package fix

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fix
- Fix
  - ARRAY
  - CompactQueue
  - DATA_FLOW_GRAPH
  - DataFlow
    
    ForCustomMaps
    
    B
    
    G
    
    P
    
    V
    
    ForHashedType
    
    G
    
    P
    
    T
    
    ForIntSegment
    
    G
    
    K
    
    P
    
    ForOrderedType
    
    G
    
    P
    
    T
    
    ForType
    
    G
    
    P
    
    T
    
    Run
    
    G
    
    M
    
    P
  - Enum
  - FINITE_TYPE
  - Fix
    
    ForHashedType
    
    P
    
    T
    
    ForOrderedType
    
    P
    
    T
    
    ForType
    
    P
    
    T
    
    Make
    
    M
    
    P
  - GRAPH
  - Gensym
  - Glue
    
    ArraysAsImperativeMaps
    
    K
    
    CHAR
    
    HashTablesAsImperativeMaps
    
    H
    
    INT
    
    InjectHashedType
    
    I
    
    U
    
    InjectImperativeMaps
    
    I
    
    J
    
    M
    
    InjectMinimalImperativeMaps
    
    I
    
    M
    
    InjectOrderedType
    
    I
    
    U
    
    MinimalSemiLattice
    
    P
    
    PersistentMapsToImperativeMaps
    
    M
    
    STRING
    
    TrivialHashedType
    
    T
    
    TrivialOrderedType
    
    T
    
    WeakHashTablesAsImperativeMaps
    
    H
  - GraphNumbering
    
    ForHashedType
    
    G
    
    T
    
    ForOrderedType
    
    G
    
    T
    
    ForType
    
    G
    
    T
    
    Make
    
    G
    
    M
  - HashCons
    
    ForHashedType
    
    T
    
    ForHashedTypeWeak
    
    T
    
    Make
    
    M
    
    SERVICE
  - IMPERATIVE_MAPS
  - INJECTION
  - Indexing
    
    CARDINAL
    
    Const
    
    X
    
    Empty
    
    Gensym
    
    Index
    
    SUM
    
    Sum
    
    L
    
    R
    
    Vector
    
    Of_array
    
    A
    
    V
  - MEMOIZER
  - MINIMAL_IMPERATIVE_MAPS
  - MINIMAL_SEMI_LATTICE
  - Make
    
    M
    
    P
  - Memoize
    
    Char
    
    ForHashedType
    
    T
    
    ForOrderedType
    
    T
    
    ForType
    
    T
    
    Int
    
    Make
    
    M
    
    String
  - Minimize
    
    DFA
    
    Minimize
    
    A
    
    Label
  - NUMBERING
  - Numbering
    
    ForHashedType
    
    Done
    
    T
    
    ForOrderedType
    
    Done
    
    T
    
    ForType
    
    Done
    
    T
    
    Make
    
    Done
    
    M
  - ONGOING_NUMBERING
  - PERSISTENT_MAPS
  - PROPERTY
  - Partition
  - Prop
    
    Boolean
    
    Option
    
    X
    
    Set
    
    X
  - SEMI_LATTICE
  - SOLUTION
  - SOLVER
  - TABULATOR
  - TWO_PHASE_NUMBERING
    
    Done
  - TYPE
  - Tabulate
    
    ForHashedType
    
    F
    
    T
    
    ForIntSegment
    
    K
    
    ForOrderedType
    
    F
    
    T
    
    ForType
    
    F
    
    Make
    
    F
    
    M

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This module performs a forward data flow analysis over a (possibly cyclic) directed graph. Like Fix.Fix, it computes the least function of type variable -> property that satisfies a fixed point equation. It is less widely applicable than Fix.Fix, but, when it is applicable, it can be both easier to use and more efficient. It does not perform dynamic dependency discovery. The submodule Fix.DataFlow.ForCustomMaps is particularly tuned for performance.

module Run (M : sig ... end) (P : sig ... end) (G : sig ... end) : sig ... end

Run requires a type variable that is equipped with an implementation of imperative maps, a type property that is equipped with leq and join functions, and a data flow graph whose edges describe the propagation of properties. It performs a forward data flow analysis and returns its result.

module ForOrderedType
  (T : Map.OrderedType)
  (P : sig ... end)
  (G : sig ... end) : 
  sig ... end

ForOrderedType is a special case of Run where it suffices to pass an ordered type T as an argument. A reference to a persistent map is used to hold the memoization table.

module ForHashedType
  (T : Hashtbl.HashedType)
  (P : sig ... end)
  (G : sig ... end) : 
  sig ... end

ForHashedType is a special case of Run where it suffices to pass a hashed type T as an argument. A hash table is used to hold the memoization table.

module ForType
  (T : sig ... end)
  (P : sig ... end)
  (G : sig ... end) : 
  sig ... end

ForType is a special case of Run where it suffices to pass an arbitrary type T as an argument. A hash table is used to hold the memoization table. OCaml's built-in generic equality and hash functions are used.

module ForIntSegment
  (K : sig ... end)
  (P : sig ... end)
  (G : sig ... end) : 
  sig ... end

ForIntSegment is a special case of Run where the type of variables is the integer segment [0..n). An array is used to hold the table.

module ForCustomMaps
  (P : sig ... end)
  (G : sig ... end)
  (V : sig ... end)
  (B : sig ... end) : 
  sig ... end

ForCustomMaps is a forward data flow analysis that is tuned for greater performance. It internally relies on CompactQueue, instead of Queue. Furthermore, instead of relying on a full-fledged implementation of maps as described by MINIMAL_IMPERATIVE_MAPS, it expects the user to create and initialize two maps V and B that satisfy the signature ARRAY. This typically allows the user to choose an efficient, specialized data representation.