Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51:201-206, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....says that, when allocated, a memory object should (conceptually) be stamped with its type, and that the type of the object should not change during evaluation. When this property is maintained, it is straightforward to prove a subject reduction or type preservation property (see for example [44, 16]) which is in turn crucial to establishing type soundness. There are many examples from language design where this principle has been violated and resulted in an unsoundness. For instance, the naive treatment of polymorphic references in an ML like language, or the covariant treatment of arrays ....

Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51(4):201-206, August 1994.

....and applicative type variables respectively of Tofte s system. We say that a type scheme is weak i is unquanti ed and every type variable in is weak. Type var is the type of locations storing values of type . The rules of the type system are formulated as they are in Harper s system [Har94] and are given in Figure 1. It is a deductive proof system used to assign types to expressions. Typing judgements have the form ; e : meaning that expression e has type assuming that prescribes type schemes for locations in e and prescribes phrase types for the free identi ers of ....

....er typings. An identi er typing is a nite function mapping identi ers to phrase types; x) is the phrase type assigned to x by and [x : assigns phrase type to x and to variable x 6= x, phrase type (x ) Meta variable ranges over location typings. Unlike other approaches [Tof90, Har94, SmVo95], a location typing here is a nite function mapping locations to type schemes. This is the most novel aspect of the type system. The notational conventions for location typings are similar to those for identi er typings. The generalization of a type scheme relative to and , written Close ....

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Harper, R., A Simpli ed Account of Polymorphic References, Information Processing Letters, 51, pp. 201-206, August 1994.

....annotations [16] Our type system thus demonstrates that ML style polymorphism can be brought cleanly into the realm of traditional imperative languages. We establish the soundness of our type system with respect to a natural semantics for Polymorphic C. First we use Harper s syntactic approach [8] to establish the type preservation property (also known as the subject reduction property) We then prove a type soundness theorem that gives a rigorous and useful characterization of what can go wrong when a well typed Polymorphic C program is executed. More precisely, we show that the execution ....

....always produces a value and a memory: then v is a value and is a memory. PROOF. By induction on the structure of the derivation. 2 12 4 Type Preservation We now turn to the question of the soundness of our type system. We begin in this section by using the framework of Harper [8] to prove that our type system satis es the type preservation property (sometimes called the subject reduction property) This property basically asserts that types are preserved across evaluations; that is, if an expression of type evaluates successfully, it produces a value of type . But ....

Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51:201-206, August 1994.

....some correct forms typing lemma, you know that only values of the form needed have that type. The following is a typical type preservation theorem. If is a memory, mapping locations to values, and is a location typing, mapping locations to types, then type preservation is stated as follows [16]: Theorem. Type Preservation) If e ) v; e : and : then there exists such that , and v : The rst hypothesis of the theorem states that under memory , a closed expression e evaluates to a value v and a memory . Now e may ....

Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51:201-206, 1994.

.... semantics [45] Soundness of the constraint analysis and correctness of the specializer are proven by operational methods, similar to the approach of Hatcli and Danvy for Moggi s computational meta language [22] Building on previous work [7,28] we use syntactic type soundness techniques [20,62] to show soundness of the constraint analysis with respect to the specialization semantics. We also prove that the specialization semantics is correct with respect to the standard semantics of the region calculus. We do so by showing that each reduction step taken by the specializer is in fact a ....

Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51(4):201-206, August 1994. See also note [21].

....show how to extend the type system from the previous section in order to attain a syntactic [18] proof of type soundness. We then describe the proof, the details of which we relegate to a technical report [4] For the most part, the extensions are the conventional ones for a heap and references [5], with several tedious complications that paths introduce. The basic idea is to prove that the types of locations are invariant. That is, the value to which the heap maps a label may change, but only to a value of the same type. However, we also need to prove an additional heap invariant for ....

....integration of universal types into C. Their technical development is somewhat similar to ours, but they leave the treatment of structures to future work. It is precisely structures that motivate existential types and our treatment of them. The well studied problem of polymorphic references in ML [5, 18, 16] also results from quanti ed types, aliasing, and mutation, so it is natural to suppose the work presented here is simply the logical dual of the same problem. We have not found the correspondence between the two issues particularly illuminating, but we nonetheless point out similarities that may ....

Robert Harper. A simplied account of polymorphic references. Information Processing Letters, 51(4):201-206, August 1994.

....of state, ignoring issues regarding agents and type abstraction. The point is simply to establish basic notation for the discussion that follows. Our work follows closely the standard treatment of references in a subject reduction setting, e.g. see the work of Wright and Felleisen [1994] or Harper [1994]. We then give an informal description of the issues that make the store a particularly interesting addition to our framework. Then we formally augment our calculus with state and discuss the reasons for particular design decisions. Finally, we augment the proofs of type soundness and safety ....

Harper, R. 1994. A simplied account of polymorphic references. Information Processing Letters 51, 4 (August), 201-206.

....TTRC with operations on references. Extending the ideas of the store less calculus, we provide a small step operational semantics for IRC based on an explicit store and prove its type soundness, using the syntactic approach due to Wright and Felleisen [16] in a variation pioneered by Harper [8]. The reduction semantics in this paper follows Plotkin s approach to operational semantics [12] Section 5 contains another novel contribution of the present work. It relates the three calculi by proving the equivalence of TTRC and IRC, as well as the equivalence of IRC and SRC. These technical ....

....TTRC and IRC, as well as the equivalence of IRC and SRC. These technical results are inspired by Calcagno s work [5] The rst technical achievement of this work is the reformulation of the region calculus, so that a standard syntactic soundness proof a la Wright and 3 Felleisen [16] and Harper [8] can be constructed. We do so using a store less formulation as well as a store based one. While the store less formulation is extremely simple and elegant, the store based formulation is more complicated but supplies a soundness proof for the calculus with references, as it is actually used in ....

Robert Harper. A simplied account of polymorphic references. Information Processing Letters, 51(4):201-206, August 1994. See also note [9]. 31

....rule for poly non deterministically guesses which variants are needed. This is a simpli cation with respect to the actual implementation that generates the required variants on demand. Our type soundness proof follows the syntactic approach of Wright and Felleisen [27] as re ned by Harper [7]. De nition 1. For an expression e, free(e) is the set of free variables of e. Its usual de nition extends to the non standard expressions as follows: free(poly 1 : n x:e) free(e) n fxg free(spec e 1 e 2 ) free(e 1 ) free(e 2 ) free(POLY(x; h i ; v i 7 a i i) fxg [ S i ....

Robert Harper. A simplied account of polymorphic references. Information Processing Letters, 51(4):201-206, August 1994. See also note [8].

....are rejected. So if the type of a pair (M 1 ; M 2 ) is labelled with then 1 and 2 , the type of its components cannot be labelled with or with a locality variable. 4 Type soundness In order to prove type soundness we follow the syntactic approach of Wright and Felleisen [16] and Harper [5] : we rst prove type preservation, then we prove that expressions that may lead to execution errors are untypable. In proofs for the Hindley Milner polymorphic type discipline, it is essential to prove a substitution lemma which, in its turn, is used to prove type preservation ( 14] 16] In ....

Robert Harper. A simplied account of polymorphic references. Information Processing Letters, 51(4):201-206, August 1994. See also note [6].

....on the derivation of M j= R. Roughly speaking, we associate type with heap address h whenever the rule (heap array) is applied and a derivation is regular if a heap address is associated with at most one type. This notion of regularity is essentially the same as the notion of store typing in [2], which was used to address the circularity of references in ML. Clearly, there is no regular derivation for the above example: in order to derive M j= R, we have to associate h with at least two distinct types int (when we derive H j= R(0) R(0) and nat (when we derive H j= R(1) R(1) In ....

....may be extended by the execution of newarray) We can then prove that if M j= R[ has a regular derivation then M 0 j= R 0 [ 0 ] 0 ] also has a regular derivation, where we use the notation in the above paragraph. The proof bears a great deal of similarity to the soundness proof in [2]. In summary, if we start with an entailment that has a regular derivation, then all entailments in the proof of the type soundness of DTAL have regular derivations. Therefore, the scenario of shared pointers mentioned previously can never occur. This allows us to establish Theorem 5.1. Note the ....

R. Harper. A simplied account of polymorphic references. Information Processing Letters, 51:201-206, 1994.

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Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51:201-206, 1994.

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Robert Harper. A simpli ed account of polymorphic references. Information Processing Letters, 51(4):201-206, 1994.

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Robert Harper. A simplied account of polymorphic references. Information Processing Letters, 51(4):201-206, 1994.

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