Safe Haskell  None 

Language  Haskell2010 
Computing the free variables of a term.
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).
Synopsis
 data FreeVars = FV {
 stronglyRigidVars :: VarSet
 unguardedVars :: VarSet
 weaklyRigidVars :: VarSet
 flexibleVars :: IntMap MetaSet
 irrelevantVars :: VarSet
 newtype VarCounts = VarCounts {}
 class Free a
 class (Semigroup a, Monoid a) => IsVarSet a where
 withVarOcc :: VarOcc > a > a
 data IgnoreSorts
 runFree :: (IsVarSet c, Free a) => SingleVar c > IgnoreSorts > a > c
 rigidVars :: FreeVars > VarSet
 relevantVars :: FreeVars > VarSet
 allVars :: FreeVars > VarSet
 allFreeVars :: Free a => a > VarSet
 allFreeVarsWithOcc :: Free a => a > TheVarMap
 allRelevantVars :: Free a => a > VarSet
 allRelevantVarsIgnoring :: Free a => IgnoreSorts > a > VarSet
 freeIn :: Free a => Nat > a > Bool
 freeInIgnoringSorts :: Free a => Nat > a > Bool
 isBinderUsed :: Free a => Abs a > Bool
 relevantIn :: Free a => Nat > a > Bool
 relevantInIgnoringSortAnn :: Free a => Nat > a > Bool
 data Occurrence
 data VarOcc = VarOcc {}
 occurrence :: Free a => Nat > a > Occurrence
 closed :: Free a => a > Bool
 freeVars :: (IsVarSet c, Singleton Variable c, Free a) => a > c
 freeVars' :: (Free a, IsVarSet c) => a > FreeM c
 type MetaSet = Set MetaId
Documentation
Free variables of a term, (disjointly) partitioned into strongly and and weakly rigid variables, flexible variables and irrelevant variables.
FV  

Gather free variables in a collection.
Instances
Free EqualityView Source #  
Defined in Agda.TypeChecking.Free.Lazy  
Free Clause Source #  
Free LevelAtom Source #  
Free PlusLevel Source #  
Free Level Source #  
Free Sort Source #  
Free Term Source #  
Free Candidate Source #  
Free NLPType Source #  
Free NLPat Source #  
Free DisplayTerm Source #  
Defined in Agda.TypeChecking.Monad.Base  
Free DisplayForm Source #  
Defined in Agda.TypeChecking.Monad.Base  
Free Constraint Source #  
Defined in Agda.TypeChecking.Monad.Base  
Free a => Free [a] Source #  
Free a => Free (Maybe a) Source #  
Free a => Free (Dom a) Source #  
Free a => Free (Arg a) Source #  
Free a => Free (Tele a) Source #  
Free a => Free (Type' a) Source #  
Free a => Free (Abs a) Source #  
Free a => Free (Elim' a) Source #  
(Free a, Free b) => Free (a, b) Source #  
class (Semigroup a, Monoid a) => IsVarSet a where Source #
Any representation of a set of variables need to be able to be modified by a variable occurrence. This is to ensure that free variable analysis is compositional. For instance, it should be possible to compute `fv (v [u/x])` from `fv v` and `fv u`.
withVarOcc :: VarOcc > a > a Source #
Laws * Respects monoid operations: ``` withVarOcc o mempty == mempty withVarOcc o (x <> y) == withVarOcc o x <> withVarOcc o y ``` * Respects VarOcc composition ``` withVarOcc (composeVarOcc o1 o2) = withVarOcc o1 . withVarOcc o2 ```
Instances
IsVarSet All Source #  
Defined in Agda.TypeChecking.Free  
IsVarSet Any Source #  
Defined in Agda.TypeChecking.Free  
IsVarSet VarMap Source #  
Defined in Agda.TypeChecking.Free.Lazy  
IsVarSet VarCounts Source #  
Defined in Agda.TypeChecking.Free  
IsVarSet FreeVars Source #  
Defined in Agda.TypeChecking.Free  
IsVarSet [Int] Source #  
Defined in Agda.TypeChecking.Free 
data IgnoreSorts Source #
Where should we skip sorts in free variable analysis?
IgnoreNot  Do not skip. 
IgnoreInAnnotations  Skip when annotation to a type. 
IgnoreAll  Skip unconditionally. 
Instances
Eq IgnoreSorts Source #  
Defined in Agda.TypeChecking.Free.Lazy (==) :: IgnoreSorts > IgnoreSorts > Bool # (/=) :: IgnoreSorts > IgnoreSorts > Bool #  
Show IgnoreSorts Source #  
Defined in Agda.TypeChecking.Free.Lazy showsPrec :: Int > IgnoreSorts > ShowS # show :: IgnoreSorts > String # showList :: [IgnoreSorts] > ShowS # 
runFree :: (IsVarSet c, Free a) => SingleVar c > IgnoreSorts > a > c Source #
Compute free variables.
rigidVars :: FreeVars > VarSet Source #
Rigid variables: either strongly rigid, unguarded, or weakly rigid.
relevantVars :: FreeVars > VarSet Source #
All but the irrelevant variables.
allFreeVars :: Free a => a > VarSet Source #
Collect all free variables.
allFreeVarsWithOcc :: Free a => a > TheVarMap Source #
Collect all free variables together with information about their occurrence.
allRelevantVars :: Free a => a > VarSet Source #
Collect all relevant free variables, excluding the "unused" ones.
allRelevantVarsIgnoring :: Free a => IgnoreSorts > a > VarSet Source #
Collect all relevant free variables, possibly ignoring sorts.
isBinderUsed :: Free a => Abs a > Bool Source #
Is the variable bound by the abstraction actually used?
data Occurrence Source #
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 MetaSet  In arguments of metas. 
Instances
Eq Occurrence Source #  
Defined in Agda.TypeChecking.Free (==) :: Occurrence > Occurrence > Bool # (/=) :: Occurrence > Occurrence > Bool #  
Show Occurrence Source #  
Defined in Agda.TypeChecking.Free showsPrec :: Int > Occurrence > ShowS # show :: Occurrence > String # showList :: [Occurrence] > ShowS # 
Occurrence of free variables is classified by several dimensions.
Currently, we have FlexRig
and Relevance
.
occurrence :: Free a => Nat > a > Occurrence Source #
Compute an occurrence of a single variable in a piece of internal syntax.
freeVars :: (IsVarSet c, Singleton Variable c, Free a) => a > c Source #
Doesn't go inside solved metas, but collects the variables from a
metavariable application X ts
as flexibleVars
.