.79> R ? ? S A 0 f 0 - B 0 The terminology is motivated by the fact that edges R and S determi... more .79> R ? ? S A 0 f 0 - B 0 The terminology is motivated by the fact that edges R and S determine a relation [R ! S] ` hom(A;B) Theta hom(A 0 ; B 0 ). We assume that all our reflexive graphs are relational. A reflexive graph is symmetric if it is equipped with a family of bijections (Gamma) ` A;A 0 : edge(A; A 0 ) ¸ = edge(A 0 ; A) such that 1. (I A ) ` = I A , and 2. the left hand diagram is a parametricity square iff the right hand diagram is a parametricity square: A f - B 6 6 R ? ? S A 0 f 0 -
Functional logic languages incorporate logic programming capabilities of constraint solving withi... more Functional logic languages incorporate logic programming capabilities of constraint solving within a functional language framework. We consider a prototypical functional logic language which supports definite descriptions, ie, terms of the form the x such that p. Its ...
This thesis develops a polymorphic type system for logic programs. Our approach is semantically o... more This thesis develops a polymorphic type system for logic programs. Our approach is semantically oriented. We define a type language with precise semantics. Type inference rules are derived from the semantics of the type language and the semantics of logic programs. Algorithms for automatic type construction are developed based on the type inference rules. Soundness of the inference rules guarantees the soundness of the algorithms. A prototype system is implemented using a logic programming language Prolog.Logic programs has no standard notion of error. Thus, in order to introduce types into logic programs, a notion of type error should be defined first. In our type system, error is the guaranteed failure. Then, types of predicates are supersets of relations defined by the predicates. Such types can be incorporated into logic programs without changing the syntax and semantics of logic programs.The developed type system assumes that no type declarations or type definitions are available from programs. Types are automatically inferred by static program analysis. Regular trees constitute an effective type language for automatic type inference due to their expressive power and availability of many useful algorithms.Our type system realizes type polymorphism by using implication and universal quantification as type constructs. Compared with other work, our polymorphic types have well-defined set-theoretic semantics and more expressive power. Our framework can be used for semantic analyses of logic programs for other purpose.The developed polymorphic type system shows that logic programs can have logically sound and practically useful type systems. Moreover, we recognize that our type system has a generality as a basis for static semantic analyses of logic programs for various purpose.U of I OnlyETDs are only available to UIUC Users without author permissio
ABSTRACT Thesis (M.S.)--University of North Carolina at Chapel Hill, 1982. Includes bibliographic... more ABSTRACT Thesis (M.S.)--University of North Carolina at Chapel Hill, 1982. Includes bibliographical references (leaves 50-52).
Page 1. Arrays in Imperative Lambda Calculus Sam Kamin, Uday S. Reddy Computer Science Dept. Univ... more Page 1. Arrays in Imperative Lambda Calculus Sam Kamin, Uday S. Reddy Computer Science Dept. University of Illinois at Urbana-Champaign Urbana, IL 61820 fkamin,reddyg@cs.uiuc.edu June 15, 1992 Abstract In recent ...
... author = {Brian Patrick Dunphy}, title = {Parametricity as a Notion of Uniformity in Reflexiv... more ... author = {Brian Patrick Dunphy}, title = {Parametricity as a Notion of Uniformity in Reflexive Graphs}, year = {2002} }. ... OpenURL. Abstract: data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only ...
Page 1. Generalization at Higher Types Robert W. Hasker 1 and Uday S. Reddy Department of Compute... more Page 1. Generalization at Higher Types Robert W. Hasker 1 and Uday S. Reddy Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801 USA {hasker, reddy}@cs.uiuc.edu 1 Abstract Finding ...
Dissertation Abstracts International Part B: Science and …, 1987
Logic languages based on functions: Semantics and implementation. US Reddy Dissertation Abstracts... more Logic languages based on functions: Semantics and implementation. US Reddy Dissertation Abstracts International Part B: Science and Engineering[DISS. ABST. INT. PT. B-SCI. & ENG.], 47:77, 1987. It is shown that logic programming ...
In recent work, we defined a formal system called Imperative Lambda Calculus to provide clean int... more In recent work, we defined a formal system called Imperative Lambda Calculus to provide clean integration of functional and imperative programming styles. In this paper, we study the issues of array manipulation in this framework. It is shown that the unique features of the calculus allow one to express array algorithms using high-level abstractions that are not available in purely functional languages.
ABSTRACT The main design principles of an interactive program transformation system called FOCUS ... more ABSTRACT The main design principles of an interactive program transformation system called FOCUS are outlined. Its important characteristics are its human-oriented deduction techniques based replacement, emphasis on small search spaces, and the use of a tree structure to organize program derivations. The tree structure presents to the user a static picture of the derivation process and promotes flexibility in the development of derivations. The system keeps track of dependencies between different parts of derivations, and records the derivation activity for later use in automatic replay.
Separation Logic has witnessed tremendous success in recent years in reasoning about programs tha... more Separation Logic has witnessed tremendous success in recent years in reasoning about programs that deal with heap storage. Its success owes to the fundamental principle that one should keep separate areas of the heap storage separate in program reasoning. However, the way Separation Logic deals with program variables continues to be based on traditional Hoare Logic without taking any benefit of the separation principle. This has led to unwieldy proof rules suffering from lack of clarity as well as questions surrounding their soundness. In this paper, we extend the separation idea to the treatment of variables in Separation Logic, especially Concurrent Separation Logic, using the system of Syntactic Control of Interference proposed by Reynolds in 1978. We extend the original system with permission algebras, making it more powerful and able to deal with the issues of concurrent programs. The result is a streamined presentation of Concurrent Separation Logic, whose rules are memorable and soundness obvious. We also include a discussion of how the new rules impact the semantics and devise static analysis techniques to infer the required permissions automatically.
Our method for clausal reasoning closely follows the Knuth-Bendix method for equational reasoning... more Our method for clausal reasoning closely follows the Knuth-Bendix method for equational reasoning. (See [4] for a survey of the latter). Given a set of clauses 7" (called the theory) and a ground clause r, the problem is to decide 7" ~ F. (We call this the "clausal word ...
Are higher-order extensions to logic programming needed? We suggest a negative answer by showing ... more Are higher-order extensions to logic programming needed? We suggest a negative answer by showing that higher-order features are already available in pure logic programming. It is demonstrated that higher-order lambda ca]cttlus-based languages can be compositionally embedded in logic programming languages preserving their semantics and abstraction facilities. Further, we show that such higher-order techniques correspond to programming techniques often practiced in logic programming.
Imperative lambda calculus (ILC) is an abstract formal language obtained by extending the typed l... more Imperative lambda calculus (ILC) is an abstract formal language obtained by extending the typed lambda calculus with imperative programming features, namely references and assignments. The language shares with typed lambda calculus important properties such as the Church-Rosser property and strong normalization. In this paper, we describe the logical symmetries that underly ILC by exhibiting a constructive logic for which ILC forms the language of constructions. Central to this formulation is the view that references play a role similar to that of variables. References can be used to range over values and instantiated to specific values. Thus, we obtain a new form of universal quantification that uses references instead of variables. The essential term forms of ILC are then obtained as the constructions for the introduction and elimination of this quantifier. While references duplicate the role of variables, they also have important differences. References are semantic values whereas variables are syntactic entities and, secondly, references are reusable. These differences allow references to be used in a more flexible fashion leading to efficiency in constructions and algorithms.
.79> R ? ? S A 0 f 0 - B 0 The terminology is motivated by the fact that edges R and S determi... more .79> R ? ? S A 0 f 0 - B 0 The terminology is motivated by the fact that edges R and S determine a relation [R ! S] ` hom(A;B) Theta hom(A 0 ; B 0 ). We assume that all our reflexive graphs are relational. A reflexive graph is symmetric if it is equipped with a family of bijections (Gamma) ` A;A 0 : edge(A; A 0 ) ¸ = edge(A 0 ; A) such that 1. (I A ) ` = I A , and 2. the left hand diagram is a parametricity square iff the right hand diagram is a parametricity square: A f - B 6 6 R ? ? S A 0 f 0 -
Functional logic languages incorporate logic programming capabilities of constraint solving withi... more Functional logic languages incorporate logic programming capabilities of constraint solving within a functional language framework. We consider a prototypical functional logic language which supports definite descriptions, ie, terms of the form the x such that p. Its ...
This thesis develops a polymorphic type system for logic programs. Our approach is semantically o... more This thesis develops a polymorphic type system for logic programs. Our approach is semantically oriented. We define a type language with precise semantics. Type inference rules are derived from the semantics of the type language and the semantics of logic programs. Algorithms for automatic type construction are developed based on the type inference rules. Soundness of the inference rules guarantees the soundness of the algorithms. A prototype system is implemented using a logic programming language Prolog.Logic programs has no standard notion of error. Thus, in order to introduce types into logic programs, a notion of type error should be defined first. In our type system, error is the guaranteed failure. Then, types of predicates are supersets of relations defined by the predicates. Such types can be incorporated into logic programs without changing the syntax and semantics of logic programs.The developed type system assumes that no type declarations or type definitions are available from programs. Types are automatically inferred by static program analysis. Regular trees constitute an effective type language for automatic type inference due to their expressive power and availability of many useful algorithms.Our type system realizes type polymorphism by using implication and universal quantification as type constructs. Compared with other work, our polymorphic types have well-defined set-theoretic semantics and more expressive power. Our framework can be used for semantic analyses of logic programs for other purpose.The developed polymorphic type system shows that logic programs can have logically sound and practically useful type systems. Moreover, we recognize that our type system has a generality as a basis for static semantic analyses of logic programs for various purpose.U of I OnlyETDs are only available to UIUC Users without author permissio
ABSTRACT Thesis (M.S.)--University of North Carolina at Chapel Hill, 1982. Includes bibliographic... more ABSTRACT Thesis (M.S.)--University of North Carolina at Chapel Hill, 1982. Includes bibliographical references (leaves 50-52).
Page 1. Arrays in Imperative Lambda Calculus Sam Kamin, Uday S. Reddy Computer Science Dept. Univ... more Page 1. Arrays in Imperative Lambda Calculus Sam Kamin, Uday S. Reddy Computer Science Dept. University of Illinois at Urbana-Champaign Urbana, IL 61820 fkamin,reddyg@cs.uiuc.edu June 15, 1992 Abstract In recent ...
... author = {Brian Patrick Dunphy}, title = {Parametricity as a Notion of Uniformity in Reflexiv... more ... author = {Brian Patrick Dunphy}, title = {Parametricity as a Notion of Uniformity in Reflexive Graphs}, year = {2002} }. ... OpenURL. Abstract: data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only ...
Page 1. Generalization at Higher Types Robert W. Hasker 1 and Uday S. Reddy Department of Compute... more Page 1. Generalization at Higher Types Robert W. Hasker 1 and Uday S. Reddy Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801 USA {hasker, reddy}@cs.uiuc.edu 1 Abstract Finding ...
Dissertation Abstracts International Part B: Science and …, 1987
Logic languages based on functions: Semantics and implementation. US Reddy Dissertation Abstracts... more Logic languages based on functions: Semantics and implementation. US Reddy Dissertation Abstracts International Part B: Science and Engineering[DISS. ABST. INT. PT. B-SCI. & ENG.], 47:77, 1987. It is shown that logic programming ...
In recent work, we defined a formal system called Imperative Lambda Calculus to provide clean int... more In recent work, we defined a formal system called Imperative Lambda Calculus to provide clean integration of functional and imperative programming styles. In this paper, we study the issues of array manipulation in this framework. It is shown that the unique features of the calculus allow one to express array algorithms using high-level abstractions that are not available in purely functional languages.
ABSTRACT The main design principles of an interactive program transformation system called FOCUS ... more ABSTRACT The main design principles of an interactive program transformation system called FOCUS are outlined. Its important characteristics are its human-oriented deduction techniques based replacement, emphasis on small search spaces, and the use of a tree structure to organize program derivations. The tree structure presents to the user a static picture of the derivation process and promotes flexibility in the development of derivations. The system keeps track of dependencies between different parts of derivations, and records the derivation activity for later use in automatic replay.
Separation Logic has witnessed tremendous success in recent years in reasoning about programs tha... more Separation Logic has witnessed tremendous success in recent years in reasoning about programs that deal with heap storage. Its success owes to the fundamental principle that one should keep separate areas of the heap storage separate in program reasoning. However, the way Separation Logic deals with program variables continues to be based on traditional Hoare Logic without taking any benefit of the separation principle. This has led to unwieldy proof rules suffering from lack of clarity as well as questions surrounding their soundness. In this paper, we extend the separation idea to the treatment of variables in Separation Logic, especially Concurrent Separation Logic, using the system of Syntactic Control of Interference proposed by Reynolds in 1978. We extend the original system with permission algebras, making it more powerful and able to deal with the issues of concurrent programs. The result is a streamined presentation of Concurrent Separation Logic, whose rules are memorable and soundness obvious. We also include a discussion of how the new rules impact the semantics and devise static analysis techniques to infer the required permissions automatically.
Our method for clausal reasoning closely follows the Knuth-Bendix method for equational reasoning... more Our method for clausal reasoning closely follows the Knuth-Bendix method for equational reasoning. (See [4] for a survey of the latter). Given a set of clauses 7" (called the theory) and a ground clause r, the problem is to decide 7" ~ F. (We call this the "clausal word ...
Are higher-order extensions to logic programming needed? We suggest a negative answer by showing ... more Are higher-order extensions to logic programming needed? We suggest a negative answer by showing that higher-order features are already available in pure logic programming. It is demonstrated that higher-order lambda ca]cttlus-based languages can be compositionally embedded in logic programming languages preserving their semantics and abstraction facilities. Further, we show that such higher-order techniques correspond to programming techniques often practiced in logic programming.
Imperative lambda calculus (ILC) is an abstract formal language obtained by extending the typed l... more Imperative lambda calculus (ILC) is an abstract formal language obtained by extending the typed lambda calculus with imperative programming features, namely references and assignments. The language shares with typed lambda calculus important properties such as the Church-Rosser property and strong normalization. In this paper, we describe the logical symmetries that underly ILC by exhibiting a constructive logic for which ILC forms the language of constructions. Central to this formulation is the view that references play a role similar to that of variables. References can be used to range over values and instantiated to specific values. Thus, we obtain a new form of universal quantification that uses references instead of variables. The essential term forms of ILC are then obtained as the constructions for the introduction and elimination of this quantifier. While references duplicate the role of variables, they also have important differences. References are semantic values whereas variables are syntactic entities and, secondly, references are reusable. These differences allow references to be used in a more flexible fashion leading to efficiency in constructions and algorithms.
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