.Open Description of Standard ML .Open Syntax of Standard ML . Introduction .Open Source This message presents syntax rules for the full Standard ML language. These rules are intended to serve as documentation for programmers, and could be useful to compiler writers. They are slightly too liberal, in that they do not take account of syntactic restrictions or the precedence of certain constructs. I believe that they are complete. .Source Larry Paulson .Source Corrections by Dave Berry, Simon Finn, Kent Karlsson and David N. Turner. .Close Source The above message was translated into MATHS by Dick Botting and some extra terms were introduced to simplify some definitions. Any errors that have crept in are mine, all mine. Mail me and they will be fixed! . Notes on meta-notation .Box .See http://www.csci.csusb.edu/dick/maths/math_64_Meta_Macros.html Empty::="". -- the null string. O(...) encloses an optional phrase so O(A)::=(A|\$Empty). \$#(A) - zero or more occurences of A, and N(A) - one or more occurrences of A, so #(A)::= \$O(N(A)). N(A)::= (A) \$#(A). L(A, B) encloses a repetitive phrase of the form ABABA...BA -- 1 or more repetitions of A, separated by B. L(A,B)::= A \$#(B A). List(A)::=\$L(A, ",")= A \$#("," A). And_List(A)::=\$L(A, "and") = A \$#("and" A). Sequence(A)::=\$L(A, ";") = A \$#(";" A). O_List(A)::= \$O(\$List(A))::=`An optional \$List of A's`. Items below may be separated by spaces, newlines, and comments. Consecutive keywords and identifiers of the same sort (alphanumeric/symbolic) must be separated to avoid ambiguity. .Close.Box . Programs and Modules Program::= \$#(\$Top_Level_Declaration ";" ). Top_Level_Declaration::= \$Expression | \$Object_Declaration | \$Signature_Declaration | \$Functor_Declaration. Object_Declaration::= \$Empty | \$Declaration | "structure" \$And_List( \$Ident \$O(":" \$Signature) "=" \$Structure ) | "local" \$Object_Declaration "in" \$Object_Declaration "end" | \$Object_Declaration \$O(";") \$Object_Declaration. Module::glossary=`A separably compilable unit - typically a file - containing module systems`. Module_system::glossary=`Made of structure, signatures, and functors`. Structure::glossary=`a collection of types, datatypes, functions, exceptions, etc we wish to encapsulate`. Signature_Declaration::= \$Empty | "signature" \$And_List(\$Ident "=" \$Signature ) | \$Signature_Declaration \$O(";") \$Signature_Declaration. Signature::glossary=`A collection of info describing and specifying some elements of a structure`. Functor_Declaration::= \$Empty | "functor" \$And_List(\$Functor_Binding ) | \$Functor_Declaration \$O(";") \$Functor_Declaration. Functor::Glossary=`An Operation that takes one or more structures and produces another one`. The ML Functor meets the same need to generate special cases of code from a general form that generics do in Ada and templates do in C++. Functor_Binding::= \$Ident "(" \$Functor_Arguments ")" \$O(":" \$Signature) "=" \$Structure. Functor_Arguments::= \$Ident ":" \$Signature | \$Specification. Functor_Application::= \$Ident "(" \$Structure | \$Sequence(\$structure_declaration) ")". Structure::= "struct" \$Object_Declaration "end" | \$Compound_Ident | \$Functor_Application | \$Ident "(" \$Object_Declaration ")" | "let" \$Object_Declaration "in" \$Structure "end". Signature::= "sig" \$Specification "end" | \$Ident. Specification::= \$Empty | value_spec | \$various_type_spec | \$exception_spec | \$structure_spec | \$other_spec | inclusion | \$Specification \$O(";") \$Specification. value_specification::="val" \$And_List(\$Ident ":" \$Type ). various_type_spec::=("type" | "eqtype") \$And_List(\$Type_Var_List \$Ident ) | "datatype" \$And_List(\$Datatype_Binding ) exception_spec::="exception" \$And_List(\$Ident \$O("of" \$Type) ). structure_spec::="structure" \$And_List(\$Ident ":" \$Signature ). other_spec::="sharing" \$And_List( \$O("type") \$Ident "=" \$L(\$Ident , "=") ) | "local" \$Specification "in" \$Specification "end" | "open" \$L(\$Compound_Ident ). inclusions::= "include" \$N(\$Ident ) . . Declarations Declaration::= \$Empty | \$simple_declaration \$#(O(";")\$simple_declaration). simple_declaration::= \$value_declaration | \$function_declaration | \$type_declaration | \$abstract_data_type_declaration | \$abstract_type_declaration | exception_declaraion | \$local_declaration | \$open_declaration | \$operator_declaration. value_declaration::="val" \$And_List( \$O("rec") \$Pattern "=" \$Expression ) . function_declaration::="fun" \$And_List( \$L(\$Function_Heading \$O(":" \$Type) "=" \$Expression , "|") ). structure_declaration::="structure" And_list( \$Ident \$O(":" \$Signature) "=" \$Structure ) | \$Declaration | "local" \$structure_declaration "in" \$Sequence(\$Structure_Declarations)) type_declaration::="type" \$Type_Binding. abstract_data_type_declaration::="datatype" \$Datatype_Binding \$O("withtype" \$Type_Binding). abstract_type_declaration::="abstype" \$Datatype_Binding \$O("withtype" \$Type_Binding) "with" \$Declaration "end". In the above the \$Datatype_Binding defiing the structure of the data is hidden from all but the functions etc in the part of the declaration after the "withs". exception_declaration::="exception" \$And_List( \$Name \$O( "of" \$Type | "=" \$Compound_Name ) ). local_declaration::="local" \$Declaration "in" \$Declaration "end". open_declaration::="open" \$N(\$Compound_Ident ). An Open declaration allows you to refer to the contents of a structure without having to include the name of the structure each time. The names of parts of the openned structure override those declared before the open. operator_declaration::=\$infix_declaration | "nonfix" \$N(\$Ident ). infix_declaration::=("infix" | "infixr") \$N(\$Ident). infix_operator::=\$Ident & `visible in an infix declaration` & (`declared as or in a function of two parameters`|`declared as \$constructor with two parts`). Function_Heading::= \$Name \$N(\$Atomic_Pattern) | "(" \$Atomic_Pattern \$Infix_Operator \$Atomic_Pattern ")" \$#(\$Atomic_Pattern) | \$Atomic_Pattern \$Infix_Operator \$Atomic_Pattern. Type_Binding::= \$And_List(\$Type_Var_List \$Ident "=" \$Type ). Datatype_Binding::= \$And_List( \$Type_Var_List \$Ident "=" \$L( \$constructor \$O("of" \$Type) , "|" ) ). constructor::=\$Ident & `visible in a datatype_binding`. . Expressions Expression::= \$Infix_Expression | \$Expression ":" \$Type | \$Expression \$boolean_operator \$Expression | \$Expression "handle" \$Match | "raise" \$Expression | \$selection| \$loop | "fn" \$Match. boolean_operator::="andalso" | "orelse". loop::= "while" \$Expression "do" \$Expression. selection::= "if" \$Expression "then" \$Expression "else" \$Expression | "case" \$Expression "of" \$Match. Infix_Expression::= \$N(\$Atomic_Expression ) | \$Infix_Expression \$Infix_Operator \$Infix_Expression. Atomic_Expression::= \$Compound_Name | \$Constant | "(" \$O_List(\$Expression ) ")" | "[" \$List(\$Expression ) "]" | "{" \$O_List(\$Label "=" \$Expression ) "}" | "\$#" \$Label | "(" \$L(\$Expression , ";") ")" | "let" \$Declaration "in" \$L(\$Expression , ";") "end". . Matches and \$Patterns Match::= \$L(\$Pattern "=>" \$Expression , "|"). Pattern::= \$Atomic_Pattern | \$Compound_Name \$Atomic_Pattern | \$Pattern \$infix_constructor \$Pattern | \$Pattern ":" \$Type | \$Name \$O(":" \$Type) "as" \$Pattern. infix_constructor::=\$Infix_Operator & \$constructor. Infix_constructor::= "::" | ... ; Atomic_Pattern::= "_" | \$Compound_Name | \$Constant | "(" \$O_List(\$Pattern ) ")" | "[" \$List(\$Pattern ) "]" | "{" \$O_List(\$Field_Pattern ) \$O("...") "}". Field_Pattern::= \$Label "=" \$Pattern | \$Ident \$O(":" \$Type) \$O("as" \$Pattern). . Types Type::= \$Type_Var | \$Type_Var_List \$Compound_Ident | \$Type "*" \$L(\$Type , "*") | \$Type "->" \$Type | "{" \$O_List( \$Label ":" \$Type ) "}" | "(" \$Type ")". Type_Var_List::= \$Empty | \$Type_Var | "(" \$List(\$Type_Var ) ")". . Lexicon Use MATHS.Lexemes Compound_Ident::= \$L(\$Ident , ".") . Compound_Name::= \$Compound_Ident | "op" \$Infix_Operator. Name::= \$Ident | "op" \$Infix_Operator. Infix_Operator::= `any identifier that has been declared to be infix`. Constant::= \$Numeral \$O( "." \$N(digit ) ) \$O("E" \$Numeral) | double_quote \$#(character ~ (backslash | double_quotes) | "\" \$String_Escape ) double_quote. String_Escape::= "n" | "t" | "^" img("@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_") | digit digit digit | double_quote | "\" | \$N( SP | HT | EOLN | FF ) "\". Numeral::= \$O("~") \$N(digit ). Type_Var::= "'" \$O("'") \$O("_") \$Alphanumeric_Ident. Ident::= \$Alphanumeric_Ident | \$N(\$Symbol). Label::= \$Ident | (digit~"0") \$#(digit). Alphanumeric_Ident::= letter \$#( letter | digit | "_" | "'"). Symbol::= img("!%&\$#+-/:<=>?@\~`^|*"). Comment::= "(*" \$L(\$Commentary, \$Comment) "*)". Commentary::= `any text that does not include (* or *) as a substring`. .Close .Open See Also... . Functions of SML-NJ .See http://www/dick/samples/ml.functions.html . Syntax Diagrams Tobias Nipkow(nipkow@informatik.tu-muenchen.de) has translated Larry Paulson's BNF syntax for Standard ML into diagram form. The result is available as a compressed DVI file from Germany: .See http://www.in.tum.de/~nipkow/misc/ml-syntax.dvi.gz (Thanks to .See mailto:Tobias.Nipkow@informatik.tu-muenchen.de for updating this link). . Source .Source Used with permission from Larry.Paulson@cl.cam.ac.uk from the Usenet SML Archives for 1991, message \$# .See http://www.cs.cmu.edu:8001/afs/cs.cmu.edu/user/mleone/web/sml-list/91-sml/2.txt .Close See Also... .Close Description of Standard ML