# TypeState Note

"Typestate" is the refinment of the concept "type". Whereas the type of a date object determines the set of operations ever permitted on the object, typestate detemines the subset of these oprations which is permitted in a particular context.

Typestate tracking is a program analysis technique which enhances program reliability by detecting at compile-time syntactically legal but semantically undefined execution sequences.

What's more, this can also be applied in automatically insert finalization.

Typestate captures the notion of an object's being in an (in)appropriate state for the application of a particular operation. Each type has an associated set of typestates. An object of a given type is at each point in a program in a single one of the typestates assocated with its type.

A partial order can be defined on the typestates of a given type. Intuitively, a "higher" typestate corresponds to a larger amount of resources allocated to the object.

From one typestate to another typestate, there will be a "typestate transition" accompanying some operation. The typestate transition is defined by

1. A typestate precondition
2. One or more typestate postconditions

And among the various outcomes, one outcome is called "normal outcome", others called "exceptional outcomes"

To track typestate in a program at compile-time, we make typestate a static invariant property of each variable name at each point in the program text.

To preserve the static invariance of typestates, we define a rule for resolving the typestate of variable names at points where execution paths merge, such as the beginning of a loop, the end of a conditional statement, or the entry of an exception handler. The rule of determining typestate at a merge statement S is to defined the typestate of each variable name as the greatest lower bound of the typestates of that same name on all paths merging at S.

A program execution is typestate-correct iff:

1. Before the applications of each operation in the program, each operand $v_i$ has a typestate matching its typestate precondition for the operation.
2. On termination of a program, all objects declared in the program are returned to the bottom typestate.

A program text is typestate-consistent iff it can be transformed by the addition of typestate-lowering coercions into a program each which can be executed typestate-correctly following any path.

Typestate tracking adds typestate labels to each node of the program graph. These labels associate each program variable $v_i$ with its typestate $s_i$ at that node. We shall denote these typestate labels by tuples.

### With calls

To archieve independent typestate checking in the presence of calls, we have interface definition -- seperate modules which specify the assumptions shared by the calling and called modules.

For caller, it has some pre/postconditions defined on calling. While for callee, it has extractly the reverse: post-condition on accept and pre-condition on return.

Lanaguages that allow unrestricted pointer assignment do not support tracking typestate at compile-time since the mapping between symbol and object is not determined.

Except for that, the concurrency data-sharing will also interfere with typestate tracking.