Specifying and implementing theorem provers in a higher. This book was published by cambridge university press in june 2012. Main challenges for the integration of logic programming and arti. Terms from the higher order language are defined via abstraction. Implementing hol in an higher order logic programming language. One line of research is higher order logic programming. Semantics of lazy higherorder functional and logic programming. Such large speci cations have put to test implementations of logical frameworks and exposed several problems.
It therefore forms a much more practical basis for higherorder logic programming with its pervasive use of uni. The big difference between propositional logic and first order logic is that we can talk about things, and so theres a new kind of syntactic element. Prolog, which represents programs as higherorder defi nite clauses and interprets them using a. The aim of this course is to introduce you to the theory and practice of logic programming.
Pdf in this paper we consider the problem of extending prolog to include predicate and function variables and typed terms. Higher order logic programming in radial basis function. Dale miller we argue that a logic programming language with a higher order intuitionistic logic as its foundation can be used both to naturally. Pdf higher order logic programming in radial basis. This book objectives to level out that a programming language based mostly totally on a merely typed mannequin of higherorder logic provides a classy, declarative means for providing such a treatment. Higher order functions characterise most functional programming. There are many ways to further extend secondorder logic. Three broad topics are covered in pursuit of this goal.
However, these systems often embody variable binding, a. Various stages of compilation are formulated as higher order logic programming including parsing and the generation of higher order representations, type checking. A generalization of horn clauses to a higher order logic is described and examined as a basis for logic programming. Welcome to the home page for the book programming with higher order logic by dale miller and gopalan nadathur. And the term, as well see when we do the semantics, is a name for a thing. Such logic programming languages have proved useful in areas such as databases, objectoriented programming, theorem proving, and natural language parsing. This extends tabled computation to the higher order setting and forms the basis of the tabled higher order logic programming interpreter.
After briefly discuss typical logic programming and functional programming styles we show how \higher order predi cates can be coded using the calln primitive. Read online higher order logic programmingy polytechnique book pdf free download link book now. We can extend higher order logic programming with constructive negation. We propose a typed, higherorder, concurrent linear logic programming called higherorder acl, which uniformly integrates a variety of mechanisms for concurrent computation based on asynchronous. Wadge abstract we describe a fragment of higher order horn logic which can be used as a higher order extension of prolog. Proof procedures of extensional higherorder logic programming. Modularity can be built into a pure functional language objectedorientedness. Semester 1, 201516 announcements programming exam a pdf version of the sicstus manual will be available during the exam also a short description of some builtin predicates. A foundation for higherorder logic programming 1 preface. Higherorder logic programming holp languages 17 typically use a typed calculus as their domain of computation.
Higherorder linear logic programming of categorial deduction. Implementing hol in an higher order logic programming language cvetan dunchev, claudio sacerdoti coen, enrico tassi to cite this version. Download higher order logic programmingy polytechnique book pdf free download link or read online here in pdf. In mathematics and logic, a higherorder logic is a form of predicate logic that is distinguished from firstorder logic by additional quantifiers and, sometimes, stronger semantics. Download higherorder logic programmingy polytechnique book pdf free download link or read online here in pdf. We demonstrate how the framework of higherorder logic programming, as. It turns out that the extension of higher order logic programs with constructive negation o ers a much greater versatility to extensional higherorder logic programming. Higher order logics with their standard semantics are more expressive, but their modeltheoretic properties are less wellbehaved than those of first order logic. Introduction what is nowadays the central part of any introductionto logic, and indeed to some the logical theory par excellence, used to be a modest fragment of the more ambi tious language employed in the logicist program of frege and russell. Nadathur, a logic programming approach to manipulating formulas and programs. This paper describes a general method of compiler implementation using higher order abstract syntax and logic programming. Two features of logic programming play important role in this modelling. We propose a purely extensional semantics for higherorder logic programming. Programming with higher order logic, by dale miller and gopalan nadathur, cambridge university press, 2012, hardcover, isbn10.
Specifying theorem provers in a higherorder logic programming language amy felty and dale miller department of computer and informat ion science university of pennsylvania philadelphia, pa 191046389 usa abstract since logic programming systems. Iris is a higher order concurrent separation logic framework, implemented and verified in the coq proof assistant. There are, of course, many choices for the higher order logic that might be used in such a study. Logic programming provides a natural framework for encoding and animating such systems. In this paper we consider the problem of extending prolog to include predicate and function variables and typed terms. Higherorder logics with their standard semantics are more expressive, but their modeltheoretic properties are less wellbehaved than those of firstorder logic. In all of these languages, rules are written in the form of. A key feature of inductive logic programming ilp is its ability to learn firstorder programs, which are intrinsically more expressive. Using the general intensional programming system gipsy. Implementing hol in an higher order logic programming language cvetan dunchev claudio sacerdoti coen university of bologna ftsvetan.
We show that this extension possesses certain desirable computational properties. Semantics for interactive higherorder functionallogic. Sections 7, 8 and 9 will be covered in lectures 6, 7 and 8. Second, we present e cient datastructures and algorithms for. Its packed with enterpriseclass features to meet your demanding requirements. What higher order logic programming is not we have already seen that we can use prolog as ametalanguage for prolog, and so manipulate prolog programs in prolog. Higherorder constructs extend the expressiveness of firstorder constraint logic programming c lp both syntactically and semantically. We give examples to show the interaction between higher order programming and other features of prolog such as nondeterminism, logic variables. Specifying and implementing theorem provers in a higherorder.
Moreover, there exists a relative simple sound proof procedure for the new language. To appear in handbook of logic in ai and logic programming, d. Compiler construction in higher order logic programming. Fourth, we present solutions to some slightly more challenging programming tasks. Semantics of lazy higherorder functional and logic. Indeed, one could virtually ignore the logic and simply program in the lambdacalculus which, of course, is not our aim. Logiforms form designer is the most flexible form design tool available. Cvetan dunchev, claudio sacerdoti coen, enrico tassi. Although he studied logic as a basis for functional programming rather than logic programming, his ideas are more fundamental and therefore equally applicable in both paradigms.
It turns out that the extension of higher order logic programs with constructive negation o ers a much greater versatility to extensional higher order logic programming. If youre looking for a free download links of programming with higherorder logic pdf, epub, docx and torrent then this site is not for you. A number of works have proposed various higher order constructs in the logic framework l, 5, 7, 23, 24, 30, 31,42,45, but with such a diversity of syntax and. Pdf higherorder concurrent linear logic programming. Types typically have a rich structure in declarative programming languages, making their runtime processing a costly operation.
Programming with higherorder logic, by dale miller and. Some uses of higherorder logic in computational linguistics acl. Hilog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions. Pdf higherorder logic as the basis for logic programming.
Download programming with higherorder logic pdf ebook. In this paper we consider the problem of extending prolog to include predicate and function variables and typed. Dynamic assumptions are permitted and can be used during the execution. In mathematics and logic, a higher order logic is a form of predicate logic that is distinguished from first order logic by additional quantifiers and, sometimes, stronger semantics. This book aims to show that a programming language based on a simply typed version of higher order logic provides an elegant, declarative means for providing such a treatment. Prototyping a functional language using higherorder logic. Higher order logic programming in twelf extends traditional rst order logic programming in three ways. First, a prooftheoretic framework that supports a general view of logic programming is identified. In qualitative terms, these higher order horn clauses are obtained from the. The interaction between higher order programming and some of the unique features of logic programming is illustrated and some important programming techniques are discussed. Logiforms online form builder, pdf tools for workflow. Intensional programming, higher order intensional logic hoil, runtime system, general intensional programming system gipsy, multitier architecture, peertopeer architecture 1 introduction the gipsy project is an ongoing effort aiming at. They have been used for a wide range of applications including theorem proving, program. In the case of prolog 18 it is the simplytypedcalculus, while in the case of elf 22 it is a dependently typedcalculus.
Applications of hilog are discussed, including dcg grammars, higherorder and modular logic programming, and deductive databases. Most recently, higherorder logic programming has been successfully employed in several certi. Specifying and implementing theorem provers in a higherorder logic programming language amy p. Its an expression that somehow names a thing in the world. The general principle, already recognized by tarski 1933 1956, is that in higher order logic one can formalize the semanticsdefine truthof lower order logic. Section 12 contains concluding remarks and a brief discussion of future work. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher order functions. We need an improved logic programming paradigm, not just an improved language, if pure logic programming is to become practical. In this speci cation, the variable n ranges over the numerals 0. Counterexample generation for higherorder logic using. Under this semantics, every program has a unique minimum herbrand model. The most obvious is third, fourth, and so on order logic. We show that higher order programming techniques are already in use in logic programming albeit in a limited form and that these can be generalized.
Higher order logic in relation to computing and programming. However, these methods sometimes embody variable binding, a notion that should be dealt with rigorously at a computational diploma. Secondorder and higherorder logic stanford encyclopedia of. However, computationally feasible algorithms do not exist for the general case, so most approaches restrict the higher order capability to handle only specific subclasses of functions. Higherorder logic programmingy polytechnique pdf book.
All books are in clear copy here, and all files are secure so dont worry about it. It allows the programmer to axiomatize predicates of predicates and operations on predicates. We present a new method of encoding higher order logic programming in radial basis function neural network. A rewriting approach to the semantics of higher order functional logic language is given in nmi95. Welcome to the home page for the book programming with higherorder logic by dale miller and gopalan nadathur. One aim of this paper is to illustrate higher order programming techniques in prolog. Higher order logic programming holp as the programming paradigm best suited for the three tasks above. Dale miller we argue that a logic programming language with a higher order intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. Objectoriented features require state updation and can be obtained only by destroying referential.
Optimizing the runtime processing of types in a higher. First, we have a rich type system based on dependent types, which allows the user to 11. In classical logic programming a computation is said to ounder if at some point a goal is reached that contains only nonground negative literals. For this purpose, we use a higher order logic to describe a generalization to first order horn clauses. Higher order logic programming holp languages are particularly useful for various kinds of meta programming and theorem proving tasks because of the logical support for variable binding via abstraction. Major logic programming language families include prolog, answer set programming asp and datalog. Pdf higher order logic programming in radial basis function. Higher order logic programming languages such as prolog and twelf improve the notion of first order logic programming in two ways. Mechanizing programming logics in higher order logic. From the outset, even the terminology of higher orderness seems illdefined. For this purpose, we use a higherorder logic to describe a generalization to firstorder horn clauses. Introduction to higher order categorical logic pdf free.
Read online higherorder logic programmingy polytechnique book pdf free download link book now. It has also been used to design new logic programming languages for handling concurrency and for viewing program clauses as possibly limited resources. If the desire is only to emulate the higher order features. Tabled higher order logic programming allows us to ef. Optimizing the runtime processing of types in a higherorder. Higherorder logic programming as constraint logic programming. In this chapter, we develop the idea of higher order logic programming by utilizing a higher order logic as the basis for computing. First, performance of the higher order logic programming interpreter may be severely hampered. Higher order logic programming in radial basis function neural network. Programming with higher order logic miller, dale, nadathur, gopalan on. The usual resolution to this problem in the typed logic programming setting is to restrict the. In this approach, a program is an applicative term rewriting system and the presented narrowing calculus for higher order functional logic programming is shown to be sound and complete for proving. Theres a new kind of syntactic element called a term. In the longer term, we need to develop improved logic programming languages, which do not rely on extralogical features for the sake of eciency.
Logic programming is a type of programming paradigm which is largely based on formal logic. By assigning a logic programming interpretation to types 47, we obtain a higher order logic programming language. Programs are written in the language of some logic. Implementing hol in an higher order logic programming. Higher order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. Programming with higher order logic formal systems that describe computations over syntactic structures occur frequently in computer science. Third, we compare higher order programming with the skeletons and techniques approach. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. This requires a higher order unification algorithm. Since logic programming computation is proof search, to study logic programming means to study proofs. Applications of lambda prolog in higher order programming and meta programming. Specifying and implementing theorem provers in a higher order logic programming language amy p.
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