\( % cbs-katex.sty % \newcommand{\STYLE}[2]{\htmlClass{cbs-#1}{#2}} \newcommand{\DECL}[3]{\htmlId{#1:#2}{#3}} \newcommand{\REF}[3]{\href{###1:#2}{#3}} \newcommand{\HYPER}[5]{\href{#1/#2/index.html###3:#4}{#5}} % \SHADE{MATH} can be defined to produce a shaded background to highlight % inline MATH in running text: \newcommand{\SHADE}[1]{#1} % \KEY{TEXT}, \STRING{TEXT}, \ATOM{TEXT}, \LEX{TEXT} can be used in math mode: \newcommand{\KEY}[1]{\textsf{\textit{\STYLE{Key}{#1}}}} \newcommand{\STRING}[1]{\textsf{``\texttt{#1}''}} \newcommand{\ATOM}[1]{\textsf{`\texttt{#1}'}} \newcommand{\LEX}[1]{\textsf{\STYLE{Key}{`}\texttt{#1}\STYLE{Key}{'}}} % The following commands produce ASCII characters that are treated specially by LaTeX: \newcommand{\HASH}{\char`\#} \newcommand{\DOLLAR}{\char`\$} \newcommand{\PERCENT}{\char`\%} \newcommand{\AMPERSAND}{\char`\&} \newcommand{\APOSTROPHE}{\char`\'} \newcommand{\BACKSLASH}{\char`\\} \newcommand{\CARET}{\char`\^} \newcommand{\UNDERSCORE}{\char`\_} \newcommand{\GRAVE}{\char`\`} \newcommand{\LEFTBRACE}{\char`\{} \newcommand{\RIGHTBRACE}{\char`\}} \newcommand{\TILDE}{\textasciitilde} % {\char`\~} % \NAME{name} highlights the name; % \NAMEDECL{name} declares Name.name as the target of links to name; % \NAMEREF{name} links name to the target Name.name in the current file; % \NAMEHYPER{url}{file}{name} links name to Name.name at url/file/file.pdf. % Similarly for \VAR{partvariable}, \SYN{syntaxname}, \SEM{semanticsName}, % and \SECT{sectionnumber} % The kerns in \SUB and \VAR avoid overlaps with primes: \newcommand{\SUB}[1]{_{\kern-2mu\STYLE{PartVariable}{\textsf{#1}}}} % PLAIN \newcommand{\VAR}[1]{\STYLE{PartVariable}{\textsf{\textit{#1}\kern2mu}}} \newcommand{\NAME}[1]{\STYLE{Name}{\textsf{#1}}} \newcommand{\SYN}[1]{\STYLE{SyntaxName}{\textsf{#1}}} \newcommand{\SEM}[1]{\STYLE{SemanticsName}{\textsf{#1}}} \newcommand{\SECT}[1]{\STYLE{SectionNumber}{\textsf{#1}}} % DECL \newcommand{\VARDECL}[1]{\DECL{PartVariable}{#1}{\VAR{#1}}} \newcommand{\NAMEDECL}[1]{\DECL{Name}{#1}{\NAME{#1}}} \newcommand{\SYNDECL}[1]{\DECL{SyntaxName}{#1}{\SYN{#1}}} \newcommand{\SEMDECL}[1]{\DECL{SemanticsName}{#1}{\SEM{#1}}} \newcommand{\SECTDECL}[1]{\DECL{SectionNumber}{#1}{\textsf{#1}}} % REF \newcommand{\VARREF}[1]{\REF{PartVariable}{#1}{\VAR{#1}}} \newcommand{\NAMEREF}[1]{\REF{Name}{#1}{\NAME{#1}}} \newcommand{\SYNREF}[1]{\REF{SyntaxName}{#1}{\SYN{#1}}} \newcommand{\SEMREF}[1]{\REF{SemanticsName}{#1}{\SEM{#1}}} \newcommand{\SECTREF}[1]{\REF{SectionNumber}{#1}{\SECT{#1}}} % HYPER \newcommand{\VARHYPER}[3]{\HYPER{#1}{#2}{PartVariable}{#3}{\VAR{#3}}} \newcommand{\NAMEHYPER}[3]{\HYPER{#1}{#2}{Name}{#3}{\NAME{#3}}} \newcommand{\SYNHYPER}[3]{\HYPER{#1}{#2}{SyntaxName}{#3}{\SYN{#3}}} \newcommand{\SEMHYPER}[3]{\HYPER{#1}{#2}{SemanticsName}{#3}{\SEM{#3}}} \newcommand{\SECTHYPER}[3]{\HYPER{#1}{#2}{SectionNumber}{#3}{\SECT{#3}}} % \LEFTPHRASE MATH \RIGHTPHRASE produces [[ MATH ]] with proper brackets: \newcommand{\LEFTPHRASE}{\llbracket} \newcommand{\RIGHTPHRASE}{\rrbracket} % \LEFTGROUP MATH \RIGHTGROUP produces ( MATH ) where the parentheses are % highlighted the same as keywords: \newcommand{\LEFTGROUP}{\STYLE{Key}{(}} \newcommand{\RIGHTGROUP}{\STYLE{Key}{)}} % MATH\PLUS produces a superscript + % MATH\STAR produces a superscript * % MATH\QUERY produces a superscript ? \newcommand{\PLUS}{{}^{\texttt{+}}} \newcommand{\STAR}{{}^{\texttt{*}}} \newcommand{\QUERY}{{}^{\texttt{?}}} % \RULE{& PREMISE \\ & ...}{& FORMULA ... \\ & ...} produces an inference rule % with separately aligned premises and conclusion % PREMISE % ... % ----------- % FORMULA ... % ... \newcommand{\RULE}[2] {\frac{\begin{aligned}#1\end{aligned}}{\begin{aligned}#2\end{aligned}}} % \AXIOM{& FORMULA ... \\ & ...} produces an aligned formula % % FORMULA ... % ... \newcommand{\AXIOM}[1]{\begin{aligned}#1\end{aligned}} % \TO TYPE produces => TYPE \newcommand{\TO}{\mathop{\Rightarrow}} % TERM \TRANS TERM produces TERM ---> TERM \newcommand{\TRANS}{\longrightarrow} % TERM \xrightarrow{LABEL} TERM puts the label above the long arrow % \)

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

OUTLINE

$\SECT{2}$ Values

\[\KEY{Language} \quad \STRING{OCaml Light}\]

$\SECT{2}$ Values

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

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-values} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\&\quad\quad\quad \mid \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{booleans} \\&\quad\quad\quad \mid \NAMEREF{implemented-integers} \\&\quad\quad\quad \mid \NAMEREF{implemented-floats} \\&\quad\quad\quad \mid \NAMEREF{implemented-characters} \\&\quad\quad\quad \mid \NAMEREF{implemented-strings} \\&\quad\quad\quad \mid \NAMEREF{implemented-tuples} \\&\quad\quad\quad \mid \NAMEREF{implemented-lists} \\&\quad\quad\quad \mid \NAMEREF{implemented-records} \\&\quad\quad\quad \mid \NAMEREF{implemented-references} \\&\quad\quad\quad \mid \NAMEREF{implemented-vectors} \\&\quad\quad\quad \mid \NAMEREF{implemented-variants} \\&\quad\quad\quad \mid \NAMEREF{implemented-functions} \end{align*}\]

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 (…).

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-integers} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-integer}( \VAR{I} : \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers}) : \TO \NAMEREF{implemented-integers} \\&\quad \leadsto \VAR{I} \\ \KEY{Assert} \quad & \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{is-equal} ( \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null}, \\&\quad \NAMEREF{implemented-integer} ( \VAR{N} : \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{bounded-integers} ( -1073741824, 1073741823 ) ) ) \\&\quad == \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{false} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-integers-width} : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{natural-numbers} \\&\quad \leadsto 31 \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-integer-literal}( \VAR{IL} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings}) : \TO \NAMEREF{implemented-integers} \\&\quad \leadsto \NAMEREF{implemented-integer} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{decimal-natural} ( \VAR{IL} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-bit-vector}( \VAR{I} : \NAMEREF{implemented-integers}) \\&\quad : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Bits}{bit-vectors} ( \NAMEREF{implemented-integers-width} ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Bits}{integer-to-bit-vector} ( \VAR{I}, \NAMEREF{implemented-integers-width} ) \end{align*}\]

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.

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-floats} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-floats-format} : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Floats}{float-formats} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Floats}{binary64} \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-float-literal}( \VAR{FL} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{strings}) : \TO \NAMEREF{implemented-floats} \end{align*}\]

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.

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-characters} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Characters}{characters} \end{align*}\] \[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-character-points} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{bounded-integers} ( 0, 255 ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-character}( \VAR{C} : \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Characters}{characters}) : \TO \NAMEREF{implemented-characters}\QUERY \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Characters}{ascii-character} \ [ \VAR{C} ] \end{align*}\]

Character strings

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

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-strings} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{lists} ( \NAMEREF{implemented-characters} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-string}( \VAR{L} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{lists} ( \NAMEREF{implemented-characters} )) : \TO \NAMEREF{implemented-strings}\QUERY \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{when-true} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less-or-equal} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{list-elements} \ \VAR{L}, 16777211 ), \VAR{L} ) \end{align*}\]

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).

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-tuples} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuples} ( \NAMEREF{implemented-values}\STAR ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuples} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}\STAR ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-tuple}( \VAR{T} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuples} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}\STAR )) : \TO \NAMEREF{implemented-tuples}\QUERY \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{when-true} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less-or-equal} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuple-elements} \ \VAR{T}, 4194303 ), \VAR{T} ) \end{align*}\]

In OCaml Light, the unit value is represented by $\SHADE{\NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuple} ( \ )}$.

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

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-lists} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{lists} ( \NAMEREF{implemented-values} ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{lists} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-list}( \VAR{L} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{lists} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} )) : \TO \NAMEREF{implemented-lists}\QUERY \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{when-true} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less-or-equal} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Lists}{list-elements} \ \VAR{L}, 4194303 ), \VAR{L} ) \end{align*}\]

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).

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-records} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Records}{records} ( \NAMEREF{implemented-values} ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Records}{records} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-record}( \VAR{R} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Records}{records} ( \NAMEREF{implemented-values} )) : \TO \NAMEREF{implemented-records}\QUERY \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{when-true} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less-or-equal} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map-elements} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Records}{record-map} \ \VAR{R}, 4194303 ), \VAR{R} ) \end{align*}\]

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

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-references} \leadsto \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{variables} \end{align*}\]

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); (…)

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-vectors} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vectors} ( \NAMEREF{implemented-values} ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vectors} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-vector}( \VAR{V} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vectors} ( \NAMEREF{implemented-values} )) : \TO \NAMEREF{implemented-vectors}\QUERY \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{when-true} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{is-less-or-equal} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector-elements} \ \VAR{V}, 4194303 ), \VAR{V} ) \end{align*}\]

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.

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-variants} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Variants}{variants} ( \NAMEREF{implemented-values} ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Variants}{variants} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-variant}( \VAR{V} : \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Variants}{variants} ( \NAMEREF{implemented-values} )) : \TO \NAMEREF{implemented-variants} \\&\quad \leadsto \VAR{V} \end{align*}\]

Functions

Functional values are mappings from values to values.

\[\begin{align*} \KEY{Type} \quad & \NAMEDECL{implemented-functions} <: \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{functions} ( \NAMEREF{implemented-values}, \NAMEREF{implemented-values} ) \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{functions} ( \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values}, \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{values} ) \end{align*}\] \[\begin{align*} \KEY{Funcon} \quad & \NAMEDECL{implemented-function}( \VAR{F} : \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{functions} ( \NAMEREF{implemented-values}, \NAMEREF{implemented-values} )) \\&\quad : \TO \NAMEREF{implemented-functions} \\&\quad \leadsto \VAR{F} \end{align*}\]

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