[1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science

5-8 June 1989

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  • Proceedings. Fourth Annual Symposium on Logic in Computer Science (Cat. No.89CH2753-2)

    Publication Year: 1989
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    Freely Available from IEEE
  • Domains and logics

    Publication Year: 1989, Page(s):4 - 5
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    The author's discovery of domains and domain-theoretic models for the lambda -calculus in 1969 is discussed, along with the research of others working in the area at that time.<<ETX>> View full abstract»

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  • Non trivial power types can't be subtypes of polymorphic types

    Publication Year: 1989, Page(s):6 - 13
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    A new, limitative relation between the polymorphic lambda calculus and the kind of higher-order type theory embodied in the logic of topoi is established. It is shown that any embedding in a topos of the Cartesian closed category of (closed) types of a model of the polymorphic lambda calculus must place the polymorphic types well away from the power types sigma to Omega of the topos, in the sense ... View full abstract»

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  • Computational lambda-calculus and monads

    Publication Year: 1989, Page(s):14 - 23
    Cited by:  Papers (127)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (508 KB)

    The lambda -calculus is considered a useful mathematical tool in the study of programming languages. However, if one uses beta eta -conversion to prove equivalence of programs, then a gross simplification is introduced. The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific com... View full abstract»

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  • Computing with recursive types

    Publication Year: 1989, Page(s):24 - 38
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (724 KB)

    A study is made of the complete adequacy for a lambda -calculus with simple recursive types. The set of types is built using the standard domain-theoretic constructors, namely, function space, sum, cartesian and strict product, and lifting. The recursive types allow the author to solve arbitrary systems of mutually recursive domain equations. Thus, he can define in this calculus types of integers,... View full abstract»

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  • Stratified polymorphism

    Publication Year: 1989, Page(s):39 - 47
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (571 KB)

    The author considers a spectrum of predicative type abstraction disciplines based on type quantification with stratified levels. These lie in the vast middle ground between parametric abstraction and full impredicative abstraction. Stratified polymorphism has an attractive, unproblematic semantics, and has the potential of offering new approaches to type inference, without sacrificing useful expre... View full abstract»

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  • Proof theory and semantics of logic programs

    Publication Year: 1989, Page(s):50 - 62
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (934 KB)

    The authors develop a resolution logic that is based on direct proofs rather than on proofs by refutations. The deductive system studied has clauses as its formulas and resolution as the sole inference rule. They analyze this deductive system using a novel representation of resolution proofs, called resolution graphs, and obtain a general completeness theorem: a clause is a logical consequence of ... View full abstract»

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  • Negation as refutation

    Publication Year: 1989, Page(s):63 - 70
    Cited by:  Papers (5)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (508 KB)

    A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of the Ginsberg bilatt... View full abstract»

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  • Fixpoint extensions of first-order logic and datalog-like languages

    Publication Year: 1989, Page(s):71 - 79
    Cited by:  Papers (24)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (657 KB)

    Datalog extensions with fixpoint semantics motivated by database queries and updates are studied. The authors suggest nontrivial fixpoint extensions of first-order logic with nondeterministic and/or noninflationary semantics. Certain properties of the language FO+IFP, such as the collapse of the hierarchy (based on the nesting of fixpoints) or the existential normal form, hold for these various lo... View full abstract»

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  • PARTHENON: a parallel theorem prover for nonHorn clauses

    Publication Year: 1989, Page(s):80 - 89
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    A parallel resolution theorem prover, called Parthenon, that handles first-order logic is described. Parthenon is apparently the first general-purpose theorem prover to be developed for a multiprocessor. The system is based on a modification of D.H.D. Warren's SRI model (Int. Symp. on Logic Prog., pp.92-101, 1987) for OR-parallelism and implements a variant of D.W. Loveland's (J. ACM, vol.15, pp.2... View full abstract»

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  • Type inference for record concatenation and multiple inheritance

    Publication Year: 1989, Page(s):92 - 97
    Cited by:  Papers (19)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (425 KB)

    The author shows that the type inference problem for a lambda calculus with records, including a record concatenation operator, is decidable. He shows that this calculus does not have principal types but does have finite complete sets of type, that is, for any term M in the calculus, there exists an effectively generable finite set of type schemes such that every typing for M is an instance of one... View full abstract»

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  • Computational consequences and partial solutions of a generalized unification problem

    Publication Year: 1989, Page(s):98 - 105
    Cited by:  Papers (10)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (472 KB)

    A generalization of first-order unification, called semiunification, is studied with two goals in mind: (1) type-checking functional programs relative to an improved polymorphic type discipline; and (2) deciding the typability of terms in a restricted form of the polymorphic lambda -calculus.<<ETX>> View full abstract»

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  • How complete is PER?

    Publication Year: 1989, Page(s):106 - 111
    Cited by:  Papers (8)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (478 KB)

    The category of partial equivalence relations (PER) on the natural numbers has been used extensively in recent years to model various forms of higher-order type theory. It is known that PER can be viewed as a category of sets in a nonstandard model of intuitionistic Zermelo-Fraenkel set theory. The use of PER as a vehicle for modeling-type theory then arises from completeness properties of this ca... View full abstract»

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  • Inheritance and explicit coercion

    Publication Year: 1989, Page(s):112 - 129
    Cited by:  Papers (11)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (821 KB)

    A method is presented for providing semantic interpretations for languages which feature inheritance in the framework of statically checked, rich type disciplines. The approach is illustrated by an extension of the language Fun of L. Cardelli and P. Wegner (1985), which is interpreted via a translation into an extended polymorphic lambda calculus. The approach interprets inheritances in Fun as coe... View full abstract»

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  • Emil Post's contributions to computer science

    Publication Year: 1989, Page(s):134 - 136
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (226 KB)

    The work of mathematical logician Emil Post is surveyed from the viewpoint of its relevance to computer science. Computational logic and production systems are first discussed. This is followed by an examination of Post's work on finite combinatory processes and reducibility.<<ETX>> View full abstract»

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  • Towards action-refinement in process algebras

    Publication Year: 1989, Page(s):138 - 145
    Cited by:  Papers (14)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (340 KB)

    A simple process algebra which supports a form of refinement of an action by a process is presented and the question of an appropriate equivalence relation for it is addressed. The main result is that an adequate equivalence can be defined in a very intuitive manner and moreover can be axiomatized in much the same way as the standard behavioral equivalences.<<ETX>> View full abstract»

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  • A small universal model for system executions

    Publication Year: 1989, Page(s):146 - 153
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    The author shows that every consistent set of atomic relations has a unified model of size roughly O(n/sup 2/). This model can be used to give a simplified proof of completeness of some axioms. He gives several complexity results for deciding the theory of several classes of axiom sets, for both partial models and global-time models, showing many such variations to have the same complexity as tran... View full abstract»

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  • A game-theoretic modeling of concurrency

    Publication Year: 1989, Page(s):154 - 163
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (531 KB)

    A model is introduced for asynchronous concurrent communication, where each agent's perception of the system is represented by a game of interaction. The model combines strict fair merge with full recursion, and the main mathematical results provide evidence for the robustness and naturalness of his interpretation of recursive definitions of nondeterministic processes. The approach is closest to D... View full abstract»

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  • Nets and data flow interpreters

    Publication Year: 1989, Page(s):164 - 174
    Cited by:  Papers (8)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (657 KB)

    The authors investigate and compare two ways of specifying stream relations (in particular, stream functions). The first uses relational programs, i.e., netlike program schemes in which the signature primitives are interpreted as relations over a given CPO. No stream domains are assumed; semantics is in fixed-point style. The second is through data flow nets, i.e., nets whose nodes are interpreted... View full abstract»

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  • Axiomatizing net computations and processes

    Publication Year: 1989, Page(s):175 - 185
    Cited by:  Papers (26)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (778 KB)

    An algebraic axiomatization is proposed, where, given a net N, a term algebra P(N) with two operations of parallel and sequential composition is defined. The congruence classes generated by a few simple axioms are proved isomorphic to a slight refinement of classical processes. Actually, P(N) is a symmetric monoidal category, parallel composition is the monoidal operation on morphisms and sequenti... View full abstract»

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  • A probabilistic powerdomain of evaluations

    Publication Year: 1989, Page(s):186 - 195
    Cited by:  Papers (68)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (555 KB)

    A probabilistic power domain construction is given for the category of inductively complete partial orders. It is the partial order of continuous View full abstract»

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  • Equality in lazy computation systems

    Publication Year: 1989, Page(s):198 - 203
    Cited by:  Papers (44)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (426 KB)

    The author introduces a general class of lazy computation systems and defines a natural program equivalence for them. He proves that if an extensionality condition holds of each of the operators of a computational system, then the equivalence relation is a congruence, so that the usual kinds of equality reasoning are valid for it. This condition is a simple syntactic one and is easy to verify for ... View full abstract»

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  • Extending the lambda calculus with surjective pairing is conservative

    Publication Year: 1989, Page(s):204 - 215
    Cited by:  Papers (5)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (885 KB)

    Consideration is given to the equational theory lambda pi of lambda calculus extended with constants pi , pi /sub 0/, pi /sub 1/ and axioms for subjective pairing: pi /sub 0/( pi XY)=X, pi /sub 1/( pi XY)=Y, pi ( pi /sub 0/X)( pi /sub 1/X)=X. The reduction system that one obtains by reading the equations are reductions (from left to right) is not Church-Rosser. Despite this failure, the author obt... View full abstract»

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  • Faithful ideal models for recursive polymorphic types

    Publication Year: 1989, Page(s):216 - 225
    Cited by:  Papers (1)  |  Patents (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (626 KB)

    Ideal models are explored for a programming language with recursive polymorphic types, variants of the model studied by D. MacQueen et al. (Inf. Control, vol.71, pp.95-130, 1986). The use of suitable ideals yields a close fit between models and programming language. Two of the authors' semantics of type expressions are faithfully, in the sense that programs that behave identically in all contexts ... View full abstract»

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  • Structure and representation in LF

    Publication Year: 1989, Page(s):226 - 237
    Cited by:  Papers (11)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (800 KB)

    An important tool for controlling search in an object logic is the use of structured theory presentations. In order to apply these ideas to the setting of a logical framework, the authors study the behavior of structured theory presentations under representation in a framework, focusing on the problem of lifting presentations, from the object logic to the metalogic of the framework. The authors al... View full abstract»

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