type checking monad TCM by an environment with information needed by the termination checker.

Documentation

type MutualNames = [QName]

The mutual block we are checking.

The functions are numbered according to their order of appearance in this list.

type Target = QName

The target of the function we are checking.

type Guarded = Order

The current guardedness level.

data TerEnv

The termination environment.

Constructors

TerEnv

Fields

• terUseDotPatterns :: Bool

  Are we mining dot patterns to find evindence of structal descent?

• terGuardingTypeConstructors :: Bool

  Do we assume that record and data type constructors preserve guardedness?

• terInlineWithFunctions :: Bool

  Do we inline with functions to enhance termination checking of with?

• terSizeSuc :: Maybe QName

  The name of size successor, if any.

• terSharp :: Maybe QName

  The name of the delay constructor (sharp), if any.

• terCutOff :: CutOff

  Depth at which to cut off the structural order.

• terCurrent :: QName

  The name of the function we are currently checking.

• terMutual :: MutualNames

  The names of the functions in the mutual block we are checking. This includes the internally generated functions (with, extendedlambda, coinduction).

• terUserNames :: [QName]

  The list of name actually appearing in the file (abstract syntax). Excludes the internally generated functions.

• terHaveInlinedWith :: Bool

  Does the actual clause result from with-inlining? (If yes, it may be ill-typed.)

• terTarget :: Maybe Target

  Target type of the function we are currently termination checking. Only the constructors of Target are considered guarding.

• terDelayed :: Delayed

  Are we checking a delayed definition?

• terMaskArgs :: [Bool]

  Only consider the notMasked False arguments for establishing termination. See issue #1023.

• terMaskResult :: Bool

  Only consider guardedness if False (not masked).

• _terSizeDepth :: Int

  How many SIZELT relations do we have in the context (= clause telescope). Used to approximate termination for metas in call args.

• terPatterns :: MaskedDeBruijnPatterns

  The patterns of the clause we are checking.

• terPatternsRaise :: !Int

  Number of additional binders we have gone under (and consequently need to raise the patterns to compare to terms). Updated during call graph extraction, hence strict.

• terGuarded :: !Guarded

  The current guardedness status. Changes as we go deeper into the term. Updated during call graph extraction, hence strict.

• terUseSizeLt :: Bool

  When extracting usable size variables during construction of the call matrix, can we take the variable for use with SIZELT constraints from the context? Yes, if we are under an inductive constructor. No, if we are under a record constructor. (See issue #1015).

• terUsableVars :: VarSet

  Pattern variables that can be compared to argument variables using SIZELT.

defaultTerEnv :: TerEnv

An empty termination environment.

Values are set to a safe default meaning that with these initial values the termination checker will not miss termination errors it would have seen with better settings of these values.

Values that do not have a safe default are set to IMPOSSIBLE.

class (Functor m, Monad m) => MonadTer m where

Termination monad service class.

Minimal complete definition

terAsk, terLocal

Methods

terAsk :: m TerEnv

terLocal :: (TerEnv -> TerEnv) -> m a -> m a

terAsks :: (TerEnv -> a) -> m a

Instances

MonadTer TerM

Methods

terAsk :: TerM TerEnv

terLocal :: (TerEnv -> TerEnv) -> TerM a -> TerM a

terAsks :: (TerEnv -> a) -> TerM a

newtype TerM a

Termination monad.

Constructors

TerM

Fields

• terM :: ReaderT TerEnv TCM a

Instances

Monad TerM

Methods

(>>=) :: TerM a -> (a -> TerM b) -> TerM b

(>>) :: TerM a -> TerM b -> TerM b

return :: a -> TerM a

fail :: String -> TerM a

Functor TerM

Methods

fmap :: (a -> b) -> TerM a -> TerM b

(<$) :: a -> TerM b -> TerM a

Applicative TerM

Methods

pure :: a -> TerM a

(<*>) :: TerM (a -> b) -> TerM a -> TerM b

liftA2 :: (a -> b -> c) -> TerM a -> TerM b -> TerM c

(*>) :: TerM a -> TerM b -> TerM b

(<*) :: TerM a -> TerM b -> TerM a

MonadIO TerM

Methods

liftIO :: IO a -> TerM a

MonadTCM TerM

Methods

liftTCM :: TCM a -> TerM a

HasOptions TerM

Methods

pragmaOptions :: TerM PragmaOptions

commandLineOptions :: TerM CommandLineOptions

MonadDebug TerM

Methods

displayDebugMessage :: Int -> String -> TerM ()

traceDebugMessage :: Int -> String -> TerM a -> TerM a

formatDebugMessage :: VerboseKey -> Int -> TCM Doc -> TerM String

HasConstInfo TerM

Methods

getConstInfo :: QName -> TerM Definition

getConstInfo' :: QName -> TerM (Either SigError Definition)

getRewriteRulesFor :: QName -> TerM RewriteRules

MonadTer TerM

Methods

terAsk :: TerM TerEnv

terLocal :: (TerEnv -> TerEnv) -> TerM a -> TerM a

terAsks :: (TerEnv -> a) -> TerM a

MonadState TCState TerM

Methods

get :: TerM TCState

put :: TCState -> TerM ()

state :: (TCState -> (a, TCState)) -> TerM a

MonadReader TCEnv TerM

Methods

ask :: TerM TCEnv

local :: (TCEnv -> TCEnv) -> TerM a -> TerM a

reader :: (TCEnv -> a) -> TerM a

MonadError TCErr TerM

Methods

throwError :: TCErr -> TerM a

catchError :: TerM a -> (TCErr -> TerM a) -> TerM a

MonadBench Phase TerM

Methods

getBenchmark :: TerM (Benchmark Phase)

getsBenchmark :: (Benchmark Phase -> c) -> TerM c

putBenchmark :: Benchmark Phase -> TerM ()

modifyBenchmark :: (Benchmark Phase -> Benchmark Phase) -> TerM ()

finally :: TerM b -> TerM c -> TerM b

Semigroup m => Semigroup (TerM m)

Methods

(<>) :: TerM m -> TerM m -> TerM m

sconcat :: NonEmpty (TerM m) -> TerM m

stimes :: Integral b => b -> TerM m -> TerM m

(Semigroup m, Monoid m) => Monoid (TerM m)

Methods

mempty :: TerM m

mappend :: TerM m -> TerM m -> TerM m

mconcat :: [TerM m] -> TerM m

runTer :: TerEnv -> TerM a -> TCM a

Generic run method for termination monad.

runTerDefault :: TerM a -> TCM a

Run TerM computation in default environment (created from options).

Termination monad is a MonadTCM.

Modifiers and accessors for the termination environment in the monad.

terGetGuardingTypeConstructors :: TerM Bool

terGetInlineWithFunctions :: TerM Bool

terGetUseDotPatterns :: TerM Bool

terSetUseDotPatterns :: Bool -> TerM a -> TerM a

terGetSizeSuc :: TerM (Maybe QName)

terGetCurrent :: TerM QName

terSetCurrent :: QName -> TerM a -> TerM a

terGetSharp :: TerM (Maybe QName)

terGetCutOff :: TerM CutOff

terGetMutual :: TerM MutualNames

terGetUserNames :: TerM [QName]

terGetTarget :: TerM (Maybe Target)

terSetTarget :: Maybe Target -> TerM a -> TerM a

terGetHaveInlinedWith :: TerM Bool

terSetHaveInlinedWith :: TerM a -> TerM a

terGetDelayed :: TerM Delayed

terSetDelayed :: Delayed -> TerM a -> TerM a

terGetMaskArgs :: TerM [Bool]

terSetMaskArgs :: [Bool] -> TerM a -> TerM a

terGetMaskResult :: TerM Bool

terSetMaskResult :: Bool -> TerM a -> TerM a

terGetPatterns :: TerM MaskedDeBruijnPatterns

terSetPatterns :: MaskedDeBruijnPatterns -> TerM a -> TerM a

terRaise :: TerM a -> TerM a

terGetGuarded :: TerM Guarded

terModifyGuarded :: (Order -> Order) -> TerM a -> TerM a

terSetGuarded :: Order -> TerM a -> TerM a

terUnguarded :: TerM a -> TerM a

terPiGuarded :: TerM a -> TerM a

Should the codomain part of a function type preserve guardedness?

terSizeDepth :: Lens' Int TerEnv

Lens for _terSizeDepth.

terGetUsableVars :: TerM VarSet

Lens for terUsableVars.

terModifyUsableVars :: (VarSet -> VarSet) -> TerM a -> TerM a

terSetUsableVars :: VarSet -> TerM a -> TerM a

terGetUseSizeLt :: TerM Bool

Lens for terUseSizeLt.

terModifyUseSizeLt :: (Bool -> Bool) -> TerM a -> TerM a

terSetUseSizeLt :: Bool -> TerM a -> TerM a

withUsableVars :: UsableSizeVars a => a -> TerM b -> TerM b

Compute usable vars from patterns and run subcomputation.

conUseSizeLt :: QName -> TerM a -> TerM a

Set terUseSizeLt when going under constructor c.

projUseSizeLt :: QName -> TerM a -> TerM a

Set terUseSizeLt for arguments following projection q. We disregard j<i after a non-coinductive projection. However, the projection need not be recursive (Issue 1470).

isProjectionButNotCoinductive :: MonadTCM tcm => QName -> tcm Bool

For termination checking purposes flat should not be considered a projection. That is, it flat doesn't preserve either structural order or guardedness like other projections do. Andreas, 2012-06-09: the same applies to projections of recursive records.

isCoinductiveProjection :: MonadTCM tcm => Bool -> QName -> tcm Bool

Check whether a projection belongs to a coinductive record and is actually recursive. E.g. @ isCoinductiveProjection (Stream.head) = return False

isCoinductiveProjection (Stream.tail) = return True @

De Bruijn pattern stuff

patternDepth :: forall a. Pattern' a -> Int

How long is the path to the deepest atomic pattern?

unusedVar :: DeBruijnPattern

A dummy pattern used to mask a pattern that cannot be used for structural descent.

class UsableSizeVars a where

Extract variables from DeBruijnPatterns that could witness a decrease via a SIZELT constraint.

These variables must be under an inductive constructor (with no record constructor in the way), or after a coinductive projection (with no inductive one in the way).

Minimal complete definition

usableSizeVars

Methods

usableSizeVars :: a -> TerM VarSet

Instances

UsableSizeVars DeBruijnPattern

Methods

usableSizeVars :: DeBruijnPattern -> TerM VarSet

UsableSizeVars MaskedDeBruijnPatterns

Methods

usableSizeVars :: MaskedDeBruijnPatterns -> TerM VarSet

UsableSizeVars [DeBruijnPattern]

Methods

usableSizeVars :: [DeBruijnPattern] -> TerM VarSet

UsableSizeVars (Masked DeBruijnPattern)

Methods

usableSizeVars :: Masked DeBruijnPattern -> TerM VarSet

Masked patterns (which are not eligible for structural descent, only for size descent)

type MaskedDeBruijnPatterns = [Masked DeBruijnPattern]

data Masked a

Constructors

Masked

Fields

• getMask :: Bool

  True if thing not eligible for structural descent.

• getMasked :: a

  Thing.

Instances

Functor Masked

Methods

fmap :: (a -> b) -> Masked a -> Masked b

(<$) :: a -> Masked b -> Masked a

Foldable Masked

Methods

fold :: Monoid m => Masked m -> m

foldMap :: Monoid m => (a -> m) -> Masked a -> m

foldr :: (a -> b -> b) -> b -> Masked a -> b

foldr' :: (a -> b -> b) -> b -> Masked a -> b

foldl :: (b -> a -> b) -> b -> Masked a -> b

foldl' :: (b -> a -> b) -> b -> Masked a -> b

foldr1 :: (a -> a -> a) -> Masked a -> a

foldl1 :: (a -> a -> a) -> Masked a -> a

toList :: Masked a -> [a]

null :: Masked a -> Bool

length :: Masked a -> Int

elem :: Eq a => a -> Masked a -> Bool

maximum :: Ord a => Masked a -> a

minimum :: Ord a => Masked a -> a

sum :: Num a => Masked a -> a

product :: Num a => Masked a -> a

Traversable Masked

Methods

traverse :: Applicative f => (a -> f b) -> Masked a -> f (Masked b)

sequenceA :: Applicative f => Masked (f a) -> f (Masked a)

mapM :: Monad m => (a -> m b) -> Masked a -> m (Masked b)

sequence :: Monad m => Masked (m a) -> m (Masked a)

Decoration Masked

Methods

traverseF :: Functor m => (a -> m b) -> Masked a -> m (Masked b)

distributeF :: Functor m => Masked (m a) -> m (Masked a)

UsableSizeVars MaskedDeBruijnPatterns

Methods

usableSizeVars :: MaskedDeBruijnPatterns -> TerM VarSet

Eq a => Eq (Masked a)

Methods

(==) :: Masked a -> Masked a -> Bool

(/=) :: Masked a -> Masked a -> Bool

Ord a => Ord (Masked a)

Methods

compare :: Masked a -> Masked a -> Ordering

(<) :: Masked a -> Masked a -> Bool

(<=) :: Masked a -> Masked a -> Bool

(>) :: Masked a -> Masked a -> Bool

(>=) :: Masked a -> Masked a -> Bool

max :: Masked a -> Masked a -> Masked a

min :: Masked a -> Masked a -> Masked a

Show a => Show (Masked a)

Methods

showsPrec :: Int -> Masked a -> ShowS

show :: Masked a -> String

showList :: [Masked a] -> ShowS

PrettyTCM a => PrettyTCM (Masked a)

Print masked things in double parentheses.

Methods

prettyTCM :: Masked a -> TCM Doc

UsableSizeVars (Masked DeBruijnPattern)

Methods

usableSizeVars :: Masked DeBruijnPattern -> TerM VarSet

masked :: a -> Masked a

notMasked :: a -> Masked a

Call pathes

newtype CallPath

The call information is stored as free monoid over CallInfo. As long as we never look at it, only accumulate it, it does not matter whether we use Set, (nub) list, or Tree. Internally, due to lazyness, it is anyway a binary tree of mappend nodes and singleton leafs. Since we define no order on CallInfo (expensive), we cannot use a Set or nub list. Performance-wise, I could not see a difference between Set and list.

Constructors

CallPath

Fields

• callInfos :: [CallInfo]

Instances

Show CallPath

Methods

showsPrec :: Int -> CallPath -> ShowS

show :: CallPath -> String

showList :: [CallPath] -> ShowS

Semigroup CallPath

Methods

(<>) :: CallPath -> CallPath -> CallPath

sconcat :: NonEmpty CallPath -> CallPath

stimes :: Integral b => b -> CallPath -> CallPath

Monoid CallPath

Methods

mempty :: CallPath

mappend :: CallPath -> CallPath -> CallPath

mconcat :: [CallPath] -> CallPath

Pretty CallPath

Only show intermediate nodes. (Drop last CallInfo).

Methods

pretty :: CallPath -> Doc

prettyPrec :: Int -> CallPath -> Doc

prettyList :: [CallPath] -> Doc

AllNames CallPath

Methods

allNames :: CallPath -> Seq QName

Size depth estimation

terSetSizeDepth :: Telescope -> TerM a -> TerM a

A very crude way of estimating the SIZELT chains i > j > k in context. Returns 3 in this case. Overapproximates.