Agda-2.6.0.1: A dependently typed functional programming language and proof assistant

Safe HaskellNone
LanguageHaskell2010

Agda.TypeChecking.Free.Old

Description

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).

Synopsis

Documentation

data FreeVars Source #

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.

Instances
Eq FreeVars Source # 
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Defined in Agda.TypeChecking.Free.Old

Show FreeVars Source # 
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Defined in Agda.TypeChecking.Free.Old

Semigroup FreeVars Source #

Free variable sets form a monoid under union.

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Defined in Agda.TypeChecking.Free.Old

Monoid FreeVars Source # 
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class Free a Source #

Minimal complete definition

freeVars'

Instances
Free Clause Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Clause -> FreeT

Free LevelAtom Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: LevelAtom -> FreeT

Free PlusLevel Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: PlusLevel -> FreeT

Free Level Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Level -> FreeT

Free Sort Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Sort -> FreeT

Free Type Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Type -> FreeT

Free Term Source # 
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Methods

freeVars' :: Term -> FreeT

Free a => Free [a] Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: [a] -> FreeT

Free a => Free (Maybe a) Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Maybe a -> FreeT

Free a => Free (Dom a) Source # 
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Methods

freeVars' :: Dom a -> FreeT

Free a => Free (Arg a) Source # 
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Methods

freeVars' :: Arg a -> FreeT

Free a => Free (Tele a) Source # 
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Methods

freeVars' :: Tele a -> FreeT

Free a => Free (Abs a) Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Abs a -> FreeT

Free a => Free (Elim' a) Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

freeVars' :: Elim' a -> FreeT

(Free a, Free b) => Free (a, b) Source # 
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Defined in Agda.TypeChecking.Free.Old

Methods

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

data IgnoreSorts Source #

Where should we skip sorts in free variable analysis?

Constructors

IgnoreNot

Do not skip.

IgnoreInAnnotations

Skip when annotation to a type.

IgnoreAll

Skip unconditionally.

freeVars :: Free a => a -> FreeVars Source #

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

allVars :: FreeVars -> VarSet Source #

allVars fv includes irrelevant variables.

relevantVars :: FreeVars -> VarSet Source #

All but the irrelevant variables.

rigidVars :: FreeVars -> VarSet Source #

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

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

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

Is the variable bound by the abstraction actually used?

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

data Occurrence Source #

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.

Instances
Eq Occurrence Source # 
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Defined in Agda.TypeChecking.Free.Old

Show Occurrence Source # 
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Defined in Agda.TypeChecking.Free.Old