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103
Type inference and semiunification
 In Proceedings of the ACM Conference on LISP and Functional Programming (LFP ) (Snowbird
, 1988
"... In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically type ..."
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In the last ten years declarationfree programming languages with a polymorphic typing discipline (ML, B) have been developed to approximate the flexibility and conciseness of dynamically typed languages (LISP, SETL) while retaining the safety and execution efficiency of conventional statically typed languages (Algol68, Pascal). These polymorphic languages can be type checked at compile time, yet allow functions whose arguments range over a variety of types. We investigate several polymorphic type systems, the most powerful of which, termed MilnerMycroft Calculus, extends the socalled letpolymorphism found in, e.g., ML with a polymorphic typing rule for recursive definitions. We show that semiunification, the problem of solving inequalities over firstorder terms, characterizes type checking in the MilnerMycroft Calculus to polynomial time, even in the restricted case where nested definitions are disallowed. This permits us to extend some infeasibility results for related combinatorial problems to type inference and to correct several claims and statements in the literature. We prove the existence of unique most general solutions of term inequalities, called most general semiunifiers, and present an algorithm for computing them that terminates for all known inputs due to a novel “extended occurs check”. We conjecture this algorithm to be
Type Inferencing for Polymorphic OrderSorted Logic Programs
 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1995
"... The purpose of this paper is to study the problem of complete type inferencing for polymorphic ordersorted logic programs. We show that previous approaches are incomplete even if one does not employ the full power of the used type systems. We present a complete type inferencing algorithm that cover ..."
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The purpose of this paper is to study the problem of complete type inferencing for polymorphic ordersorted logic programs. We show that previous approaches are incomplete even if one does not employ the full power of the used type systems. We present a complete type inferencing algorithm that covers the polymorphic ordersorted types in PROTOSL, a logic programming language that allows for polymorphism as in ML and for hierarchically structured monomorphic types.
Nominal logic programming
, 2006
"... Nominal logic is an extension of firstorder logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, αequivalence). This article investigates logic programming based on nominal logic. This technique is especial ..."
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Nominal logic is an extension of firstorder logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, αequivalence). This article investigates logic programming based on nominal logic. This technique is especially wellsuited for prototyping type systems, proof theories, operational semantics rules, and other formal systems in which bound names are present. In many cases, nominal logic programs are essentially literal translations of “paper” specifications. As such, nominal logic programming provides an executable specification language for prototyping, communicating, and experimenting with formal systems. We describe some typical nominal logic programs, and develop the modeltheoretic, prooftheoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via two examples.
Implementing Polymorphic Typing in a Logic Programming Language
 COMPUTER LANGUAGES
, 1993
"... Introducing types into a logic programming language leads to the need for typed unification within the computation model. In the presence of polymorphism and higherorder features, this aspect forces analysis of types at runtime. We propose extensions to the Warren Abstract Machine (WAM) that permi ..."
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Cited by 18 (11 self)
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Introducing types into a logic programming language leads to the need for typed unification within the computation model. In the presence of polymorphism and higherorder features, this aspect forces analysis of types at runtime. We propose extensions to the Warren Abstract Machine (WAM) that permit such analysis to be done with reasonable efficiency. Much information about the structures of types is present at compiletime, and we show that this information can be used to considerably reduce the work during execution. We illustrate our ideas in the context of a typed version of Prolog. We describe a modified representation for terms, new instructions and additional data areas that in conjunction with existing WAM structures suffice to implement this language. The nature of compiled code is illustrated through examples, and the kind of runtime overheads that are incurred for processing types is analyzed, especially in those cases where others have shown that type checking can be eliminated during execution. The ideas
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 18 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
The Specification and Implementation of ConstraintBased Unification Grammars
, 1991
"... this paper. The research of Pollard and Franz was supported by a grant from the National Science Foundation (IRI8806913). (Empty Category Principle and Subjacency) and so forth. Patterns of crosslinguistic variation are accounted for by means of the parametrization of these principles. The method ..."
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Cited by 17 (1 self)
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this paper. The research of Pollard and Franz was supported by a grant from the National Science Foundation (IRI8806913). (Empty Category Principle and Subjacency) and so forth. Patterns of crosslinguistic variation are accounted for by means of the parametrization of these principles. The methodological distinction between these two approaches is widely supposed to be that rules enumerate possibilities, while principles eliminate possibilities. But it is quite difficult to distinguish formally between a parametrized disjunctive principle and a collection of schematic rules only one of which can apply to a given structure. Consider, for example, the distinction between categorial grammar application schemata, basic ID rules of GPSG, and the Cstructure constraints of LFG, on the one hand, and the disjunctive clauses of ¯ X Theory or the Empty Category Principle on the other. It should also be borne in mind that socalled rulebased approaches often employ not only rules but also global constraints on representations which behave similarly to principles, such as the Head Feature Convention and the Control Agreement Principle of GPSG or the Completeness and FunctionArgument Biuniqueness Conditions of LFG. HPSG belongs to the "unificationbased" family of linguistic theories, but differs from LFG and GPSG in that grammars are formulated entirely in terms of universal and languagespecific principles expressed as constraints on feature structures, which in turn are taken to represent possible linguistic objects. As shown by Pollard and Sag (1987), constraints on feature structures can be used to do the same duty as many of the principles and rules of GPSG, LFG and GB. Unlike rulebased theories, in HPSG, immediate dominance and linear precedence conditions (traditional...
Type Constraint Solving for Parametric and Adhoc Polymorphism
, 1999
"... . Unification has long been used as a mechanism for type checking and type inference for HindleyMilner types in functional programming. The programmer defines the possible types, and the compiler uses unification to check and infer types for function definitions. In constraint logic programming it ..."
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Cited by 16 (7 self)
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. Unification has long been used as a mechanism for type checking and type inference for HindleyMilner types in functional programming. The programmer defines the possible types, and the compiler uses unification to check and infer types for function definitions. In constraint logic programming it is natural to extend the functional programming case by allowing overloading of predicate and function definitions, that is, adhoc polymorphism. Mycroft and O'Keefe showed how to check predicate type declarations under these assumptions. In this paper, we show how to infer predicate types, by translating a constraint logic program with given types into a logic program over types. The program can then be used to check and infer the possible types for the predicates and variables appearing in the original program. Since executing the translated program can be inefficient when there are highly disjunctive type definitions, we use methods of propagation based constraint solving and memoing to ...
A Guide To The NUProlog Debugging Environment
"... The NUProlog Debugging Environment (Nude) is a collection of integrated tools for locating bugs in both pure and nonlogical NUProlog programs. It has static analyses and userdriven dynamic analyses including a fourport debugger and a declarative debugger. This document is a guide to using the e ..."
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Cited by 16 (1 self)
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The NUProlog Debugging Environment (Nude) is a collection of integrated tools for locating bugs in both pure and nonlogical NUProlog programs. It has static analyses and userdriven dynamic analyses including a fourport debugger and a declarative debugger. This document is a guide to using the environment. Contents 1 introduction 3 1.1 Nude at a glance : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.2 limitations of Nude : : : : : : : : : : : : : : : : : : : : : : : : : 4 2 background on debugging 4 2.1 traditional Prolog debugging : : : : : : : : : : : : : : : : : : : : 4 2.2 declarative debugging : : : : : : : : : : : : : : : : : : : : : : : : 5 2.2.1 how does it work? : : : : : : : : : : : : : : : : : : : : : : 5 2.2.2 what problems are there? : : : : : : : : : : : : : : : : : : 5 3 components of Nude 6 3.1 static analyses : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 3.1.1 Nit : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 3.1.2 th...
A Framework for Analysis of Typed Logic Programs
 IN PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON FUNCTIONAL AND LOGIC PROGRAMMING, VOLUME 2024 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2001
"... The paper presents a novel approach to the analysis of typed logic programs. We assume regular type descriptions of logic program variables provided by regular tree grammars. Types are used to identify components of terms which can be equated during the programs execution. This information is ..."
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Cited by 15 (5 self)
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The paper presents a novel approach to the analysis of typed logic programs. We assume regular type descriptions of logic program variables provided by regular tree grammars. Types are used to identify components of terms which can be equated during the programs execution. This information is
Mode Analysis Domains for Typed Logic Programs
, 2000
"... . Precise mode information is important for compiler optimisations and in program development tools. Within the framework of abstract compilation, the precision of a mode analysis depends, in part, on the expressiveness of the abstract domain and its associated abstraction function. This paper consi ..."
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. Precise mode information is important for compiler optimisations and in program development tools. Within the framework of abstract compilation, the precision of a mode analysis depends, in part, on the expressiveness of the abstract domain and its associated abstraction function. This paper considers abstract domains for polymorphically typed logic programs and shows how specialised domains may be constructed for each type in the program. These domains capture the degree of instantiation to a high level of precision. By providing a generic definition of abstract unication, the abstraction of a program using these domains is formalised. The domain construction procedure is fully implemented using the Godel language and tested on a number of example programs to demonstrate the viability of the approach. Note: Some proofs have been omitted for space reasons. They can be found in the full version of this paper [17]. 1 Introduction 1.1 Background Typed logic programming languages su...