Safe Haskell	None
Language	Haskell2010

Agda.TypeChecking.Rewriting.NonLinMatch

Description

Non-linear matching of the lhs of a rewrite rule against a neutral term.

Given a lhs

Δ ⊢ lhs : B

and a candidate term

Γ ⊢ t : A

we seek a substitution Γ ⊢ σ : Δ such that

Γ ⊢ B[σ] = A and Γ ⊢ lhs[σ] = t : A

Synopsis

class PatternFrom a b where
type NLM = ExceptT Blocked_ (StateT NLMState ReduceM)
data NLMState = NLMState {
- _nlmSub :: Sub
- _nlmEqs :: PostponedEquations
}
nlmSub :: Lens' Sub NLMState
nlmEqs :: Lens' PostponedEquations NLMState
liftRed :: ReduceM a -> NLM a
runNLM :: NLM () -> ReduceM (Either Blocked_ NLMState)
matchingBlocked :: Blocked_ -> NLM ()
tellSub :: Relevance -> Int -> Term -> NLM ()
tellEq :: Telescope -> Telescope -> Term -> Term -> NLM ()
type Sub = IntMap (Relevance, Term)
data PostponedEquation = PostponedEquation {
- eqFreeVars :: Telescope
- eqLhs :: Term
- eqRhs :: Term
}
type PostponedEquations = [PostponedEquation]
class Match a b where
reallyFree :: (Reduce a, Normalise a, Free a) => (Int -> Bool) -> a -> ReduceM (Either Blocked_ (Maybe a))
makeSubstitution :: Telescope -> Sub -> Substitution
checkPostponedEquations :: Substitution -> PostponedEquations -> ReduceM (Maybe Blocked_)
nonLinMatch :: Match a b => Telescope -> a -> b -> ReduceM (Either Blocked_ Substitution)
equal :: Term -> Term -> ReduceM (Maybe Blocked_)
normaliseB' :: (Reduce t, Normalise t) => t -> ReduceM (Blocked t)

Documentation

class PatternFrom a b where #

Turn a term into a non-linear pattern, treating the free variables as pattern variables. The first argument indicates the relevance we are working under: if this is Irrelevant, then we construct a pattern that never fails to match. The second argument is the number of bound variables (from pattern lambdas).

Minimal complete definition

patternFrom

Methods

patternFrom :: Relevance -> Int -> a -> TCM b #

Instances

PatternFrom Sort NLPat #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Sort -> TCM NLPat #
PatternFrom Type NLPType #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Type -> TCM NLPType #
PatternFrom Term NLPat #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Term -> TCM NLPat #
PatternFrom a b => PatternFrom [a] [b] #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> [a] -> TCM [b] #
PatternFrom a b => PatternFrom (Dom a) (Dom b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Dom a -> TCM (Dom b) #
PatternFrom a b => PatternFrom (Arg a) (Arg b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Arg a -> TCM (Arg b) #
PatternFrom a b => PatternFrom (Abs a) (Abs b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Abs a -> TCM (Abs b) #
PatternFrom a NLPat => PatternFrom (Elim' a) (Elim' NLPat) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods patternFrom :: Relevance -> Int -> Elim' a -> TCM (Elim' NLPat) #

type NLM = ExceptT Blocked_ (StateT NLMState ReduceM) #

Monad for non-linear matching.

data NLMState #

Constructors

NLMState
Fields _nlmSub :: Sub _nlmEqs :: PostponedEquations

Instances

Null NLMState #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods empty :: NLMState # null :: NLMState -> Bool #

nlmSub :: Lens' Sub NLMState #

nlmEqs :: Lens' PostponedEquations NLMState #

liftRed :: ReduceM a -> NLM a #

runNLM :: NLM () -> ReduceM (Either Blocked_ NLMState) #

matchingBlocked :: Blocked_ -> NLM () #

tellSub :: Relevance -> Int -> Term -> NLM () #

Add substitution i |-> v to result of matching.

tellEq :: Telescope -> Telescope -> Term -> Term -> NLM () #

type Sub = IntMap (Relevance, Term) #

data PostponedEquation #

Matching against a term produces a constraint which we have to verify after applying the substitution computed by matching.

Constructors

PostponedEquation
Fields eqFreeVars :: Telescope Telescope of free variables in the equation eqLhs :: Term Term from pattern, living in pattern context. eqRhs :: Term Term from scrutinee, living in context where matching was invoked.

type PostponedEquations = [PostponedEquation] #

class Match a b where #

Match a non-linear pattern against a neutral term, returning a substitution.

Minimal complete definition

match

Methods

match #

Arguments

:: Relevance	Are we currently matching in an irrelevant context?
-> Telescope	The telescope of pattern variables
-> Telescope	The telescope of lambda-bound variables
-> a	The pattern to match
-> b	The term to be matched against the pattern
-> NLM ()

Instances

Match NLPType Type #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> NLPType -> Type -> NLM () #
Match NLPat Level #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> NLPat -> Level -> NLM () #
Match NLPat Sort #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> NLPat -> Sort -> NLM () #
Match NLPat Term #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> NLPat -> Term -> NLM () #
Match a b => Match [a] [b] #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> [a] -> [b] -> NLM () #
Match a b => Match (Dom a) (Dom b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> Dom a -> Dom b -> NLM () #
Match a b => Match (Arg a) (Arg b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> Arg a -> Arg b -> NLM () #
(Match a b, Subst t1 a, Subst t2 b) => Match (Abs a) (Abs b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> Abs a -> Abs b -> NLM () #
Match a b => Match (Elim' a) (Elim' b) #
Instance details Defined in Agda.TypeChecking.Rewriting.NonLinMatch Methods match :: Relevance -> Telescope -> Telescope -> Elim' a -> Elim' b -> NLM () #

reallyFree :: (Reduce a, Normalise a, Free a) => (Int -> Bool) -> a -> ReduceM (Either Blocked_ (Maybe a)) #

makeSubstitution :: Telescope -> Sub -> Substitution #

checkPostponedEquations :: Substitution -> PostponedEquations -> ReduceM (Maybe Blocked_) #

nonLinMatch :: Match a b => Telescope -> a -> b -> ReduceM (Either Blocked_ Substitution) #

equal :: Term -> Term -> ReduceM (Maybe Blocked_) #

Untyped βη-equality, does not handle things like empty record types. Returns Nothing if the terms are equal, or `Just b` if the terms are not (where b contains information about possible metas blocking the comparison)

normaliseB' :: (Reduce t, Normalise t) => t -> ReduceM (Blocked t) #

Normalise the given term but also preserve blocking tags TODO: implement a more efficient version of this.