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

Safe Haskell | None
Language | Haskell2010

Agda.TypeChecking.SizedTypes.WarshallSolver

Contents

- Edge weights
- Edge labels
- Semiring with idempotent `+` == dioid
- Graphs
  - Nodes
  - Edges
  - Graphs
- Compute solution from constraint graph.
- Verify solution
- Tests

Synopsis

- type Graph r f a = Graph (Node r f) a
- type Edge' r f a = Edge (Node r f) a
- type Key r f = Edge' r f ()
- type Nodes r f = Nodes (Node r f)
- type LabelledEdge r f = Edge' r f Label
- src :: Edge n e -> n
- dest :: Edge n e -> n
- lookupEdge :: Ord n => Graph n e -> n -> n -> Maybe e
- graphToList :: Graph n e -> [Edge n e]
- graphFromList :: Ord n => [Edge n e] -> Graph n e
- insertEdge :: (Ord n, MeetSemiLattice e, Top e) => Edge n e -> Graph n e -> Graph n e
- outgoing :: (Ord r, Ord f) => Graph r f a -> Node r f -> [Edge' r f a]
- incoming :: (Ord r, Ord f) => Graph r f a -> Node r f -> [Edge' r f a]
- setFoldl :: (b -> a -> b) -> b -> Set a -> b
- transClos :: forall n a. (Ord n, Dioid a) => Graph n a -> Graph n a
- data Weight
  - = Offset Offset
  - | Infinity
- class Negative a where
  - negative :: a -> Bool
- data Label
  - = Label {
    - lcmp :: Cmp
    - loffset :: Offset
    }
  - | LInf
- toWeight :: Label -> Weight
- data Node rigid flex
  - = NodeZero
  - | NodeInfty
  - | NodeRigid rigid
  - | NodeFlex flex
- isFlexNode :: Node rigid flex -> Maybe flex
- isZeroNode :: Node rigid flex -> Bool
- isInftyNode :: Node rigid flex -> Bool
- nodeToSizeExpr :: Node rigid flex -> SizeExpr' rigid flex
- type Graphs r f a = [Graph r f a]
- emptyGraphs :: Graphs r f a
- mentions :: (Ord r, Ord f) => Node r f -> Graphs r f a -> (Graphs r f a, Graphs r f a)
- addEdge :: (Ord r, Ord f, MeetSemiLattice a, Top a) => Edge' r f a -> Graphs r f a -> Graphs r f a
- reflClos :: (Ord r, Ord f, Dioid a) => Set (Node r f) -> Graph r f a -> Graph r f a
- implies :: (Ord r, Ord f, Pretty r, Pretty f, Pretty a, Top a, Ord a, Negative a) => Graph r f a -> Graph r f a -> Bool
- nodeFromSizeExpr :: SizeExpr' rigid flex -> (Node rigid flex, Offset)
- edgeFromConstraint :: Constraint' rigid flex -> LabelledEdge rigid flex
- graphFromConstraints :: (Ord rigid, Ord flex) => [Constraint' rigid flex] -> Graph rigid flex Label
- graphsFromConstraints :: (Ord rigid, Ord flex) => [Constraint' rigid flex] -> Graphs rigid flex Label
- type Hyp = Constraint
- type Hyp' = Constraint'
- type HypGraph r f = Graph r f Label
- hypGraph :: (Ord rigid, Ord flex, Pretty rigid, Pretty flex) => Set rigid -> [Hyp' rigid flex] -> Either String (HypGraph rigid flex)
- hypConn :: (Ord r, Ord f) => HypGraph r f -> Node r f -> Node r f -> Label
- simplifyWithHypotheses :: (Ord rigid, Ord flex, Pretty rigid, Pretty flex) => HypGraph rigid flex -> [Constraint' rigid flex] -> Either String [Constraint' rigid flex]
- type ConGraph r f = Graph r f Label
- constraintGraph :: (Ord r, Ord f, Pretty r, Pretty f) => [Constraint' r f] -> HypGraph r f -> Either String (ConGraph r f)
- type ConGraphs r f = Graphs r f Label
- constraintGraphs :: (Ord r, Ord f, Pretty r, Pretty f) => [Constraint' r f] -> HypGraph r f -> Either String ([f], ConGraphs r f)
- infinityFlexs :: (Ord r, Ord f) => ConGraph r f -> ([f], ConGraph r f)
- class SetToInfty f a where
  - setToInfty :: [f] -> a -> a
- type Bound r f = Map f (Set (SizeExpr' r f))
- emptyBound :: Bound r f
- data Bounds r f = Bounds {
  - lowerBounds :: Bound r f
  - upperBounds :: Bound r f
  - mustBeFinite :: Set f
  }
- edgeToLowerBound :: LabelledEdge r f -> Maybe (f, SizeExpr' r f)
- edgeToUpperBound :: LabelledEdge r f -> Maybe (f, Cmp, SizeExpr' r f)
- graphToLowerBounds :: (Ord r, Ord f) => [LabelledEdge r f] -> Bound r f
- graphToUpperBounds :: (Ord r, Ord f) => [LabelledEdge r f] -> (Bound r f, Set f)
- bounds :: (Ord r, Ord f) => ConGraph r f -> Bounds r f
- smallest :: (Ord r, Ord f) => HypGraph r f -> [Node r f] -> [Node r f]
- largest :: (Ord r, Ord f) => HypGraph r f -> [Node r f] -> [Node r f]
- commonSuccs :: (Ord r, Ord f) => Graph r f a -> [Node r f] -> Map (Node r f) [Edge' r f a]
- commonPreds :: (Ord r, Ord f) => Graph r f a -> [Node r f] -> Map (Node r f) [Edge' r f a]
- lub' :: forall r f. (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> (Node r f, Offset) -> (Node r f, Offset) -> Maybe (SizeExpr' r f)
- glb' :: forall r f. (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> (Node r f, Offset) -> (Node r f, Offset) -> Maybe (SizeExpr' r f)
- lub :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> SizeExpr' r f -> SizeExpr' r f -> Maybe (SizeExpr' r f)
- glb :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> SizeExpr' r f -> SizeExpr' r f -> Maybe (SizeExpr' r f)
- findRigidBelow :: (Ord r, Ord f) => HypGraph r f -> SizeExpr' r f -> Maybe (SizeExpr' r f)
- solveGraph :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => Polarities f -> HypGraph r f -> ConGraph r f -> Either String (Solution r f)
- solveGraphs :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => Polarities f -> HypGraph r f -> ConGraphs r f -> Either String (Solution r f)
- verifySolution :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> [Constraint' r f] -> Solution r f -> Either String ()
- iterateSolver :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => Polarities f -> HypGraph r f -> [Constraint' r f] -> Solution r f -> Either String (Solution r f)
- testSuccs :: Ord f => Map (Node [Char] f) [Edge' [Char] f Label]
- testLub :: (Pretty f, Ord f, Show f) => Maybe (SizeExpr' [Char] f)

# Documentation

type Graph r f a = Graph (Node r f) a Source #

type Edge' r f a = Edge (Node r f) a Source #

type Key r f = Edge' r f () Source #

type Nodes r f = Nodes (Node r f) Source #

type LabelledEdge r f = Edge' r f Label Source #

src :: Edge n e -> n Source #

dest :: Edge n e -> n Source #

lookupEdge :: Ord n => Graph n e -> n -> n -> Maybe e Source #

graphToList :: Graph n e -> [Edge n e] Source #

graphFromList :: Ord n => [Edge n e] -> Graph n e Source #

insertEdge :: (Ord n, MeetSemiLattice e, Top e) => Edge n e -> Graph n e -> Graph n e Source #

outgoing :: (Ord r, Ord f) => Graph r f a -> Node r f -> [Edge' r f a] Source #

Compute list of edges that start in a given node.

incoming :: (Ord r, Ord f) => Graph r f a -> Node r f -> [Edge' r f a] Source #

Compute list of edges that target a given node.

Note: expensive for unidirectional graph representations.

setFoldl :: (b -> a -> b) -> b -> Set a -> b Source #

`Set.foldl` does not exist in legacy versions of the `containers` package.

transClos :: forall n a. (Ord n, Dioid a) => Graph n a -> Graph n a Source #

Floyd-Warshall algorithm.

# Edge weights

data Weight Source #

Constructors

Offset Offset |
Infinity |

Instances

Enum Weight Source # |

Instance details

Defined in Agda.TypeChecking.SizedTypes.WarshallSolver

Methods

succ :: Weight -> Weight Source #

pred :: Weight -> Weight Source #

toEnum :: Int -> Weight Source #

fromEnum :: Weight -> Int Source #

enumFrom :: Weight -> [Weight] Source #

enumFromThen :: Weight -> Weight -> [Weight] Source #

enumFromTo :: Weight -> Weight -> [Weight] Source #

enumFromThenTo :: Weight -> Weight -> Weight -> [Weight] Source #

Eq Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods (==) :: Weight -> Weight -> Bool Source # (/=) :: Weight -> Weight -> Bool Source #
Num Weight Source # | Partial implementation of `Num`.
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods (+) :: Weight -> Weight -> Weight Source # (-) :: Weight -> Weight -> Weight Source # (*) :: Weight -> Weight -> Weight Source # negate :: Weight -> Weight Source # abs :: Weight -> Weight Source # signum :: Weight -> Weight Source # fromInteger :: Integer -> Weight Source #
Ord Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods compare :: Weight -> Weight -> Ordering Source # (<) :: Weight -> Weight -> Bool Source # (<=) :: Weight -> Weight -> Bool Source # (>) :: Weight -> Weight -> Bool Source # (>=) :: Weight -> Weight -> Bool Source # max :: Weight -> Weight -> Weight Source # min :: Weight -> Weight -> Weight Source #
Show Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods showsPrec :: Int -> Weight -> ShowS Source # show :: Weight -> String Source # showList :: [Weight] -> ShowS Source #
Dioid Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods compose :: Weight -> Weight -> Weight Source # unitCompose :: Weight Source #
MeetSemiLattice Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods meet :: Weight -> Weight -> Weight Source #
Top Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods top :: Weight Source # isTop :: Weight -> Bool Source #
Pretty Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods pretty :: Weight -> Doc Source # prettyPrec :: Int -> Weight -> Doc Source # prettyList :: [Weight] -> Doc Source #
Negative Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Weight -> Bool Source #
Plus Offset Weight Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods plus :: Offset -> Weight -> Weight Source #
Plus Weight Offset Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods plus :: Weight -> Offset -> Weight Source #
Plus (SizeExpr' r f) Weight (SizeExpr' r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods plus :: SizeExpr' r f -> Weight -> SizeExpr' r f Source #

class Negative a where Source #

Test for negativity, used to detect negative cycles.

Methods

negative :: a -> Bool Source #

Instances

Negative Int Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Int -> Bool Source #
Negative Offset Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Offset -> Bool Source #
Negative Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Label -> Bool Source #
Negative Weight Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Weight -> Bool Source #
(Ord r, Ord f, Negative a) => Negative (Graphs r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Graphs r f a -> Bool Source #
Negative a => Negative (Edge' r f a) Source # | An edge is negative if its label is.
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Edge' r f a -> Bool Source #
(Ord r, Ord f, Negative a) => Negative (Graph r f a) Source # | A graph is `negative` if it contains a negative loop (diagonal edge). Makes sense on transitive graphs.
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Graph r f a -> Bool Source #

# Edge labels

data Label Source #

Going from `Lt` to `Le` is `pred`, going from `Le` to `Lt` is `succ`.

`X --(R,n)--> Y` means `X (R) Y + n`. [ ... if `n` positive and `X + (-n) (R) Y` if `n` negative. ]

Constructors

Label |

Fields

- lcmp :: Cmp
- loffset :: Offset

LInf | Nodes not connected.

Instances

Eq Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods (==) :: Label -> Label -> Bool Source # (/=) :: Label -> Label -> Bool Source #
Ord Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods compare :: Label -> Label -> Ordering Source # (<) :: Label -> Label -> Bool Source # (<=) :: Label -> Label -> Bool Source # (>) :: Label -> Label -> Bool Source # (>=) :: Label -> Label -> Bool Source # max :: Label -> Label -> Label Source # min :: Label -> Label -> Label Source #
Show Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods showsPrec :: Int -> Label -> ShowS Source # show :: Label -> String Source # showList :: [Label] -> ShowS Source #
Dioid Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods compose :: Label -> Label -> Label Source # unitCompose :: Label Source #
MeetSemiLattice Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods meet :: Label -> Label -> Label Source #
Top Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods top :: Label Source # isTop :: Label -> Bool Source #
Pretty Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods pretty :: Label -> Doc Source # prettyPrec :: Int -> Label -> Doc Source # prettyList :: [Label] -> Doc Source #
Negative Label Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Label -> Bool Source #
(Ord r, Ord f) => SetToInfty f (ConGraph r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> ConGraph r f -> ConGraph r f Source #
Plus (SizeExpr' r f) Label (SizeExpr' r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods plus :: SizeExpr' r f -> Label -> SizeExpr' r f Source #

toWeight :: Label -> Weight Source #

Convert a label to a weight, decrementing in case of `Lt`.

# Semiring with idempotent `+` == dioid

# Graphs

## Nodes

data Node rigid flex Source #

Constructors

NodeZero |
NodeInfty |
NodeRigid rigid |
NodeFlex flex |

Instances

(Ord r, Ord f) => SetToInfty f (ConGraph r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> ConGraph r f -> ConGraph r f Source #
Eq f => SetToInfty f (Node r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> Node r f -> Node r f Source #
Eq f => SetToInfty f (Edge' r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> Edge' r f a -> Edge' r f a Source #
(Eq rigid, Eq flex) => Eq (Node rigid flex) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods (==) :: Node rigid flex -> Node rigid flex -> Bool Source # (/=) :: Node rigid flex -> Node rigid flex -> Bool Source #
(Ord rigid, Ord flex) => Ord (Node rigid flex) Source # |

Instance details

Defined in Agda.TypeChecking.SizedTypes.WarshallSolver

Methods

compare :: Node rigid flex -> Node rigid flex -> Ordering Source #

(<) :: Node rigid flex -> Node rigid flex -> Bool Source #

(<=) :: Node rigid flex -> Node rigid flex -> Bool Source #

(>) :: Node rigid flex -> Node rigid flex -> Bool Source #

(>=) :: Node rigid flex -> Node rigid flex -> Bool Source #

max :: Node rigid flex -> Node rigid flex -> Node rigid flex Source #

min :: Node rigid flex -> Node rigid flex -> Node rigid flex Source #

(Show rigid, Show flex) => Show (Node rigid flex) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods showsPrec :: Int -> Node rigid flex -> ShowS Source # show :: Node rigid flex -> String Source # showList :: [Node rigid flex] -> ShowS Source #
(Pretty rigid, Pretty flex) => Pretty (Node rigid flex) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods pretty :: Node rigid flex -> Doc Source # prettyPrec :: Int -> Node rigid flex -> Doc Source # prettyList :: [Node rigid flex] -> Doc Source #
(Ord r, Ord f, Dioid a) => Dioid (Edge' r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods compose :: Edge' r f a -> Edge' r f a -> Edge' r f a Source # unitCompose :: Edge' r f a Source #
(Ord r, Ord f, MeetSemiLattice a) => MeetSemiLattice (Edge' r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods meet :: Edge' r f a -> Edge' r f a -> Edge' r f a Source #
(Ord r, Ord f, Top a) => Top (Edge' r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods top :: Edge' r f a Source # isTop :: Edge' r f a -> Bool Source #
(Ord r, Ord f, Negative a) => Negative (Graphs r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Graphs r f a -> Bool Source #
Negative a => Negative (Edge' r f a) Source # | An edge is negative if its label is.
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Edge' r f a -> Bool Source #
(Ord r, Ord f, Negative a) => Negative (Graph r f a) Source # | A graph is `negative` if it contains a negative loop (diagonal edge). Makes sense on transitive graphs.
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods negative :: Graph r f a -> Bool Source #

isFlexNode :: Node rigid flex -> Maybe flex Source #

isZeroNode :: Node rigid flex -> Bool Source #

isInftyNode :: Node rigid flex -> Bool Source #

nodeToSizeExpr :: Node rigid flex -> SizeExpr' rigid flex Source #

## Edges

## Graphs

type Graphs r f a = [Graph r f a] Source #

A graph forest.

emptyGraphs :: Graphs r f a Source #

mentions :: (Ord r, Ord f) => Node r f -> Graphs r f a -> (Graphs r f a, Graphs r f a) Source #

Split a list of graphs `gs` into those that mention node `n` and those that do not. If `n` is zero or infinity, we regard it as "not mentioned".

addEdge :: (Ord r, Ord f, MeetSemiLattice a, Top a) => Edge' r f a -> Graphs r f a -> Graphs r f a Source #

Add an edge to a graph forest. Graphs that share a node with the edge are joined.

reflClos :: (Ord r, Ord f, Dioid a) => Set (Node r f) -> Graph r f a -> Graph r f a Source #

Reflexive closure. Add edges `0 -> n -> n -> oo` for all nodes `n`.

implies :: (Ord r, Ord f, Pretty r, Pretty f, Pretty a, Top a, Ord a, Negative a) => Graph r f a -> Graph r f a -> Bool Source #

`h `implies` g` if any edge in `g` between rigids and constants is implied by a corresponding edge in `h`, which means that the edge in `g` carries at most the information of the one in `h`.

Application: Constraint implication: Constraints are compatible with hypotheses.

nodeFromSizeExpr :: SizeExpr' rigid flex -> (Node rigid flex, Offset) Source #

edgeFromConstraint :: Constraint' rigid flex -> LabelledEdge rigid flex Source #

graphFromConstraints :: (Ord rigid, Ord flex) => [Constraint' rigid flex] -> Graph rigid flex Label Source #

Build a graph from list of simplified constraints.

graphsFromConstraints :: (Ord rigid, Ord flex) => [Constraint' rigid flex] -> Graphs rigid flex Label Source #

Build a graph from list of simplified constraints.

type Hyp = Constraint Source #

type Hyp' = Constraint' Source #

type HypGraph r f = Graph r f Label Source #

hypGraph :: (Ord rigid, Ord flex, Pretty rigid, Pretty flex) => Set rigid -> [Hyp' rigid flex] -> Either String (HypGraph rigid flex) Source #

hypConn :: (Ord r, Ord f) => HypGraph r f -> Node r f -> Node r f -> Label Source #

simplifyWithHypotheses :: (Ord rigid, Ord flex, Pretty rigid, Pretty flex) => HypGraph rigid flex -> [Constraint' rigid flex] -> Either String [Constraint' rigid flex] Source #

type ConGraph r f = Graph r f Label Source #

constraintGraph :: (Ord r, Ord f, Pretty r, Pretty f) => [Constraint' r f] -> HypGraph r f -> Either String (ConGraph r f) Source #

type ConGraphs r f = Graphs r f Label Source #

constraintGraphs :: (Ord r, Ord f, Pretty r, Pretty f) => [Constraint' r f] -> HypGraph r f -> Either String ([f], ConGraphs r f) Source #

infinityFlexs :: (Ord r, Ord f) => ConGraph r f -> ([f], ConGraph r f) Source #

If we have an edge `X + n <= X` (with n >= 0), we must set `X = oo`.

class SetToInfty f a where Source #

Methods

setToInfty :: [f] -> a -> a Source #

Instances

(Ord r, Ord f) => SetToInfty f (ConGraph r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> ConGraph r f -> ConGraph r f Source #
Eq f => SetToInfty f (Node r f) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> Node r f -> Node r f Source #
Eq f => SetToInfty f (Edge' r f a) Source # |
Instance details Defined in Agda.TypeChecking.SizedTypes.WarshallSolver Methods setToInfty :: [f] -> Edge' r f a -> Edge' r f a Source #

# Compute solution from constraint graph.

type Bound r f = Map f (Set (SizeExpr' r f)) Source #

Lower or upper bound for a flexible variable

emptyBound :: Bound r f Source #

data Bounds r f Source #

Constructors

Bounds |

Fields

- lowerBounds :: Bound r f
- upperBounds :: Bound r f
- mustBeFinite :: Set f

  These metas are < ∞.

edgeToLowerBound :: LabelledEdge r f -> Maybe (f, SizeExpr' r f) Source #

Compute a lower bound for a flexible from an edge.

edgeToUpperBound :: LabelledEdge r f -> Maybe (f, Cmp, SizeExpr' r f) Source #

Compute an upper bound for a flexible from an edge.

graphToLowerBounds :: (Ord r, Ord f) => [LabelledEdge r f] -> Bound r f Source #

Compute the lower bounds for all flexibles in a graph.

graphToUpperBounds :: (Ord r, Ord f) => [LabelledEdge r f] -> (Bound r f, Set f) Source #

Compute the upper bounds for all flexibles in a graph.

bounds :: (Ord r, Ord f) => ConGraph r f -> Bounds r f Source #

Compute the bounds for all flexibles in a graph.

smallest :: (Ord r, Ord f) => HypGraph r f -> [Node r f] -> [Node r f] Source #

Compute the relative minima in a set of nodes (those that do not have a predecessor in the set).

largest :: (Ord r, Ord f) => HypGraph r f -> [Node r f] -> [Node r f] Source #

Compute the relative maxima in a set of nodes (those that do not have a successor in the set).

commonSuccs :: (Ord r, Ord f) => Graph r f a -> [Node r f] -> Map (Node r f) [Edge' r f a] Source #

Given source nodes n1,n2,... find all target nodes m1,m2, such that for all j, there are edges n_i --l_ij--> m_j for all i. Return these edges as a map from target notes to a list of edges. We assume the graph is reflexive-transitive.

commonPreds :: (Ord r, Ord f) => Graph r f a -> [Node r f] -> Map (Node r f) [Edge' r f a] Source #

Given target nodes m1,m2,... find all source nodes n1,n2, such that for all j, there are edges n_i --l_ij--> m_j for all i. Return these edges as a map from target notes to a list of edges. We assume the graph is reflexive-transitive.

lub' :: forall r f. (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> (Node r f, Offset) -> (Node r f, Offset) -> Maybe (SizeExpr' r f) Source #

Compute the sup of two different rigids or a rigid and a constant.

glb' :: forall r f. (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> (Node r f, Offset) -> (Node r f, Offset) -> Maybe (SizeExpr' r f) Source #

Compute the inf of two different rigids or a rigid and a constant.

lub :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> SizeExpr' r f -> SizeExpr' r f -> Maybe (SizeExpr' r f) Source #

Compute the least upper bound (sup).

glb :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> SizeExpr' r f -> SizeExpr' r f -> Maybe (SizeExpr' r f) Source #

Compute the greatest lower bound (inf) of size expressions relative to a hypotheses graph.

findRigidBelow :: (Ord r, Ord f) => HypGraph r f -> SizeExpr' r f -> Maybe (SizeExpr' r f) Source #

solveGraph :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => Polarities f -> HypGraph r f -> ConGraph r f -> Either String (Solution r f) Source #

solveGraphs :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => Polarities f -> HypGraph r f -> ConGraphs r f -> Either String (Solution r f) Source #

Solve a forest of constraint graphs relative to a hypotheses graph. Concatenate individual solutions.

# Verify solution

verifySolution :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) => HypGraph r f -> [Constraint' r f] -> Solution r f -> Either String () Source #

Check that after substitution of the solution, constraints are implied by hypotheses.

iterateSolver Source #

Arguments

:: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f) |
=> Polarities f | Meta variable polarities (prefer lower or upper solution?).
-> HypGraph r f | Hypotheses (assumed to have no metas, so, fixed during iteration).
-> [Constraint' r f] | Constraints to solve.
-> Solution r f | Previous substitution (already applied to constraints).
-> Either String (Solution r f) | Accumulated substition.

Iterate solver until no more metas can be solved.

This might trigger a (wanted) error on the second iteration (see Issue 2096) which would otherwise go unnoticed.

# Tests

testSuccs :: Ord f => Map (Node [Char] f) [Edge' [Char] f Label] Source #

testLub :: (Pretty f, Ord f, Show f) => Maybe (SizeExpr' [Char] f) Source #