package fix

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package fix

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
  - 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
  - MEMOIZER
  - MINIMAL_IMPERATIVE_MAPS
  - MINIMAL_SEMI_LATTICE
  - Make
    
    M
    
    P
  - Memoize
    
    Char
    
    ForHashedType
    
    T
    
    ForOrderedType
    
    T
    
    ForType
    
    T
    
    Int
    
    Make
    
    M
    
    String
  - NUMBERING
  - Numbering
    
    ForHashedType
    
    Done
    
    T
    
    ForOrderedType
    
    Done
    
    T
    
    ForType
    
    Done
    
    T
    
    Make
    
    Done
    
    M
  - ONGOING_NUMBERING
  - PERSISTENT_MAPS
  - PROPERTY
  - 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

Legend:
Library
Module
Module type
Parameter
Class
Class type

type key = int

A type of keys.

val memoize : (key -> 'a) -> key -> 'a

A memoization combinator for this type.

type 'a t

A memoization combinator where the memoization table is exposed.

val visibly_memoize : (key -> 'a) -> (key -> 'a) * 'a t

val fix : ((key -> 'a) -> key -> 'a) -> key -> 'a

A recursive memoization combinator.

exception Cycle of key list * key

defensive_fix works like fix, except it additionally detects circular dependencies, which can arise if the second-order function supplied by the user does not follow a well-founded recursion pattern. When the user invokes f x, where f is the function returned by defensive_fix, if a cyclic dependency is detected, then Cycle (zs, z) is raised, where the list zs begins with z and continues with a series of intermediate keys, leading back to z. Note that undetected divergence remains possible; this corresponds to an infinite dependency chain, without a cycle.

val defensive_fix : ((key -> 'a) -> key -> 'a) -> key -> 'a

val curried : 
  (((('a * 'b) -> 'c) -> ('a * 'b) -> 'c) -> ('a * 'b) -> 'c) ->
  (('a -> 'b -> 'c) -> 'a -> 'b -> 'c) ->
  'a ->
  'b ->
  'c

This combinator can be used to obtain a curried version of fix or defensive_fix in a concrete instance where the type key is a product type.