Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMUCS -90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are given in Section 3. In Section 4 we discuss applications of our technique with respect to separate compilation and other issues, including the formulation of type inference as proof search. We will also discuss related work, in particular those of Leivant [9] Appel and Shao [1] and Harper [5]. 1 Of Variables, Free, Bound, and Fugitive Strictly speaking, the algorithm W infers types, and not type schemes. Let v m denote v 1 ; v m . Whenever a typing assumption f : Piv m :t is used, a copy of the type t[x m =v m ] is created using a set of new free variables xm . This ....

....either took short cuts with the let case or were stopped by gen. In [4] Hannan gave proof theoretic formulations of the natural semantics of ML. But his technique for let was basically to replace let x = M in N with N [M=x] To allow let expressions to be typed naturally, Harper defined in [5] an algorithmic version of the Damas Milner calculus for the express purpose of allowing the modified typing rules of the new calculus to become logic programs that yield principal type schemes. He defined a predicate called witnessed that captures the maximality condition implemented by gen. ....

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS90 -144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....as types. 27 In any case, the above program can at most be called a type checker, when T is instead some closed type expression. In [6] Hannan examined the specification of type inferencing in detail, but was also stopped short of a complete, declarative formulation because of this problem. In [7], Harper defined non deterministic type inferencing proof systems in the Edinburgh LF logical framework, which has a close relationship with Prolog (see next chapter) Unification, however, was not part of this specification. One would have to guess the correct form of type expressions such as oe ....

Robert Harper. Systems of polymorphic type assignment in lf. Technical Report CMU-CS90 -144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....either took short cuts with the let case or were stopped by gen. In [6] Hannan gave prooftheoretic formulations of the natural semantics of ML. But his technique for let was basically to replace let x = M in N with N [M=x] To allow let expressions to be typed naturally, Harper defined in [7] an algorithmic version of the Damas Milner calculus for the express purpose of allowing the modified typing rules of the new calculus to become logic programs that yield principal type schemes. He defined a predicate called witnessed that captures the maximality condition implemented by gen. ....

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS-90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....types inductifs, est un sujet de recherche actuel. Une impl ementation de Mini ML a l ordre sup erieur dans Coq est etudi ee dans [DH92] Une etude tr es int eressante des diff erentes impl ementations du syst eme de type de Mini ML a l ordre sup erieur dans LF a egalement ete effectu ee dans [Har90] La d efinition du constructeur lam : exp exp) exp, empeche exp d etre d efini dans Coq comme un type inductif. En premiere approximation, nous n utiliserons pas les types inductifs pour traduire exp mais une liste de constantes introduites par l instruction Parameter : Parameter exp : ....

R. Harper. Systems of Polymorphic type assignment in LF. Technical Report CMUCS -90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....concatenation and [ e = x ] e 0 for the result of substituting e for x in e 0 , renaming bound variables as necessary to avoid capture. Furthermore, we say that Pi(x) if the rightmost occurrence of x in Pi is assigned . Type assignment in an environment is written as x : Harper [9] studied several formulations for the Damas Milner fragment of ML [4] with a view toward their formalization in LF, and discussed their suitability for direct execution. We use a simpler encoding that is sufficient for our purposes. The idea for this also goes back to Hannan and Miller [7] 2 ....

....in Elf. Dietzen and Pfenning [5] show how this problem can be overcome for Prolog by adding a special construct called rule to the language, and a similar extension to Elf seems to be possible. For a number of variants of declarative presentations of the type system with explicit type schemas, see [9]. 4.3 Natural Operational Semantics Sometimes the most natural semantics for a programming language is nondeterministic in the sense that its execution would require backtracking in our chosen implementation language. However, the corresponding deterministic version is usually more ....

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS90 -144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....(abs y y) x (app x x) since x can not have both A and (arr A A) as types. In any case, the above program can at most be called a type checker, when T is instead some closed type expression. In [19] Hannan specified type inferencing as logic programming, up to the limitations described here. In [21], Harper defined several type inferencing proof systems in the Edinburgh LF logical framework [22] which has a close relationship with Prolog. Unification, however, was not present in any of his formulations, and none of the formulations can lead directly to a practical logic program. One would ....

....as principal types within the meta logic for the reasons we have discussed. Furthermore, Hannan had to bypass the difficulties of let typing in the same manner as our quicktype program. Full fi reduction was used instead of fi 0 reduction. To allow let expressions to be typed naturally, in [21] Harper defined an algorithmic version of the Damas Milner calculus for the express purpose of allowing the modified typing rules of the new calculus to become (Elf) logic programs that yield principal type schemes. He defined a predicate called witnessed that formulates, proof theoretically, ....

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS-90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

.... in [EP88] and is currently being revisited in [DH94] Higher order abstract syntax is now commonly used, at least by people who use either the Prolog language [MN88] or the Elf language [Pfe89] an implementation of the LF Logical Framework) both for writing semantics of languages [HM88] Har90] and for developing proofs in those semantics [HP92] MP91] PR91] Proofs in Elf [HP92] MP91] PR91] use induction. All these proofs rely on the introduction of an adequate induction principle. On the other hand, using systematically Coq s inductive types, Gerard Huet developed in Coq a theory of ....

R. Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS-90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990. RR n2292 18 J. Despeyroux & A. Hirschowitz

....proof checking. Unification and proof search algorithms have been developed [7, 27, 28, 24] and it has been amenable to an operational interpretation which is realized in the Elf programming language [21, 23] A wide range of deductive systems have been specified in LF and implemented in Elf [1, 15, 19, 20]. In this paper we investigate the use of Elf to implement the meta theory of deductive systems, thus addressing the third of the principal applications listed above. Our approach is based on three observations. Firstly, in LF deductions are represented as objects and can thus be part of ....

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS-90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....between an object and its type. In our example, we will represent various reduction and conversion relations in this style. Similar techniques have been used to specify type systems, operational semantics, compilation and other aspects of the semantics of programming languages (see, for example, [Han91, HP92, Har90, MP91]) The third stage is the formalization of the proofs of meta theorems in the framework. The construction which is implicit in the proof is represented as a judgment which relates deductions. For example, in the proof of the Church Rosser theorem we have to show the existence of certain reduction ....

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMUCS -90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

....LF. These include two different variations on Hoare logic [4] 3] modal logics from K to S4 [4] various calculi, including I, v , and linear calculus [4] 3] various type theories, including the LF type system itself, Martin Lof s type theory, and the Damas Milner type assignment system [22]. A natural deduction approach to operational semantics based on the ideas of LF has also been developed [5] A general theory of search, including a unification algorithm for the LF type theory, has been developed [44, 45] Elliott has also developed a unification algorithm for LF [16] which has ....

Harper, R. Systems of polymorphic type assignment in LF. Tech. Rep. CMU--CS--90--144, School of Computer Science, Carnegie Mellon University, June 1990.

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Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMUCS -90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

No context found.

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMU-CS90 -144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

No context found.

Robert Harper. Systems of polymorphic type assignment in LF. Technical Report CMUCS -90-144, Carnegie Mellon University, Pittsburgh, Pennsylvania, June 1990.

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