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

Safe Haskell | None
Language | Haskell2010

Agda.TypeChecking.SizedTypes.Solve

Description

Solving size constraints under hypotheses.

The size solver proceeds as follows:

1. Get size constraints, cluster into connected components.

All size constraints that mention the same metas go into the same cluster. Each cluster can be solved by itself.

Constraints that do not fit our format are ignored. We check whether our computed solution fulfills them as well in the last step.

1. Find a joint context for each cluster.

Each constraint comes with its own typing context, which contains size hypotheses `j : Size< i`. We need to find a common super context in which all constraints of a cluster live, and raise all constraints to this context.

There might not be a common super context. Then we are screwed, since our solver is not ready to deal with such a situation. We will blatantly refuse to solve this cluster and blame it on the user.

1. Convert the joint context into a hypothesis graph.

This is straightforward. Each de Bruijn index becomes a rigid variable, each typing assumption `j : Size< i` becomes an arc.

1. Convert the constraints into a constraint graph.

Here we need to convert `MetaV`s into flexible variables.

1. Run the solver
2. Convert the solution into meta instantiations.
3. Double-check whether the constraints are solved.

Synopsis

- type CC = Closure Constraint
- data DefaultToInfty
  - = DefaultToInfty
  - | DontDefaultToInfty
- solveSizeConstraints :: DefaultToInfty -> TCM ()
- castConstraintToCurrentContext' :: Closure Constraint -> MaybeT TCM Constraint
- castConstraintToCurrentContext :: Closure Constraint -> MaybeT TCM Constraint
- solveSizeConstraints_ :: DefaultToInfty -> [CC] -> TCM (Set MetaId)
- solveCluster :: DefaultToInfty -> [(CC, HypSizeConstraint)] -> TCM ()
- getSizeHypotheses :: Context -> TCM [(CtxId, SizeConstraint)]
- canonicalizeSizeConstraint :: SizeConstraint -> Maybe SizeConstraint
- data NamedRigid = NamedRigid {
  - rigidName :: String
  - rigidIndex :: Int
  }
- data SizeMeta = SizeMeta {
  - sizeMetaId :: MetaId
  - sizeMetaArgs :: [Int]
  }
- type DBSizeExpr = SizeExpr' NamedRigid SizeMeta
- type SizeConstraint = Constraint' NamedRigid SizeMeta
- data HypSizeConstraint = HypSizeConstraint {
  - sizeContext :: Context
  - sizeHypIds :: [CtxId]
  - sizeHypotheses :: [SizeConstraint]
  - sizeConstraint :: SizeConstraint
  }
- computeSizeConstraint :: Closure Constraint -> TCM (Maybe HypSizeConstraint)
- sizeExpr :: Term -> TCM (Maybe DBSizeExpr)
- unSizeExpr :: DBSizeExpr -> TCM Term

# Documentation

type CC = Closure Constraint #

data DefaultToInfty #

Flag to control the behavior of size solver.

Constructors

DefaultToInfty | Instantiate all unconstrained size variables to ∞.
DontDefaultToInfty | Leave unconstrained size variables unsolved.

Instances

Eq DefaultToInfty # |
Methods (==) :: DefaultToInfty -> DefaultToInfty -> Bool # (/=) :: DefaultToInfty -> DefaultToInfty -> Bool #
Ord DefaultToInfty # |
Methods compare :: DefaultToInfty -> DefaultToInfty -> Ordering # (<) :: DefaultToInfty -> DefaultToInfty -> Bool # (<=) :: DefaultToInfty -> DefaultToInfty -> Bool # (>) :: DefaultToInfty -> DefaultToInfty -> Bool # (>=) :: DefaultToInfty -> DefaultToInfty -> Bool # max :: DefaultToInfty -> DefaultToInfty -> DefaultToInfty # min :: DefaultToInfty -> DefaultToInfty -> DefaultToInfty #
Show DefaultToInfty # |
Methods showsPrec :: Int -> DefaultToInfty -> ShowS # show :: DefaultToInfty -> String # showList :: [DefaultToInfty] -> ShowS #

solveSizeConstraints :: DefaultToInfty -> TCM () #

Solve size constraints involving hypotheses.

castConstraintToCurrentContext' :: Closure Constraint -> MaybeT TCM Constraint #

TODO: this does not actually work!

We would like to use a constraint `c` created in context `Δ` from module `N` in the current context `Γ` and current module `M`.

`Δ` is module tel `Δ₁` of `N` extended by some local bindings `Δ₂`. `Γ` is the current context. The module parameter substitution from current `M` to `N` be `Γ ⊢ σ : Δ₁`.

If `M == N`, we do not need the parameter substitution. We try raising.

We first strengthen `Δ ⊢ c` to live in `Δ₁` and obtain `c₁ = strengthen Δ₂ c`. We then transport `c₁` to `Γ` and obtain `c₂ = applySubst σ c₁`.

This works for different modules, but if `M == N` we should not strengthen and then weaken, because strengthening is a partial operation. We should rather lift the substitution `σ` by `Δ₂` and then raise by `Γ₂ - Δ₂`. This "raising" might be a strengthening if `Γ₂` is shorter than `Δ₂`.

(TODO: If the module substitution does not exist, because `N` is not a parent of `M`, we cannot use the constraint, as it has been created in an unrelated context.)

castConstraintToCurrentContext :: Closure Constraint -> MaybeT TCM Constraint #

A hazardous hack, may the Gods have mercy on us.

To cast to the current context, we match the context of the given constraint by `CtxId`, and as fallback, by variable name (douh!).

This hack lets issue 2046 go through.

solveSizeConstraints_ :: DefaultToInfty -> [CC] -> TCM (Set MetaId) #

Return the size metas occurring in the simplified constraints. A constraint like `↑ _j =< ∞ : Size` simplifies to nothing, so `_j` would not be in this set.

solveCluster :: DefaultToInfty -> [(CC, HypSizeConstraint)] -> TCM () #

Solve a cluster of constraints sharing some metas.

getSizeHypotheses :: Context -> TCM [(CtxId, SizeConstraint)] #

Collect constraints from a typing context, looking for SIZELT hypotheses.

canonicalizeSizeConstraint :: SizeConstraint -> Maybe SizeConstraint #

Convert size constraint into form where each meta is applied to indices `n-1,...,1,0` where `n` is the arity of that meta.

`X[σ] <= t` becomes `X[id] <= t[σ^-1]`

`X[σ] ≤ Y[τ]` becomes `X[id] ≤ Y[τ[σ^-1]]` or `X[σ[τ^1]] ≤ Y[id]` whichever is defined. If none is defined, we give up.

Cf. `SizedTypes.oldCanonicalizeSizeConstraint`.

Fixes (the rather artificial) issue 300. But it is unsound when pruned metas occur and triggers issue 1914. Thus we deactivate it. This needs to be properly implemented, possibly using the metaPermuatation of each meta variable.

data NamedRigid #

Identifiers for rigid variables.

Constructors

NamedRigid |
Fields rigidName :: String Name for printing in debug messages. rigidIndex :: Int De Bruijn index.

Instances

Eq NamedRigid # |
Methods (==) :: NamedRigid -> NamedRigid -> Bool # (/=) :: NamedRigid -> NamedRigid -> Bool #
Ord NamedRigid # |
Methods compare :: NamedRigid -> NamedRigid -> Ordering # (<) :: NamedRigid -> NamedRigid -> Bool # (<=) :: NamedRigid -> NamedRigid -> Bool # (>) :: NamedRigid -> NamedRigid -> Bool # (>=) :: NamedRigid -> NamedRigid -> Bool # max :: NamedRigid -> NamedRigid -> NamedRigid # min :: NamedRigid -> NamedRigid -> NamedRigid #
Show NamedRigid # |
Methods showsPrec :: Int -> NamedRigid -> ShowS # show :: NamedRigid -> String # showList :: [NamedRigid] -> ShowS #
PrettyTCM SizeConstraint # | Assumes we are in the right context.
Methods prettyTCM :: SizeConstraint -> TCM Doc #
Subst Term SizeConstraint # |
Methods applySubst :: Substitution' Term -> SizeConstraint -> SizeConstraint #
Plus NamedRigid Int NamedRigid # |
Methods plus :: NamedRigid -> Int -> NamedRigid #
Subst Term (SizeExpr' NamedRigid SizeMeta) # | Only for `raise`.
Methods applySubst :: Substitution' Term -> SizeExpr' NamedRigid SizeMeta -> SizeExpr' NamedRigid SizeMeta #

data SizeMeta #

Size metas in size expressions.

Constructors

SizeMeta |
Fields sizeMetaId :: MetaId sizeMetaArgs :: [Int] De Bruijn indices.

Instances

Eq SizeMeta # | An equality which ignores the meta arguments.
Methods (==) :: SizeMeta -> SizeMeta -> Bool # (/=) :: SizeMeta -> SizeMeta -> Bool #
Ord SizeMeta # | An order which ignores the meta arguments.
Methods compare :: SizeMeta -> SizeMeta -> Ordering # (<) :: SizeMeta -> SizeMeta -> Bool # (<=) :: SizeMeta -> SizeMeta -> Bool # (>) :: SizeMeta -> SizeMeta -> Bool # (>=) :: SizeMeta -> SizeMeta -> Bool # max :: SizeMeta -> SizeMeta -> SizeMeta # min :: SizeMeta -> SizeMeta -> SizeMeta #
Show SizeMeta # |
Methods showsPrec :: Int -> SizeMeta -> ShowS # show :: SizeMeta -> String # showList :: [SizeMeta] -> ShowS #
PrettyTCM SizeConstraint # | Assumes we are in the right context.
Methods prettyTCM :: SizeConstraint -> TCM Doc #
PrettyTCM SizeMeta # |
Methods prettyTCM :: SizeMeta -> TCM Doc #
Flexs SizeMeta HypSizeConstraint # |
Methods flexs :: HypSizeConstraint -> Set SizeMeta #
Subst Term SizeConstraint # |
Methods applySubst :: Substitution' Term -> SizeConstraint -> SizeConstraint #
Subst Term SizeMeta # |
Methods applySubst :: Substitution' Term -> SizeMeta -> SizeMeta #
Subst Term (SizeExpr' NamedRigid SizeMeta) # | Only for `raise`.
Methods applySubst :: Substitution' Term -> SizeExpr' NamedRigid SizeMeta -> SizeExpr' NamedRigid SizeMeta #

type DBSizeExpr = SizeExpr' NamedRigid SizeMeta #

Size expression with de Bruijn indices.

type SizeConstraint = Constraint' NamedRigid SizeMeta #

data HypSizeConstraint #

Size constraint with de Bruijn indices.

Constructors

HypSizeConstraint |
Fields sizeContext :: Context sizeHypIds :: [CtxId] sizeHypotheses :: [SizeConstraint] Living in `Context`. sizeConstraint :: SizeConstraint Living in `Context`.

Instances

PrettyTCM HypSizeConstraint # |
Methods prettyTCM :: HypSizeConstraint -> TCM Doc #
Flexs SizeMeta HypSizeConstraint # |
Methods flexs :: HypSizeConstraint -> Set SizeMeta #

computeSizeConstraint :: Closure Constraint -> TCM (Maybe HypSizeConstraint) #

Turn a constraint over de Bruijn indices into a size constraint.

sizeExpr :: Term -> TCM (Maybe DBSizeExpr) #

Turn a term into a size expression.

Returns `Nothing` if the term isn't a proper size expression.

unSizeExpr :: DBSizeExpr -> TCM Term #

Turn a de size expression into a term.