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<H1>Tutorial on Type Analysis</H1>
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<H1><A NAME="SEC13" HREF="typetutorial_toc.html#SEC13">Functions</A></H1>
<P>
We now introduce function declarations to our language.
A function is characterized by its signature.
Function types are an example of types that have properties which
are lists of types, the types of the parameters.
<P>
We extend the concrete grammar by productions for
function declarations:
<P>
<B>Function.con</B>[57]==
<PRE>
<TT>
Declaration: FunctionDecl.
FunctionDecl: 'fun' DefIdent Function ';'.
Function: FunctionHead Block.
FunctionHead: '(' Parameters ')' TypeDenoter.
Parameters: [Parameter // ','].
Parameter: TypeDenoter DefIdent.
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
Here is an example program that defines some functions.
The grammar for function calls and return statements is
given below.
<B>FunctionExamp</B>[58]==
<PRE>
<TT>begin
var int i, int j,
bool b, bool c,
real r, real s;
fun f (int x, real y) real
begin r = x * y; return r;end;
fun g (real z) void
begin r = z; return; end;
s = f (i+1, 3.4);
g (f (j, s));
return;
end
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
A function signature consists of the result type and a
list of parameter types. Hence, we use an instance of
the <CODE>LidoList</CODE> module in order to compose such
type lists.
(Note: If we had more than one mode of parameter passing,
the abstraction of a parameter in the function signature
would be a pair: parameter passing mode and parameter type.)
<P>
<B>Function.specs</B>[59]==
<PRE>
<TT>
$/Adt/LidoList.gnrc+instance=DefTableKey+referto=deftbl:inst
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
The use of the module requires a particular name for the non-existing
list element:
<P>
<B>Function.head</B>[60]==
<PRE>
<TT>
#define NoDefTableKey NoKey
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
A function type is described by two properties, the result type and
and the list of parameter types as introduced by the following
PDL specifications:
<P>
<B>Function.pdl</B>[61]==
<PRE>
<TT>
ParamTypes: DefTableKeyList; "DefTableKeyList.h"
ResultType: DefTableKey [KReset];
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
We first consider the name analysis aspect of a function
declaration. The <CODE>Function</CODE> subtree is a range where the
parameter definitions are valid. The function <CODE>Block</CODE> is
nested in that range. Since the <CODE>DefIdent</CODE> for parameters
are already completely specified for name analysis, we need
only:
<P>
<B>FunctionScope.lido</B>[62]==
<PRE>
<TT>
SYMBOL Function INHERITS RangeScope END;
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
Now we consider a function declaration as a definition
of a typed object, and apply the same specification pattern
as used for variable declarations.
Furthermore, each <CODE>Parameter</CODE> is also a <CODE>TypedDefinition</CODE>.
There is no problem in nesting definitions of a typed objects
this way.
<P>
<B>FunctionDecl.lido</B>[63]==
<PRE>
<TT>
SYMBOL FunctionDecl INHERITS TypedDefinition END;
RULE: FunctionDecl ::= 'fun' DefIdent Function ';' COMPUTE
FunctionDecl.Type = Function.Type;
END;
RULE: Function ::= FunctionHead Block COMPUTE
Function.Type = FunctionHead.Type;
END;
SYMBOL Parameter INHERITS TypedDefinition END;
RULE: Parameter ::= TypeDenoter DefIdent COMPUTE
Parameter.Type = TypeDenoter.Type;
DefIdent.IsVariable = 1;
END;
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
Now we specify how the type of a function is composed.
The <CODE>FunctionHead</CODE>, which contains the signature,
is treated as a <CODE>TypeDenotation</CODE> for a function type.
Its <CODE>ResultType</CODE> property is obtained from the
<CODE>TypeDenoter</CODE> of the result type. The <CODE>ParamTypes</CODE>
property is the list of parameter types.
That list is simply composed from the <CODE>Root</CODE> and <CODE>Elem</CODE>
role of the <CODE>LidoList</CODE> module instantiated for lists
of <CODE>DefTableKey</CODE>s.
<P>
<B>FunctDeclType.lido</B>[64]==
<PRE>
<TT>
SYMBOL FunctionHead INHERITS TypeDenotation END;
RULE: FunctionHead ::= '(' Parameters ')' TypeDenoter COMPUTE
FunctionHead.GotType =
ResetParamTypes
(KResetResultType
(KResetTypeName (FunctionHead.Type, "function..."),
TypeDenoter.Type),
Parameters.DefTableKeyList);
END;
SYMBOL Parameters INHERITS DefTableKeyListRoot END;
SYMBOL Parameter INHERITS DefTableKeyListElem END;
RULE: Parameter ::= TypeDenoter DefIdent COMPUTE
Parameter.DefTableKeyElem = TypeDenoter.Type;
END;
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
Function calls are integrated in the expression syntax of
our language. We chose a very general form of an <CODE>Expression</CODE>
to denote the function to be called. That allows us to later expand the
language by expressions which yield a function.
That feature does not create additional problems for type analysis.
<P>
We also introduce return statements into our language.
<P>
<B>Call.con</B>[65]==
<PRE>
<TT>
Expression: Expression '(' Arguments ')'.
Arguments: [Argument // ','].
Argument: Expression.
Statement: 'return' ';'.
Statement: 'return' Expression ';'.
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
Type analysis for a function call is straight-forward:
We access the <CODE>ResultType</CODE> from the type of the
function <CODE>Expression</CODE>; it is the type of the call.
The list of parameter types is passed to the <CODE>Arguments</CODE>.
There it is decomposed into its elements using the list decomposition
roles of the <CODE>LidoList</CODE> module, <CODE>DeListRoot</CODE> and
<CODE>DeListElem</CODE>. That mechanism also works if in erroneous
cases the lengths of the parameter list and the structural
argument list are different.
<P>
<B>Call.lido</B>[66]==
<PRE>
<TT>
SYMBOL Arguments INHERITS DefTableKeyDeListRoot END;
RULE: Expression ::= Expression '(' Arguments ')' COMPUTE
Expression[1].Type =
TransDefer (GetResultType (Expression[2].Type, NoKey));
Arguments.DefTableKeyList =
GetParamTypes (Expression[2].Type, NULLDefTableKeyList);
END;
SYMBOL Argument INHERITS DefTableKeyDeListElem END;
RULE: Argument ::= Expression COMPUTE
Expression.ReqType = Argument.DefTableKeyElem;
END;
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
The computation of the <CODE>ReqType</CODE> attribute above
completely captures type checking for each argument.
For the function <CODE>Expression</CODE> we only have to check
whether it really yields a function, the first check below.
The other two checks issue messages if the lengths of the
lists are different.
<P>
<B>CallCheck.lido</B>[67]==
<PRE>
<TT>
RULE: Expression ::= Expression '(' Arguments ')' COMPUTE
Expression[2].ReqType = Expression[2].Type;
IF (EQ (Expression[1].Type, NoKey),
message (ERROR, "call applied to non function", 0, COORDREF));
IF (NE (Arguments.DefTableKeyListTail, NULLDefTableKeyList),
message (ERROR, "arguments missing", 0, COORDREF));
END;
RULE: Argument ::= Expression COMPUTE
IF (EQ (Argument.DefTableKeyElem, NoDefTableKey),
message (ERROR, "too many arguments", 0, COORDREF));
END;
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
A return statement refers to the immediately enclosing function
declaration. We have to check that a value of a type compatible
to the result type is returned if the latter is not <CODE>void</CODE>.
A return from the outermost program level is considered as if
the program was a <CODE>void</CODE> function.
<P>
<B>Return.lido</B>[68]==
<PRE>
<TT>
SYMBOL Program COMPUTE
SYNT.Type = KResetResultType (NewKey(), voidType);
END;
ATTR resType: DefTableKey;
RULE: Statement ::= 'return' ';' COMPUTE
.resType =
TransDefer
(GetResultType
(INCLUDING (FunctionDecl.Type, Program.Type),
NoKey))
<- INCLUDING Program.GotType;
IF (NOT (EqualTypes (.resType, voidType)),
message (ERROR, "return value required", 0, COORDREF));
END;
RULE: Statement ::= 'return' Expression ';' COMPUTE
.resType =
TransDefer
(GetResultType
(INCLUDING (FunctionDecl.Type, Program.Type),
NoKey))
<- INCLUDING Program.GotType;
IF (EqualTypes (.resType, voidType),
message (ERROR, "return value not allowed", 0, COORDREF));
Expression.ReqType = .resType;
END;
</TT>
</PRE>
<FONT SIZE=1>
<PRE>
This macro is attached to a product file.
</PRE>
</FONT>
<P>
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