The type system and how it is used is a commonly misunderstood aspect of the Dylan language. Although it lacks some forms of expressiveness in the current incarnation, it also has some features that aren't found in many languages, such as singleton types. It is also very important in helping the compiler to generate faster yet still safe code.

One interesting feature in Dylan is that it is optionally typed. While this is more common today and sometimes has fancy names applied like 'gradually typed', the overall point is the same: Your code can start out untyped and looking like code does in Ruby or Python. However, when you want or need additional performance or correctness guarantees, you can supply type annotations that the compiler can use. The compiler can also infer some types from the values used or other type annotations.

In this post, we'll explain some of the basic concepts of the Dylan type system and show how it is used by the compiler.

Type and Value Relationships There are 2 important relationships between values and types in Dylan. They are instance? and subtype? . Other relationships, such as known-disjoint? are used within the compiler to assist with type inference, but these other relationships are not regularly of use to the typical Dylan programmer. instance? : The instance? relationship holds between a value and a type. A value can be an instance of a type (or not). subtype? : The subtype? relationship holds between two types. One type can be a subtype of another type. When a type A is a subtype of type B, then an instance of A can be used anywhere that expects an instance of B. From the Dylan Reference Manual (DRM): The following is an informal description of type relationships: The function subtype? defines a partial ordering of all types. Type t1 is a subtype of type t2 (i.e., subtype?(t1, t2) is true) if it is impossible to encounter an object that is an instance of t1 but not an instance of t2. It follows that every type is a subtype of itself. Two types t1 and t2 are said to be equivalent types if subtype?(t1, t2) and subtype?(t2, t1) are both true. t1 is said to be a proper subtype of t2 if t1 is a subtype of t2 and t2 is not a subtype of t1. As we will discuss below, there are multiple kinds of types and each kind of type defines its own rules for how subtype relationships involving that kind of type operate. The specifics of these subtype relationships are discussed in the Dylan Reference Manual.

How is the type system used? The DRM doesn't specify much about how the type system should be used and enforced. In general, it assumes that at a minimum, run-time enforcement via type checks will occur, and leaves any further checks and optimization up to the implementation. In practice though, the Open Dylan compiler makes extensive use of type annotations at compile time as we will discuss shortly. Variable bindings A variable may have its type restricted by specifying a type: let x = 123 ; // x can be re-assigned to any type of value let y :: <integer> = 123 ; // the value of y must be an instance of <integer> Method Dispatch The type system plays a very important role in method dispatch. Method dispatch is the act (or art) of choosing which of several possible methods should be invoked for a given set of arguments. This is covered in some depth in the Method Dispatch section of the DRM. Two important things to note here are subtype? relationships are a key part of ordering methods and choosing which one to invoke.

relationships are a key part of ordering methods and choosing which one to invoke. instance? relationships must also hold for a method to be chosen.

Compile vs Run Time The Open Dylan compiler makes extensive use of type annotations and type inference to remove as many run-time type checks from the generated code as possible, as well as to perform other optimizations. The compiler also seeks to provide compile time warnings about as many type errors as it can. One of the major parts of the Dylan language design that increases what is possible to optimize at compile time is sealing. Sealing plays a very important role in the optimization of a Dylan program. It even gets an entire chapter of the DRM dedicated to it. Function Call Upgrades One of the important things that is made possible by the Open Dylan compiler and the judicious use of sealing is moving some of the work involved in method dispatch from run time to compile time. It is through this mechanism that we are able to often avoid performing an expensive dispatch at all, inline methods, upgrade from a function call to a direct slot access and many other optimizations. Examples We can define a simple sealed method that simply returns false ( #f ). We seal the method so that the compiler is aware that it knows of all implementations of the generic function. By sealing the method, no new methods may be added to the generic function outside of the library being built. define sealed method foo ( a :: <string> ) #f end ; define function main ( name :: <string> , arguments :: <vector> ) foo ( "abc" ); exit-application ( 0 ) end ; If we go and call foo with a value of the wrong type, we'll see that we get an error (which Open Dylan calls a serious warning): foo.dylan:9: Serious warning - Invalid type for argument a in call to method foo (a :: <string>, #next next-method :: <object>) => (): singleton(123 :: <integer>) supplied, <string> expected. -------- foo(123); -------- (An interesting side note here is that the compiler inferred a very specific type for the value passed in: singleton(123 :: <integer>) rather than just <integer> . We'll learn about singleton types below.) Now, we can take a look at the C code that is generated for foo . The compiler generated no type checks within the method. The name of the method is mangled by the compiler so that it is unique and obeys C function name rules. dylan_value KfooVfooMM0I ( dylan_value a_ ) { dylan_value T2 ; T2 = & KPfalseVKi ; MV_SET_COUNT ( 0 ); return ( T2 ); } Similarly, if we look at some code that invokes foo and immediately exits, we'll see that the compiler was able to directly invoke the appropriate methods without going through generic dispatch and without performing any unnecessary type checks: dylan_value KmainVfooI ( dylan_value name_ , dylan_value arguments_ ) { dylan_value T2 ; KfooVfooMM0I ( & K5 ); T2 = Kexit_applicationYcommon_extensionsVcommon_dylanI (( dylan_value ) 1 ); return ( T2 ); } If the compiler were not sure what exactly to invoke for foo("abc") , we would have seen it performing a generic dispatch in the generated C rather than directly invoking a C function as it did ( KfooVfooMM0I ). Similarly, if the compiler wasn't sure about what was happening at the type level, it may have emitted code for a run-time type check to be sure that the types were correct. Hopefully, this helps to make it more clear how the type system is used at compile time and how it helps us to generate faster code while still maintaining the safety checks where required. We will see another example of this in the section below on limited types.

Kinds of Types The DRM specifies 4 kinds of types: Classes

Limited Types

Union Types

Singleton Types These are discussed in detail in the DRM. In the near future, we are likely to see this list of types expand. For example, function types are already being discussed. Classes Classes are described in detail in the DRM. The important parts for now are: Classes are used to define the inheritance, structure, and initialization of objects.

Every object is a direct instance of exactly one class, and a general instance of the superclasses of that class.

A class determines which slots its instances have. Slots are the local storage available within instances. They are used to store the state of objects. An interesting tidbit is that new classes can be created at run-time. Limited Types Limited types consist of a base type and a restricted set of constraints to be applied. Currently, integers and collections can be limited. Limited integers have minimum and maximum bounds. Limited collections can constrain the type of the elements stored in the collection as well as the size or dimensions of the collection. Simple examples: define constant <byte> = limited ( <integer> , min: 0 , max: 255 ); define constant <float32x4> = limited ( <vector> , of: <single-float> , size: 4 ); The last example is particularly interesting (to me at least). In Dylan, <single-float> is a 32 bit float, but will usually be stored in a boxed form. By creating a limited vector of <single-float> with a size of 4, the compiler is able to optimize away bounds checks and it is able to store the floating point values without being boxed. For example, storing some floating point values into an instance of the above <float32x4> limited type would look like: fs [ 0 ] := 1.0 s0 ; fs [ 1 ] := 2.0 s0 ; fs [ 2 ] := 3.0 s0 ; fs [ 3 ] := 4.0 s0 ; That compiles to this in C: REPEATED_DSFLT_SLOT_VALUE_TAGGED_SETTER ( 1.0000000 , fs_ , 1 , 1 ); REPEATED_DSFLT_SLOT_VALUE_TAGGED_SETTER ( 2.0000000 , fs_ , 1 , 5 ); REPEATED_DSFLT_SLOT_VALUE_TAGGED_SETTER ( 3.0000000 , fs_ , 1 , 9 ); REPEATED_DSFLT_SLOT_VALUE_TAGGED_SETTER ( 4.0000000 , fs_ , 1 , 13 ); REPEATED_DSFLT_SLOT_VALUE_TAGGED_SETTER is a C preprocessor definition that results in a direct memory access without any function call overhead. To confirm that and just for fun, here is the resulting assembler code (x86): movl $0x3f800000, 0x8(%eax) movl $0x40000000, 0xc(%eax) movl $0x40400000, 0x10(%eax) movl $0x40800000, 0x14(%eax) Doing the same thing, but with a regular vector would require boxing each value. For literals, this generates a static file-scope value in the C back-end, increasing the memory usage: static _KLsingle_floatGVKd K3 = { & KLsingle_floatGVKdW , // wrapper 5.0000000 }; Similarly, when we go to fetch and add the values, using the limited vector will be far more efficient as it already knows the type of the value involved and no additional checks need to be done. We'll use this snippet to demonstrate where fs is a limited vector as above and bfs is a normal vector with boxed values: let s = fs [ 0 ] + fs [ 1 ]; let bs = bfs [ 0 ] + bfs [ 1 ]; This results in the following code // Limited vector T9 = REPEATED_DSFLT_SLOT_VALUE_TAGGED ( fs_ , 1 , 1 ); T10 = REPEATED_DSFLT_SLOT_VALUE_TAGGED ( fs_ , 1 , 5 ); T11 = primitive_single_float_add ( T9 , T10 ); // Normal vector with boxed floats T19 = KelementVKdMM11I ( bfs_ , ( dylan_value ) 1 , & KPempty_vectorVKi , & Kunsupplied_objectVKi ); T20 = KelementVKdMM11I ( bfs_ , ( dylan_value ) 5 , & KPempty_vectorVKi , & Kunsupplied_objectVKi ); CONGRUENT_CALL_PROLOG ( & KAVKd , 2 ); T3 = CONGRUENT_CALL2 ( T19 , T20 ); There's a lot going on there. With the limited vector, REPEATED_DSFLT_SLOT_VALUE_TAGGED is a direct memory access, while with the normal vector, it is going through the element method (whose mangled name is KelementVKdMM11I ) and doing bounds checks. When performing the addition, the limited vector code is able to directly add the floating point values. However, with the normal vector, it may have gotten any type of object out of the vector, so it has to go through a generic dispatch ( CONGRUENT_CALL_PROLOG and CONGRUENT_CALL2 ) to invoke the method for + which is mangled to be KAVKd in C. This should help you understand that limited types can help the compiler greatly optimize the resulting code and improve the memory usage. Union Types In Dylan, union types represent a way to specify that a given value is one of a two or more types. They are frequently used to represent that a value does not exist: let x :: type-union ( singleton ( #f ), <integer> ) = bar ( 3 ); As we can see, union types are created using the type-union function. Dylan provides a shorthand for the above technique, a method false-or , which returns the union of #f and a given type: let x :: false-or ( <integer> ) = bar ( 3 ); Singleton Types What Dylan calls singleton types are a way to create a new type that indicates that an individual object is expected. This is commonly used in method dispatch: define method factorial ( n :: singleton ( 0 )) 1 end ; An alternative syntax makes this a bit more readable to many people: define method factorial ( n == 0 ) 1 end ; Singletons are described in the DRM in a bit more detail, but the important thing to note is that for a value to match a singleton type, it must be == to the object used to create the singleton. This means that not all objects can be used as singleton types; in particular, strings are a notable exception. Also important is that a method specializer that is a singleton is considered to be the most specific match. This is because it is directly matching against the value passed in. A common use of singleton types is in defining make methods by using a singleton type for the class argument: define method make ( class == <file-stream> , #rest initargs , #key locator , element-type = <byte-character> , encoding ) => ( stream :: <file-stream> ) let type = apply ( type-for-file-stream , locator , element-type , encoding , initargs ); if ( type == class ) next-method () else apply ( make , type , initargs ) end end method make ; This example is also interesting as it demonstrates that the type is a first class object by using type-for-file-stream to look up which type should be used to instantiate the file stream. (This way of implementing a make method specialized on an abstract class like <file-stream> is a common way to implement a factory method in Dylan.)

Types Are Values As described in the DRM: All types are first class objects, and are general instances of <type> . Implementations may add additional kinds of types. The language does not define any way for programmers to define new subclasses of <type> . This means that functions can return instances of a type and type objects are treated like any other value in Dylan. This is used in many places, including type-for-copy in the standard library. A common example of treating types as values was the shorthand function introduced above when discussing type unions: false-or .