Principal type-schemes for functional programs

Damas, Lúıs; Milner, Robin

doi:10.1145/582153.582176

Cited by 784 publications

(553 citation statements)

References 5 publications

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“…Hence we have implemented the resolution of polymorphic logic programs as a precompiler to a Prolog system: It takes a polymorphic logic program as input and produces a Prolog program as output. The clauses of the input program need not be annotated with types, because the precompiler computes the most general type of each danse by the type inference algorithm of [DM82]. predicates in a polymorphic logic program, then type annotations must be deleted in argument terms before calling a type-generally defined predicate.…”

Section: Methodsmentioning

confidence: 99%

“…Since we have translated higher-order objects into polymorphic logic programs, the use of higher-order objects is type secure in our framework. We have similar typing rules as in functional languages [DM82], and therefore functions and predicates have always appropriate arguments at run-time.…”

Section: S(s(s(z)))]mentioning

confidence: 99%

“…We are interested in a polymorphic type system where type declarations may contain type variables that are universally quantified over all types [DM82]. Mycroft and O'Keefe [MO84] have investigated such a type system for Prolog.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Horn clause programs with polymorphic types: Semantics and resolution

Hanus¹

1989

Tapsoft '89

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This paper presents a Horn clanse logic where functions and predicates are declared with polymorphic types. Types are parameterized with type variables. This leads to an ML-like polymorphic type system. A type declaration of a function or predicate restricts the possible use of this function or predicate so that only certain terms are allowed to be arguments for this function or predicate. The semantic models for polymorphic Horn clause programs are defined and a resolution method for this kind of logic programs is given. It will be shown that several optimizations in the resolution method are possible for specific kinds of programs. Moreover, it is shown that higher-order programming techniques can be applied in our framework.

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Section: Methodsmentioning

confidence: 99%

Section: S(s(s(z)))]mentioning

confidence: 99%

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Horn clause programs with polymorphic types: Semantics and resolution

Hanus¹

1989

Tapsoft '89

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“…Consider an ML-polymorphic type system [11,5,4], extended with a rule for polymorphic recursion [12]:…”

Section: Polymorphic Recursion Revisited: Kleene-mycroft Iterationmentioning

confidence: 99%

Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

Dussart

Henglein²,

Mossin³

1995

Static Analysis

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Abstract. The combination of parameter polymorphism, subtyping extended to qualified and polymorphic types, and polymorphic recursion is useful in standard type inference and gives expressive type-based program analyses, but raises difficult algorithmic problems. In a program analysis context we show how Mycroft's iterative method of computing principal types for a type system with polymorphic recursion can be generalized and adapted to work in a setting with subtyping. This does not only yield a proof of existence of principal types (most general properties), but also an algorithm for computing them. The punch-line of the development is that a very simple modification of the basic algorithm reduces its computational complexity from exponential time to polynomial time relative to the size of the given, explicitly typed program.This solves the open problem of finding an inference algorithm for polymorphic binding-time analysis [7].

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“…This implies that the possible solution to program verification problem is either by abstract interpretation to simplify the given proof obligation, or by interactive manner to acquire some oracles during verification, or by developing specific methods for specific verification problems which are decidable. Following the above three lines, there are various techniques to program verification that have been well established so far, e.g., the abstraction-based techniques [11] such as static program analysis [12,16] and program typing [13,19], theorem-proving based deductive methods [20,21], model-checking [4,5,6,24], etc. The main disadvantage of the abstraction-based techniques is that complicated properties cannot be dealt with well because complicated properties closely interwind with the actual executions of a program, but normally in abstract executions of the program lots of useful information will be lost.…”

Section: Introductionmentioning

confidence: 99%

Program Verification by Using DISCOVERER

Yang

Zhan

Xia

et al. 2008

Verified Software: Theories, Tools, Experiments

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Abstract. Recent advances in program verification indicate that various verification problems can be reduced to semi-algebraic system (SAS for short) solving. An SAS consists of polynomial equations and polynomial inequalities. Algorithms for quantifier elimination of real closed fields are the general method for those problems. But the general method usually has low efficiency for specific problems. To overcome the bottleneck of program verification with a symbolic approach, one has to combine special techniques with the general method. Based on the work of complete discrimination systems of polynomials [33,31], we invented new theories and algorithms [32,30,35] for SAS solving and partly implemented them as a real symbolic computation tool in Maple named DISCOVERER. In this paper, we first summarize the results that we have done so far both on SAS-solving and program verification with DISCOVERER, and then discuss the future work in this direction, including SAS-solving itself, termination analysis and invariant generation of programs, and reachability computation of hybrid systems etc.

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Principal type-schemes for functional programs

Cited by 784 publications

References 5 publications

Horn clause programs with polymorphic types: Semantics and resolution

Horn clause programs with polymorphic types: Semantics and resolution

Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

Program Verification by Using DISCOVERER

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