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Tutorial on Type Analysis

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Type Conversion

This chapter introduces type conversion to our language. We say, a value of a certain type t is converted into a corresponding value of some other type s. For example, a conversion of integral values into floating point values is defined for many languages. We consider such a conversion be executed by a conversion operator that has a signature t->s. We call a conversion coercion if the application of a conversion operator is determined implicitly, for example in the process of overloading resolution.

In order to demonstrate type conversion, we extend our language by a second arithmetic type for floating point values an call the type real.

The type representation is extended by:

Real type representation[37]==

realType -> TypeName = {"real"};
This macro is invoked in definition 44.

We add a new type denoter to the language

Real type denoter[38]==

RULE: TypeDenoter ::= 'real' COMPUTE TypeDenoter.Type = realType; END;
This macro is invoked in definition 45.

and introduce literals of type real:

Real literals[39]==

RULE: Expression ::= RealNumber COMPUTE
  PrimaryContext (Expression, realType);
This macro is invoked in definition 45.

Now we extend the set of operator specifications by operators for the type real:

Real operators[40]==

  rAdd  (realType,realType):realType;
  rSub  (realType,realType):realType;
  rMul  (realType,realType):realType;
  rDiv  (realType,realType):realType;

  rPlus (realType):realType;
  rNeg  (realType):realType;
This macro is invoked in definition 46.

We specify that the real operators overload the corresponding ones for the type int by adding them to the corresponding indication:

Real operators overload[41]==

  AddOp: rAdd;
  SubOp: rSub;
  MulOp: rMul;
  DivOp: rDiv;
  PlusOp: rPlus;
  NegOp:  rNeg;
This macro is invoked in definition 46.

Now we want to allow that overloading resolution takes conversion from int to real into account. That means in an expression like a + 1 the operand types need not match exactly to the signature of a + operator, if coercion could convert the operand types into those required by the signature. In particular a could have type real. In that case coercion from int to real would be applied to 1 in order to use the real addition operator.

So, we define such a coercion operator iTor with the signature int->real:

Predefined Coercion Operator[42]==

  iTor (intType):realType;
This macro is invoked in definition 46.

Finally we reconsider the type rules for assignments. We want to allow to have an int variable on the left-hand side and a real expression on the right, say i = 3.4; That means the result of the expression is to be converted to an int value, which is then assigned to the variable.

For that purpose we specify a conversion operator rToi with the signature real->int, and associate it to the operator indication assignOpr which has been introduced for the assignment context:

Assignment Conversion Operator[43]==

   rToi (realType):intType;
  assignOpr: rToi;
This macro is invoked in definition 46.

Note: The conversion operator rToi is only applicable in a context that is chacterized by the indication assignOpr, it is NOT applied as a coercion when resolving overloaded operators.


Real type representation[37]
This macro is attached to a product file.


Real type denoter[38]
Real literals[39]
This macro is attached to a product file.


Real operators[40]
Real operators overload[41]
Assignment Conversion Operator[43]
Predefined Coercion Operator[42]
This macro is attached to a product file.

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