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\( % 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 : MiniJava-Dynamics.cbs | PLAIN | PDF

OUTLINE

\[\KEY{Language} \quad \STRING{MiniJava}\]

\(\SECT{1}\) Programs

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{P} : \SYNDECL{program} \ ::= \ & \ \SYNREF{main-class} \ \SYNREF{class-declaration}\STAR \\ \VARDECL{MC} : \SYNDECL{main-class} \ ::= \ & \ \LEX{class} \ \SYNREF{identifier} \ \LEX{{\LEFTBRACE}} \\ & \ \LEX{public} \ \LEX{static} \ \LEX{void} \ \LEX{main} \ \LEX{{(}} \ \LEX{String} \ \LEX{{[}} \ \LEX{{]}} \ \SYNREF{identifier} \ \LEX{{)}} \ \LEX{{\LEFTBRACE}} \\ & \ \SYNREF{statement} \\ & \ \LEX{{\RIGHTBRACE}} \\ & \ \LEX{{\RIGHTBRACE}} \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{run} \LEFTPHRASE \ \VARREF{P} : \SYNREF{program} \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\ \KEY{Rule} \quad & \SEMREF{run} \LEFTPHRASE \ \LEX{class} \ \VARREF{ID}\SUB{1} \ \LEX{{\LEFTBRACE}} \\&\quad \LEX{public} \ \LEX{static} \ \LEX{void} \ \LEX{main} \ \LEX{{(}} \ \LEX{String} \ \LEX{{[}} \ \LEX{{]}} \ \VARREF{ID}\SUB{2} \ \LEX{{)}} \ \LEX{{\LEFTBRACE}} \\&\quad \VARREF{S} \\&\quad \LEX{{\RIGHTBRACE}} \\&\quad \LEX{{\RIGHTBRACE}} \\&\quad \VARREF{CD}\STAR \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{scope} ( \\&\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{recursive} ( \SEMREF{bound-names} \LEFTPHRASE \ \VAR{CD}\STAR \ \RIGHTPHRASE , \SEMREF{declare-classes} \LEFTPHRASE \ \VAR{CD}\STAR \ \RIGHTPHRASE ), \\&\quad\quad \SEMREF{execute} \LEFTPHRASE \ \VAR{S} \ \RIGHTPHRASE ) \end{align*}\]

\(\SHADE{\VAR{ID}\SUB{1}}\) and \(\SHADE{\VAR{ID}\SUB{2}}\) are not referenced in \(\SHADE{\VAR{S}}\) or \(\SHADE{\VAR{CD}\STAR}\)

\(\SECT{2}\) Declarations

Classes

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{CD} : \SYNDECL{class-declaration} \ ::= \ & \ \LEX{class} \ \SYNREF{identifier} \ \LEFTGROUP \LEX{extends} \ \SYNREF{identifier} \RIGHTGROUP\QUERY \ \LEX{{\LEFTBRACE}} \\ & \ \SYNREF{var-declaration}\STAR \\ & \ \SYNREF{method-declaration}\STAR \\ & \ \LEX{{\RIGHTBRACE}} \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{bound-names} \LEFTPHRASE \ \VARREF{CD}\STAR : \SYNREF{class-declaration}\STAR \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sets}{sets} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{ids} ) \\ \KEY{Rule} \quad & \SEMREF{bound-names} \LEFTPHRASE \ \LEX{class} \ \VARREF{ID}\SUB{1} \ \LEX{{\LEFTBRACE}} \ \VARREF{VD}\STAR \ \VARREF{MD}\STAR \ \LEX{{\RIGHTBRACE}} \ \RIGHTPHRASE = \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{1} \ \RIGHTPHRASE \} \\ \KEY{Rule} \quad & \SEMREF{bound-names} \LEFTPHRASE \ \LEX{class} \ \VARREF{ID}\SUB{1} \ \LEX{extends} \ \VARREF{ID}\SUB{2} \ \LEX{{\LEFTBRACE}} \ \VARREF{VD}\STAR \ \VARREF{MD}\STAR \ \LEX{{\RIGHTBRACE}} \ \RIGHTPHRASE = \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{1} \ \RIGHTPHRASE \} \\ \KEY{Rule} \quad & \SEMREF{bound-names} \LEFTPHRASE \ \ \RIGHTPHRASE = \{ \ \} \\ \KEY{Rule} \quad & \SEMREF{bound-names} \LEFTPHRASE \ \VARREF{CD} \ \VARREF{CD}\PLUS \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sets}{set-unite} ( \SEMREF{bound-names} \LEFTPHRASE \ \VAR{CD} \ \RIGHTPHRASE , \SEMREF{bound-names} \LEFTPHRASE \ \VAR{CD}\PLUS \ \RIGHTPHRASE ) \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{declare-classes} \LEFTPHRASE \ \VARREF{CD}\STAR : \SYNREF{class-declaration}\STAR \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{envs} \\ \KEY{Rule} \quad & \SEMREF{declare-classes} \LEFTPHRASE \ \LEX{class} \ \VARREF{ID}\SUB{1} \ \LEX{{\LEFTBRACE}} \ \VARREF{VD}\STAR \ \VARREF{MD}\STAR \ \LEX{{\RIGHTBRACE}} \ \RIGHTPHRASE = \\&\quad \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{1} \ \RIGHTPHRASE \mapsto \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Classes}{class} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Thunks}{thunk} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Generic}{closure} \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{reference} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{object} ( \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Generating}{fresh-atom}, \\&\quad\quad\quad\quad\quad\quad \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{1} \ \RIGHTPHRASE , \\&\quad\quad\quad\quad\quad\quad \SEMREF{declare-variables} \LEFTPHRASE \ \VAR{VD}\STAR \ \RIGHTPHRASE ), \\&\quad\quad\quad\quad \SEMREF{declare-methods} \LEFTPHRASE \ \VAR{MD}\STAR \ \RIGHTPHRASE ) \} \\ \KEY{Rule} \quad & \SEMREF{declare-classes} \LEFTPHRASE \ \LEX{class} \ \VARREF{ID}\SUB{1} \ \LEX{extends} \ \VARREF{ID}\SUB{2} \ \LEX{{\LEFTBRACE}} \ \VARREF{VD}\STAR \ \VARREF{MD}\STAR \ \LEX{{\RIGHTBRACE}} \ \RIGHTPHRASE = \\&\quad \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{1} \ \RIGHTPHRASE \mapsto \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Classes}{class} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Thunks}{thunk} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Generic}{closure} \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{reference} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{object} ( \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Generating}{fresh-atom}, \\&\quad\quad\quad\quad\quad\quad \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{1} \ \RIGHTPHRASE , \\&\quad\quad\quad\quad\quad\quad \SEMREF{declare-variables} \LEFTPHRASE \ \VAR{VD}\STAR \ \RIGHTPHRASE , \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{dereference} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Thunks}{force} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Classes}{class-instantiator} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{2} \ \RIGHTPHRASE ), \\&\quad\quad\quad\quad \SEMREF{declare-methods} \LEFTPHRASE \ \VAR{MD}\STAR \ \RIGHTPHRASE , \\&\quad\quad\quad\quad \SEMREF{id} \LEFTPHRASE \ \VAR{ID}\SUB{2} \ \RIGHTPHRASE ) \} \\ \KEY{Rule} \quad & \SEMREF{declare-classes} \LEFTPHRASE \ \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map} ( \ ) \\ \KEY{Rule} \quad & \SEMREF{declare-classes} \LEFTPHRASE \ \VARREF{CD} \ \VARREF{CD}\PLUS \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{collateral} ( \SEMREF{declare-classes} \LEFTPHRASE \ \VAR{CD} \ \RIGHTPHRASE , \SEMREF{declare-classes} \LEFTPHRASE \ \VAR{CD}\PLUS \ \RIGHTPHRASE ) \end{align*}\]

Variables

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{VD} : \SYNDECL{var-declaration} \ ::= \ & \ \SYNREF{type} \ \SYNREF{identifier} \ \LEX{{;}} \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{declare-variables} \LEFTPHRASE \ \VARREF{VD}\STAR : \SYNREF{var-declaration}\STAR \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{envs} \\ \KEY{Rule} \quad & \SEMREF{declare-variables} \LEFTPHRASE \ \VARREF{T} \ \VARREF{ID} \ \LEX{{;}} \ \RIGHTPHRASE = \\&\quad \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE \mapsto \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \SEMREF{type} \LEFTPHRASE \ \VAR{T} \ \RIGHTPHRASE , \SEMREF{initial-value} \LEFTPHRASE \ \VAR{T} \ \RIGHTPHRASE ) \} \\ \KEY{Rule} \quad & \SEMREF{declare-variables} \LEFTPHRASE \ \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map} ( \ ) \\ \KEY{Rule} \quad & \SEMREF{declare-variables} \LEFTPHRASE \ \VARREF{VD} \ \VARREF{VD}\PLUS \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{collateral} ( \SEMREF{declare-variables} \LEFTPHRASE \ \VAR{VD} \ \RIGHTPHRASE , \SEMREF{declare-variables} \LEFTPHRASE \ \VAR{VD}\PLUS \ \RIGHTPHRASE ) \end{align*}\]

Types

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{T} : \SYNDECL{type} \ ::= \ & \ \LEX{int} \ \LEX{{[}} \ \LEX{{]}} \\ \ \mid \ & \ \LEX{boolean} \\ \ \mid \ & \ \LEX{int} \\ \ \mid \ & \ \SYNREF{identifier} \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{type} \LEFTPHRASE \ \VARREF{T} : \SYNREF{type} \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Values}{Value-Types}{types} \\ \KEY{Rule} \quad & \SEMREF{type} \LEFTPHRASE \ \LEX{int} \ \LEX{{[}} \ \LEX{{]}} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vectors} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{variables} ) \\ \KEY{Rule} \quad & \SEMREF{type} \LEFTPHRASE \ \LEX{boolean} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{booleans} \\ \KEY{Rule} \quad & \SEMREF{type} \LEFTPHRASE \ \LEX{int} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers} \\ \KEY{Rule} \quad & \SEMREF{type} \LEFTPHRASE \ \VARREF{ID} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{pointers} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{objects} ) \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{initial-value} \LEFTPHRASE \ \VARREF{T} : \SYNREF{type} \ \RIGHTPHRASE : \TO \NAMEREF{minijava-values} \\ \KEY{Rule} \quad & \SEMREF{initial-value} \LEFTPHRASE \ \LEX{int} \ \LEX{{[}} \ \LEX{{]}} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector} ( \ ) \\ \KEY{Rule} \quad & \SEMREF{initial-value} \LEFTPHRASE \ \LEX{boolean} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{false} \\ \KEY{Rule} \quad & \SEMREF{initial-value} \LEFTPHRASE \ \LEX{int} \ \RIGHTPHRASE = 0 \\ \KEY{Rule} \quad & \SEMREF{initial-value} \LEFTPHRASE \ \VARREF{ID} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{pointer-null} \end{align*}\]

Methods

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{MD} : \SYNDECL{method-declaration} \ ::= \ & \ \LEX{public} \ \SYNREF{type} \ \SYNREF{identifier} \ \LEX{{(}} \ \SYNREF{formal-list}\QUERY \ \LEX{{)}} \ \LEX{{\LEFTBRACE}} \\ & \ \SYNREF{var-declaration}\STAR \\ & \ \SYNREF{statement}\STAR \\ & \ \LEX{return} \ \SYNREF{expression} \ \LEX{{;}} \\ & \ \LEX{{\RIGHTBRACE}} \end{align*}\] \[\begin{align*} \KEY{Type} \quad & \NAMEDECL{methods} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{functions} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuples} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{references} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{objects} ), \NAMEREF{minijava-values}\STAR ), \NAMEREF{minijava-values} ) \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{declare-methods} \LEFTPHRASE \ \VARREF{MD}\STAR : \SYNREF{method-declaration}\STAR \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{envs} \\ \KEY{Rule} \quad & \SEMREF{declare-methods} \LEFTPHRASE \ \LEX{public} \ \VARREF{T} \ \VARREF{ID} \ \LEX{{(}} \ \VARREF{FL}\QUERY \ \LEX{{)}} \ \LEX{{\LEFTBRACE}} \ \VARREF{VD}\STAR \ \VARREF{S}\STAR \ \LEX{return} \ \VARREF{E} \ \LEX{{;}} \ \LEX{{\RIGHTBRACE}} \ \RIGHTPHRASE = \\&\quad \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE \mapsto \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{function} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Generic}{closure} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{scope} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{collateral} ( \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Patterns}{match} ( \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given}, \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuple} ( \\&\quad\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Patterns}{pattern} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Generic}{abstraction} \\&\quad\quad\quad\quad\quad\quad\quad\quad \{ \STRING{this} \mapsto \\&\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{pointers} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{objects} ), \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given} ) \}, \\&\quad\quad\quad\quad\quad\quad\quad \SEMREF{bind-formals} \LEFTPHRASE \ \VAR{FL}\QUERY \ \RIGHTPHRASE ) ), \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{object-single-inheritance-feature-map} \\&\quad\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{dereference} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{first} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuple-elements} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given}, \\&\quad\quad\quad\quad\quad \SEMREF{declare-variables} \LEFTPHRASE \ \VAR{VD}\STAR \ \RIGHTPHRASE ), \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{sequential} ( \SEMREF{execute} \LEFTPHRASE \ \VAR{S}\STAR \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE ) ) \} \\ \KEY{Rule} \quad & \SEMREF{declare-methods} \LEFTPHRASE \ \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{map} ( \ ) \\ \KEY{Rule} \quad & \SEMREF{declare-methods} \LEFTPHRASE \ \VARREF{MD} \ \VARREF{MD}\PLUS \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{collateral} ( \SEMREF{declare-methods} \LEFTPHRASE \ \VAR{MD} \ \RIGHTPHRASE , \SEMREF{declare-methods} \LEFTPHRASE \ \VAR{MD}\PLUS \ \RIGHTPHRASE ) \end{align*}\]

Formals

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{FL} : \SYNDECL{formal-list} \ ::= \ & \ \SYNREF{type} \ \SYNREF{identifier} \ \LEFTGROUP \LEX{{,}} \ \SYNREF{formal-list} \RIGHTGROUP\QUERY \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{bind-formals} \LEFTPHRASE \ \VARREF{FL}\QUERY : \SYNREF{formal-list}\QUERY \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Patterns}{patterns}\STAR \\ \KEY{Rule} \quad & \SEMREF{bind-formals} \LEFTPHRASE \ \VARREF{T} \ \VARREF{ID} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Patterns}{pattern} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Generic}{abstraction} \\&\quad\quad \{ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE \mapsto \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \SEMREF{type} \LEFTPHRASE \ \VAR{T} \ \RIGHTPHRASE , \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given} ) \} \\ \KEY{Rule} \quad & \SEMREF{bind-formals} \LEFTPHRASE \ \VARREF{T} \ \VARREF{ID} \ \LEX{{,}} \ \VARREF{FL} \ \RIGHTPHRASE = \SEMREF{bind-formals} \LEFTPHRASE \ \VAR{T} \ \VAR{ID} \ \RIGHTPHRASE , \SEMREF{bind-formals} \LEFTPHRASE \ \VAR{FL} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{bind-formals} \LEFTPHRASE \ \ \RIGHTPHRASE = ( \ ) \end{align*}\]

\(\SECT{3}\) Statements

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{S} : \SYNDECL{statement} \ ::= \ & \ \LEX{{\LEFTBRACE}} \ \SYNREF{statement}\STAR \ \LEX{{\RIGHTBRACE}} \\ \ \mid \ & \ \LEX{if} \ \LEX{{(}} \ \SYNREF{expression} \ \LEX{{)}} \ \SYNREF{statement} \ \LEX{else} \ \SYNREF{statement} \\ \ \mid \ & \ \LEX{while} \ \LEX{{(}} \ \SYNREF{expression} \ \LEX{{)}} \ \SYNREF{statement} \\ \ \mid \ & \ \LEX{System} \ \LEX{{.}} \ \LEX{out} \ \LEX{{.}} \ \LEX{println} \ \LEX{{(}} \ \SYNREF{expression} \ \LEX{{)}} \ \LEX{{;}} \\ \ \mid \ & \ \SYNREF{identifier} \ \LEX{{=}} \ \SYNREF{expression} \ \LEX{{;}} \\ \ \mid \ & \ \SYNREF{identifier} \ \LEX{{[}} \ \SYNREF{expression} \ \LEX{{]}} \ \LEX{{=}} \ \SYNREF{expression} \ \LEX{{;}} \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{execute} \LEFTPHRASE \ \VARREF{S}\STAR : \SYNREF{statement}\STAR \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null-type} \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \LEX{{\LEFTBRACE}} \ \VARREF{S}\STAR \ \LEX{{\RIGHTBRACE}} \ \RIGHTPHRASE = \SEMREF{execute} \LEFTPHRASE \ \VAR{S}\STAR \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \LEX{if} \ \LEX{{(}} \ \VARREF{E} \ \LEX{{)}} \ \VARREF{S}\SUB{1} \ \LEX{else} \ \VARREF{S}\SUB{2} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{if-true-else} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE , \SEMREF{execute} \LEFTPHRASE \ \VAR{S}\SUB{1} \ \RIGHTPHRASE , \SEMREF{execute} \LEFTPHRASE \ \VAR{S}\SUB{2} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \LEX{while} \ \LEX{{(}} \ \VARREF{E} \ \LEX{{)}} \ \VARREF{S} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{while-true} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE , \SEMREF{execute} \LEFTPHRASE \ \VAR{S} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \LEX{System} \ \LEX{{.}} \ \LEX{out} \ \LEX{{.}} \ \LEX{println} \ \LEX{{(}} \ \VARREF{E} \ \LEX{{)}} \ \LEX{{;}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Interacting}{print} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Strings}{to-string} \ \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE , \STRING{{\BACKSLASH}n} ) \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \VARREF{ID} \ \LEX{{=}} \ \VARREF{E} \ \LEX{{;}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \VARREF{ID} \ \LEX{{[}} \ \VARREF{E}\SUB{1} \ \LEX{{]}} \ \LEX{{=}} \ \VARREF{E}\SUB{2} \ \LEX{{;}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assign} ( \\&\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{index} ( \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE , 1 ), \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector-elements} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE ), \\&\quad\quad \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Null}{null} \\ \KEY{Rule} \quad & \SEMREF{execute} \LEFTPHRASE \ \VARREF{S} \ \VARREF{S}\PLUS \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{sequential} ( \SEMREF{execute} \LEFTPHRASE \ \VAR{S} \ \RIGHTPHRASE , \SEMREF{execute} \LEFTPHRASE \ \VAR{S}\PLUS \ \RIGHTPHRASE ) \end{align*}\]

\(\SECT{4}\) Expressions

\[\begin{align*} \KEY{Syntax} \quad \VARDECL{E} : \SYNDECL{expression} \ ::= \ & \ \SYNREF{expression} \ \LEX{{\AMPERSAND}{\AMPERSAND}} \ \SYNREF{expression} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{<}} \ \SYNREF{expression} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{+}} \ \SYNREF{expression} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{-}} \ \SYNREF{expression} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{*}} \ \SYNREF{expression} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{[}} \ \SYNREF{expression} \ \LEX{{]}} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{.}} \ \LEX{length} \\ \ \mid \ & \ \SYNREF{expression} \ \LEX{{.}} \ \SYNREF{identifier} \ \LEX{{(}} \ \SYNREF{expression-list}\QUERY \ \LEX{{)}} \\ \ \mid \ & \ \SYNREF{integer-literal} \\ \ \mid \ & \ \LEX{true} \\ \ \mid \ & \ \LEX{false} \\ \ \mid \ & \ \SYNREF{identifier} \\ \ \mid \ & \ \LEX{this} \\ \ \mid \ & \ \LEX{new} \ \LEX{int} \ \LEX{{[}} \ \SYNREF{expression} \ \LEX{{]}} \\ \ \mid \ & \ \LEX{new} \ \SYNREF{identifier} \ \LEX{{(}} \ \LEX{{)}} \\ \ \mid \ & \ \LEX{{!}} \ \SYNREF{expression} \\ \ \mid \ & \ \LEX{{(}} \ \SYNREF{expression} \ \LEX{{)}} \end{align*}\] \[\begin{align*} \KEY{Type} \quad & \NAMEDECL{minijava-values} \\&\quad \leadsto \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{booleans} \mid \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers} \mid \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vectors} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{variables} ) \mid \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{pointers} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{objects} ) \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{evaluate} \LEFTPHRASE \ \VARREF{E} : \SYNREF{expression} \ \RIGHTPHRASE : \TO \NAMEREF{minijava-values} \end{align*}\]

\(\SHADE{\SEMREF{evaluate} \LEFTPHRASE \ \_ \ \RIGHTPHRASE }\) is a well-typed funcon term only when \(\SHADE{\_}\) is a well-typed MiniJava expression.

\[\begin{align*} \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E}\SUB{1} \ \LEX{{\AMPERSAND}{\AMPERSAND}} \ \VARREF{E}\SUB{2} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Flowing}{if-true-else} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE , \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{false} ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E}\SUB{1} \ \LEX{{<}} \ \VARREF{E}\SUB{2} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-is-less} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E}\SUB{1} \ \LEX{{+}} \ \VARREF{E}\SUB{2} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E}\SUB{1} \ \LEX{{-}} \ \VARREF{E}\SUB{2} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-subtract} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E}\SUB{1} \ \LEX{{*}} \ \VARREF{E}\SUB{2} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-multiply} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE , \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E}\SUB{1} \ \LEX{{[}} \ \VARREF{E}\SUB{2} \ \LEX{{]}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{index} ( \\&\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integer-add} ( \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{2} \ \RIGHTPHRASE , 1 ), \\&\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector-elements} \ \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E}\SUB{1} \ \RIGHTPHRASE ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E} \ \LEX{{.}} \ \LEX{length} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Sequences}{length} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector-elements} \ \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{E} \ \LEX{{.}} \ \VARREF{ID} \ \LEX{{(}} \ \VARREF{EL}\QUERY \ \LEX{{)}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{give} ( \\&\quad\quad \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE , \\&\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Functions}{apply} ( \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Maps}{lookup} ( \\&\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Classes}{class-name-single-inheritance-feature-map} \\&\quad\quad\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Objects}{object-class-name} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Abnormal}{Failing}{checked} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{References}{dereference} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given}, \\&\quad\quad\quad\quad \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE ), \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Tuples}{tuple} ( \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{given}, \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VAR{EL}\QUERY \ \RIGHTPHRASE ) ) ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{IL} \ \RIGHTPHRASE = \SEMREF{integer-value} \LEFTPHRASE \ \VAR{IL} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{true} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{true} \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{false} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{false} \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \VARREF{ID} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{this} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{assigned} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \STRING{this} \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{new} \ \LEX{int} \ \LEX{{[}} \ \VARREF{E} \ \LEX{{]}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Vectors}{vector} ( \\&\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Giving}{interleave-repeat} ( \\&\quad\quad\quad \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Storing}{allocate-initialised-variable} ( \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers}, 0 ), 1, \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE ) ) \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{new} \ \VARREF{ID} \ \LEX{{(}} \ \LEX{{)}} \ \RIGHTPHRASE = \\&\quad \NAMEHYPER{../../../../../Funcons-beta/Values/Abstraction}{Thunks}{force} \ \NAMEHYPER{../../../../../Funcons-beta/Values/Composite}{Classes}{class-instantiator} \ \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{bound} \ \SEMREF{id} \LEFTPHRASE \ \VAR{ID} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{{!}} \ \VARREF{E} \ \RIGHTPHRASE = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Booleans}{not} \ \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate} \LEFTPHRASE \ \LEX{{(}} \ \VARREF{E} \ \LEX{{)}} \ \RIGHTPHRASE = \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE \end{align*}\] \[\begin{align*} \KEY{Syntax} \quad \VARDECL{EL} : \SYNDECL{expression-list} \ ::= \ & \ \SYNREF{expression} \ \LEFTGROUP \LEX{{,}} \ \SYNREF{expression-list} \RIGHTGROUP\QUERY \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{evaluate-actuals} \LEFTPHRASE \ \VARREF{EL}\QUERY : \SYNREF{expression-list}\QUERY \ \RIGHTPHRASE : ( \TO \NAMEREF{minijava-values} )\STAR \\ \KEY{Rule} \quad & \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VARREF{E} \ \RIGHTPHRASE = \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VARREF{E} \ \LEX{{,}} \ \VARREF{EL} \ \RIGHTPHRASE = \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE , \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VAR{EL} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate-actuals} \LEFTPHRASE \ \ \RIGHTPHRASE = ( \ ) \end{align*}\]

\(\SECT{5}\) Lexemes

\[\begin{align*} \KEY{Lexis} \quad \VARDECL{ID} : \SYNDECL{identifier} \ ::= \ & \ \SYNREF{letter} \ \LEFTGROUP \SYNREF{letter} \mid \SYNREF{digit} \mid \LEX{{\UNDERSCORE}} \RIGHTGROUP\STAR \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{id} \LEFTPHRASE \ \VARREF{ID} : \SYNREF{identifier} \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Computations/Normal}{Binding}{ids} \\&\quad = \textsf{\textquotedblleft}\VAR{ID}\textsf{\textquotedblright} \end{align*}\] \[\begin{align*} \KEY{Lexis} \quad \VARDECL{IL} : \SYNDECL{integer-literal} \ ::= \ & \ \SYNREF{digit}\PLUS \\ \SYNDECL{letter} \ ::= \ & \ \LEX{a} {-} \LEX{z} \mid \LEX{A} {-} \LEX{Z} \\ \SYNDECL{digit} \ ::= \ & \ \LEX{0} {-} \LEX{9} \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{integer-value} \LEFTPHRASE \ \VARREF{IL} : \SYNREF{integer-literal} \ \RIGHTPHRASE : \TO \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{integers} \\&\quad = \NAMEHYPER{../../../../../Funcons-beta/Values/Primitive}{Integers}{decimal-natural} \ \textsf{\textquotedblleft}\VAR{IL}\textsf{\textquotedblright} \end{align*}\]