Agda-2.5.2: A dependently typed functional programming language and proof assistant

Safe Haskell | None
Language | Haskell2010

Agda.TypeChecking.Free.Old

Description

Computing the free variables of a term.

This is the old version of '`Free'`, using `IntSet`s 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).

Synopsis

- data FreeVars = FV {
  - stronglyRigidVars :: VarSet
  - unguardedVars :: VarSet
  - weaklyRigidVars :: VarSet
  - flexibleVars :: VarSet
  - irrelevantVars :: VarSet
  - unusedVars :: VarSet
  }
- class Free a
- data IgnoreSorts
  - = IgnoreNot
  - | IgnoreInAnnotations
  - | IgnoreAll
- freeVars :: Free a => a -> FreeVars
- freeVarsIgnore :: Free a => IgnoreSorts -> a -> FreeVars
- allVars :: FreeVars -> VarSet
- relevantVars :: FreeVars -> VarSet
- rigidVars :: FreeVars -> VarSet
- freeIn :: Free a => Nat -> a -> Bool
- isBinderUsed :: Free a => Abs a -> Bool
- 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
  - = NoOccurrence
  - | Irrelevantly
  - | StronglyRigid
  - | Unguarded
  - | WeaklyRigid
  - | Flexible
  - | Unused
- occurrence :: Nat -> FreeVars -> Occurrence

# 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 `UnusedArg`uments.

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 #