Languages-beta : OC-L-02-Values.cbs | PRETTY | PDF

Language "OCaml Light"

2 Values

The comments below are excerpts from section 7.2 of The OCaml System, release 4.06.

// FIX-ME: Allow implementation-dependent variations

Type
  implemented-values
   ~> null-type
    | booleans
    | implemented-integers
    | implemented-floats
    | implemented-characters
    | implemented-strings
    | implemented-tuples
    | implemented-lists
    | implemented-records
    | implemented-references
    | implemented-vectors
    | implemented-variants
    | implemented-functions

Base values

Integer numbers

Integer values are integer numbers from -2^{30} to 2^{30}-1, that is -1073741824 to 1073741823. The implementation may support a wider range of integer values (…).

Type
  implemented-integers // <: integers
   ~> integers

// FIX-ME

Funcon
  implemented-integer(I:integers) : =>implemented-integers
    ~> I // FIX-ME: Two's complement, modulo 2^31
Assert
  is-equal(null,
    implemented-integer(N:bounded-integers(-1073741824,1073741823)))
    == false

Funcon
  implemented-integers-width : =>natural-numbers
   ~> 31

Funcon
  implemented-integer-literal(IL:strings) : => implemented-integers
   ~> implemented-integer decimal-natural(IL)

// FIX-ME: allow negatives

Funcon
  implemented-bit-vector(I:implemented-integers) : 
   => bit-vectors(implemented-integers-width)
   ~> integer-to-bit-vector(I, implemented-integers-width)

Floating-point numbers

Floating-point values are numbers in floating-point representation. The current implementation uses double-precision floating-point numbers conforming to the IEEE 754 standard, with 53 bits of mantissa and an exponent ranging from -1022 to 1023.

Type
  implemented-floats // ~> floats(implemented-floats-format)

Funcon
  implemented-floats-format : =>float-formats
   ~> binary64

Funcon
  implemented-float-literal(FL:strings) : =>implemented-floats

Characters

Character values are represented as 8-bit integers between 0 and 255. Character codes between 0 and 127 are interpreted following the ASCII standard. The current implementation interprets character codes between 128 and 255 following the ISO 8859-1 standard.

Type
  implemented-characters <: characters

Type
  implemented-character-points
   ~> bounded-integers(0,255)

Funcon
  implemented-character(C:characters) : =>implemented-characters?
   ~> ascii-character[C]

// FIX-ME: allow ISO-Latin-1

Character strings

String values are finite sequences of characters. The current implementation supports strings containing up to 2^24 - 5 characters (16777211 characters); (…)

Type
  implemented-strings <: lists(implemented-characters)

Funcon
  implemented-string(L:lists(implemented-characters)) : =>implemented-strings?
    ~> when-true(is-less-or-equal(length list-elements L, 16777211), L)

Tuples

Tuples of values are written (v_1, …, v_n), standing for the n-tuple of values v_1 to v_n. The current implementation supports tuples of up to 2^22 - 1 elements (4194303 elements).

Type
  implemented-tuples <: tuples(implemented-values*)
   ~> tuples(values*)

// FIX-ME: remove

Funcon
  implemented-tuple(T:tuples(values*)) : =>implemented-tuples?
    ~> when-true(is-less-or-equal(length tuple-elements T, 4194303), T)

In OCaml Light, the unit value is represented by tuple( ).

In OCaml Light, lists are written [v_1; …; v_n], and their values are represented by list values in CBS.

Type
  implemented-lists <: lists(implemented-values)
   ~> lists(values)

// FIX-ME: remove

Funcon
  implemented-list(L:lists(values)) : =>implemented-lists?
    ~> when-true(is-less-or-equal(length list-elements L, 4194303), L)

Records

Record values are labeled tuples of values. The record value written { field_1 = v_1; …; field_n = v_n } associates the value v_i to the record field field_i, for i = 1 … n. The current implementation supports records with up to 2^22 - 1 fields (4194303 fields).

Type
  implemented-records <: records(implemented-values)
   ~> records(values)

// FIX-ME: remove

Funcon
  implemented-record(R:records(implemented-values)) : =>implemented-records?
    ~> when-true(is-less-or-equal(length map-elements record-map R, 4194303), R)

In OCaml Light, records are non-mutable, and references are represented by mutable variables.

Type
  implemented-references ~> variables

Arrays

Arrays are finite, variable-sized sequences of values of the same type. The current implementation supports arrays containing up to 2^22 - 1 elements (4194303 elements) unless the elements are floating-point numbers (2097151 elements in this case); (…)

Type
  implemented-vectors <: vectors(implemented-values)
   ~> vectors(values)

// FIX-ME: remove

Funcon
  implemented-vector(V:vectors(implemented-values)) : =>implemented-vectors?
    ~> when-true(is-less-or-equal(length vector-elements V, 4194303),V)

Variant values

Variant values are either a constant constructor, or a pair of a non-constant constructor and a value. The former case is written constr; the latter case is written (v1, …, vn), where the vi are said to be the arguments of the non-constant constructor constr. The parentheses may be omitted if there is only one argument. (…) The current implementation limits each variant type to have at most 246 non-constant constructors and 2^30-1 constant constructors.

Type
  implemented-variants <: variants(implemented-values)
   ~> variants(values)

// FIX-ME: remove

Funcon
  implemented-variant(V:variants(implemented-values)) : =>implemented-variants
    ~> V

Functions

Functional values are mappings from values to values.

Type
  implemented-functions <: functions(implemented-values, implemented-values)
   ~> functions(values, values)

// FIX-ME: remove

Funcon
  implemented-function(F:functions(implemented-values, implemented-values)) : 
                                                       =>implemented-functions
    ~> F

← ↑ →