Agda-2.4.0.2: A dependently typed functional programming language and proof assistant

Safe HaskellNone
LanguageHaskell98

Agda.TypeChecking.Positivity

Description

Check that a datatype is strictly positive.

Synopsis

Documentation

checkStrictlyPositive :: Set QName -> TCM ()

Check that the datatypes in the mutual block containing the given declarations are strictly positive.

Also add information about positivity and recursivity of records to the signature.

data OccursWhere

Description of an occurrence.

Constructors

LeftOfArrow OccursWhere 
DefArg QName Nat OccursWhere

in the nth argument of a define constant

UnderInf OccursWhere

in the principal argument of built-in ∞

VarArg OccursWhere

as an argument to a bound variable

MetaArg OccursWhere

as an argument of a metavariable

ConArgType QName OccursWhere

in the type of a constructor

IndArgType QName OccursWhere

in a datatype index of a constructor

InClause Nat OccursWhere

in the nth clause of a defined function

Matched OccursWhere

matched against in a clause of a defined function

InDefOf QName OccursWhere

in the definition of a constant

Here 
Unknown

an unknown position (treated as negative)

data Item

Constructors

AnArg Nat 
ADef QName 

Instances

onlyVarsUpTo :: Nat -> Occurrences -> Occurrences

onlyVarsUpTo n occs discards occurrences of de Bruijn index >= n.

data OccEnv

Context for computing occurrences.

Constructors

OccEnv 

Fields

vars :: [Maybe Item]

Items corresponding to the free variables.

inf :: Maybe QName

Name for ∞ builtin.

type OccM = Reader OccEnv

Monad for computing occurrences.

getOccurrences :: ComputeOccurrences a => [Maybe Item] -> a -> TCM Occurrences

Running the monad

computeOccurrences :: QName -> TCM Occurrences

Compute the occurrences in a given definition.

etaExpandClause :: Nat -> Clause -> Clause

Eta expand a clause to have the given number of variables. Warning: doesn't update telescope or permutation! This is used instead of special treatment of lambdas (which was unsound: issue 121)

data Node

Constructors

DefNode QName 
ArgNode QName Nat 

data WithNode n a

Pairing something with a node (for printing only).

Constructors

WithNode n a 

data Edge

Edge labels for the positivity graph.

Instances

Show Edge 
SemiRing Edge

These operations form a semiring if we quotient by the relation "the Occurrence components are equal".

PrettyTCM n => PrettyTCM (WithNode n Edge) 

computeEdge :: Set QName -> OccursWhere -> TCM (Node, Edge)

Given an OccursWhere computes the target node and an Edge. The first argument is the set of names in the current mutual block.