Mads Tofte and Lars Birkedal. Unification and polymorphism in region inference. In Proof, Language, and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....found its way in many modern languages such as Smalltalk, ML and Java. The desire to have static control of memory management, retaining deallocation safety, led to the introduction of regions [14, 27,46, 50] Region annotations can be automatically inferred by means of a type and e#ect analysis [6,47,48,51]. As such, it is possible to eliminate the runtime cost of trace based garbage collection without losing deallocation safety. Based on the region calculus by Tofte and Talpin [51] the ML kit [49] a compiler for the functional programming language Standard ML [34] implements a practical ....

....2 . Its arrow e#ect #.# describes the e#ect of the body and is discharged on function application. The e#ect variable # stands for the arrow e#ect of the function. It implements a mechanism for parametric polymorphism over arrow e#ects, particularly useful in the presence of higher order functions [48]. E#ect variables can also occur in an e#ect set. A result type # abstracts a type over region and e#ect variables. As an extension to the Tofte Talpin system, we take a type with place # to be a pair of a result type # and a region #. Type variables, #, are taken from a denumerable set TypeVar ....

Mads Tofte and Lars Birkedal. Unification and polymorphism in region inference. In Proof, Language, and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

....for Standard ML [40] without trace based garbage collection [59] and forms the basis for the o#ine partial evaluator of this paper. A region is a part of memory of potentially unbounded size. In # , regions are allocated and deallocated as a whole in a stack like manner. Region inference [3,57,58] translates an ML typeable program into a # expression. The following grammar defines its terms: RegionTerm # #. e Constants and lambda expressions are values and the annotation at # indicates that the object is to be allocated in the region bound to #. Regions are ....

....the set of regions that are a#ected by its evaluation. A type is either a type variable, #, an integer type, or a function type. Function types carry an arrow e#ect #.#, which is a pair of an e#ect variable and a latent effect. E#ect variables are a technical device for type reconstruction of # [58]. They play no active role during constraint analysis. The e#ect variable identifies a group of functions that share at least one application. The use of e#ect variables corresponds to a simple control flow analysis. The latent e#ect of an arrow e#ect contains the regions a#ected by the body of ....

Mads Tofte and Lars Birkedal. Unification and polymorphism in region inference. In Proof, Language, and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

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Mads Tofte and Lars Birkedal. Unification and polymorphism in region inference. In Proof, Language, and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

....in type environment TE the term e has type with place and effect #. It differs from the presentation of Tofte and Talpin [15] in two respects: first, as stated earlier, we are omitting recursion and polymorphism. Secondly, we ignore effect variables, which are an artefact for type unification [13]. In the absence of region polymorphism, they can be omitted from the type system. 3. THE STORE LESS REGION CALCULUS The store less region calculus [9] provides a very simple and elegant syntactic soundness proof. It is based on the observation that terms like c at # cannot be used as values. ....

Mads Tofte and Lars Birkedal. Unification and polymorphism in region inference. In Proof, Language, and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

....in type environment TE the term e has type with place and effect . It differs from the presentation of Tofte and Talpin [15] in two respects: first, as stated earlier, we are omitting recursion and polymorphism. Secondly, we ignore effect variables, which are an artefact for type unification [13]. In the absence of region polymorphism, they can be omitted from the type system. 3. THE STORE LESS REGION CALCULUS SYNTACTIC TYPE SOUNDNESS RESULTS FOR THE REGION CALCULUS 7 Terms e : v j x j c at j x: e at j e e j letregion in e j copy [ 1 ; 2 ] e Values v : hci j h x: ....

Mads Tofte and Lars Birkedal. Unification and polymorphism in region inference. In Proof, Language, and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

.... # 1 satisfying both # 1 = S 1 (# 1 ) S # 1 (S(# 1 ) S # 1 (# 1 ) and # 2 = S 1 (# 2 ) S # 1 (S(# 2 ) S # 1 (# 1 ) The most general way to unify arrow e#ects involves taking the union of the sets the handles denote, without performing substitution on the region variables in those sets [Tofte and Birkedal 1996]. Lemma 5.4.1. There exists an algorithm unifyArrE# with the following properties. Let B = Q, #) be a consistent basis, and let # 1 .# 1 # # and # 2 .# 2 # #. Then S e = unifyArrE# (# 1 .# 1 , # 2 .# 2 ) succeeds and (1 ) S e is a most general unifier for # 1 .# 1 and # 2 .# 2 in B; ....

Tofte, M. and Birkedal, L. 1996. Unification and polymorphism in region inference. Submitted to the Milner Festschrift. http://www.diku.dk/users/tofte/publ/milner.ps.

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