Agda.TypeChecking.Free.Old

Computing the free variables of a term.

This is the old version of 'Free', using IntSets for the separate variable categories. We keep it as a specification.

The distinction between rigid and strongly rigid occurrences comes from: Jason C. Reed, PhD thesis, 2009, page 96 (see also his LFMTP 2009 paper)

The main idea is that x = t(x) is unsolvable if x occurs strongly rigidly in t. It might have a solution if the occurrence is not strongly rigid, e.g.

x = f -> suc (f (x ( y -> k))) has x = f -> suc (f (suc k))

Jason C. Reed, PhD thesis, page 106

Under coinductive constructors, occurrences are never strongly rigid. Also, function types and lambdas do not establish strong rigidity. Only inductive constructors do so. (See issue 1271).

Documentation

data FreeVars

Free variables of a term, (disjointly) partitioned into strongly and and weakly rigid variables, flexible variables and irrelevant variables.

Constructors

FV

Fields

• stronglyRigidVars :: VarSet

  Variables under only and at least one inductive constructor(s).

• unguardedVars :: VarSet

  Variables at top or only under inductive record constructors λs and Πs. The purpose of recording these separately is that they can still become strongly rigid if put under a constructor whereas weakly rigid ones stay weakly rigid.

• weaklyRigidVars :: VarSet

  Ordinary rigid variables, e.g., in arguments of variables.

• flexibleVars :: VarSet

  Variables occuring in arguments of metas. These are only potentially free, depending how the meta variable is instantiated.

• irrelevantVars :: VarSet

  Variables in irrelevant arguments and under a DontCare, i.e., in irrelevant positions.

• unusedVars :: VarSet

  Variables in UnusedArguments.

Instances

Eq FreeVars

Methods

(==) :: FreeVars -> FreeVars -> Bool

(/=) :: FreeVars -> FreeVars -> Bool

Show FreeVars

Methods

showsPrec :: Int -> FreeVars -> ShowS

show :: FreeVars -> String

showList :: [FreeVars] -> ShowS

Semigroup FreeVars

Free variable sets form a monoid under union.

Methods

(<>) :: FreeVars -> FreeVars -> FreeVars

sconcat :: NonEmpty FreeVars -> FreeVars

stimes :: Integral b => b -> FreeVars -> FreeVars

Monoid FreeVars

Methods

mempty :: FreeVars

mappend :: FreeVars -> FreeVars -> FreeVars

mconcat :: [FreeVars] -> FreeVars

class Free a

Minimal complete definition

freeVars'

Instances

Free Clause

Methods

freeVars' :: Clause -> FreeT

Free LevelAtom

Methods

freeVars' :: LevelAtom -> FreeT

Free PlusLevel

Methods

freeVars' :: PlusLevel -> FreeT

Free Level

Methods

freeVars' :: Level -> FreeT

Free Sort

Methods

freeVars' :: Sort -> FreeT

Free Type

Methods

freeVars' :: Type -> FreeT

Free Term

Methods

freeVars' :: Term -> FreeT

Free a => Free [a]

Methods

freeVars' :: [a] -> FreeT

Free a => Free (Maybe a)

Methods

freeVars' :: Maybe a -> FreeT

Free a => Free (Dom a)

Methods

freeVars' :: Dom a -> FreeT

Free a => Free (Arg a)

Methods

freeVars' :: Arg a -> FreeT

Free a => Free (Tele a)

Methods

freeVars' :: Tele a -> FreeT

Free a => Free (Abs a)

Methods

freeVars' :: Abs a -> FreeT

Free a => Free (Elim' a)

Methods

freeVars' :: Elim' a -> FreeT

(Free a, Free b) => Free (a, b)

Methods

freeVars' :: (a, b) -> FreeT

data IgnoreSorts

Where should we skip sorts in free variable analysis?

Constructors

IgnoreNot

Do not skip.

IgnoreInAnnotations

Skip when annotation to a type.

IgnoreAll

Skip unconditionally.

Instances

Eq IgnoreSorts

Methods

(==) :: IgnoreSorts -> IgnoreSorts -> Bool

(/=) :: IgnoreSorts -> IgnoreSorts -> Bool

Show IgnoreSorts

Methods

showsPrec :: Int -> IgnoreSorts -> ShowS

show :: IgnoreSorts -> String

showList :: [IgnoreSorts] -> ShowS

freeVars :: Free a => a -> FreeVars

Doesn't go inside solved metas, but collects the variables from a metavariable application X ts as flexibleVars.

freeVarsIgnore :: Free a => IgnoreSorts -> a -> FreeVars

allVars :: FreeVars -> VarSet

allVars fv includes irrelevant variables.

relevantVars :: FreeVars -> VarSet

All but the irrelevant variables.

rigidVars :: FreeVars -> VarSet

Rigid variables: either strongly rigid, unguarded, or weakly rigid.

freeIn :: Free a => Nat -> a -> Bool

isBinderUsed :: Free a => Abs a -> Bool

Is the variable bound by the abstraction actually used?

freeInIgnoringSorts :: Free a => Nat -> a -> Bool

freeInIgnoringSortAnn :: Free a => Nat -> a -> Bool

relevantIn :: Free a => Nat -> a -> Bool

relevantInIgnoringSortAnn :: Free a => Nat -> a -> Bool

data Occurrence

Constructors

NoOccurrence

Irrelevantly

StronglyRigid

Under at least one and only inductive constructors.

Unguarded

In top position, or only under inductive record constructors.

WeaklyRigid

In arguments to variables and definitions.

Flexible

In arguments of metas.

Unused

Instances

Eq Occurrence

Methods

(==) :: Occurrence -> Occurrence -> Bool

(/=) :: Occurrence -> Occurrence -> Bool

Show Occurrence

Methods

showsPrec :: Int -> Occurrence -> ShowS

show :: Occurrence -> String

showList :: [Occurrence] -> ShowS

occurrence :: Nat -> FreeVars -> Occurrence