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*}\] \[\begin{align*} \KEY{Syntax} \quad \VARDECL{EL} : \SYNDECL{expression-list} \ ::= \ & \ \SYNREF{expression} \ \LEFTGROUP \LEX{{,}} \ \SYNREF{expression-list} \RIGHTGROUP\QUERY \end{align*}\] \[\begin{align*} \KEY{Semantics} \quad & \SEMDECL{evaluate-actuals} \LEFTPHRASE \ \VARREF{EL}\QUERY : \SYNREF{expression-list}\QUERY \ \RIGHTPHRASE : ( \TO \NAMEREF{minijava-values} )\STAR \\ \KEY{Rule} \quad & \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VARREF{E} \ \RIGHTPHRASE = \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VARREF{E} \ \LEX{{,}} \ \VARREF{EL} \ \RIGHTPHRASE = \SEMREF{evaluate} \LEFTPHRASE \ \VAR{E} \ \RIGHTPHRASE , \SEMREF{evaluate-actuals} \LEFTPHRASE \ \VAR{EL} \ \RIGHTPHRASE \\ \KEY{Rule} \quad & \SEMREF{evaluate-actuals} \LEFTPHRASE \ \ \RIGHTPHRASE = ( \ ) \end{align*}\]