structural induction and coinduction in a fibrational setting we present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types our main results provide sufficient criteria for the validity of such principles in the presence of comprehension the induction principle for initial algebras is admissible and dually in the presence of quotient types the coinduction principle for terminal coalgebras is admissible after giving an alternative formulation of induction in terms of binary relations we combine both principles and obtain a mixed induction coinduction principle which allows us to reason about minimal solutionsx x wherexmay occur both positively and negatively in the type constructor we further strengthen these logical principles to deal with contexts and prove that such strengthening is valid when the abstract logic we consider is contextually functionally complete all the main results follow from a basic result about adjunctions between categories of algebras inserters

polymorphic lambda calculus and subtyping we present a denotational model for f the extension of second order lambda calculus with subtyping defined in cardelli and wegner acm comput surveys 17 4 1985 471 522 types are interpreted as arbitrary cpos and elements of types as natural transformations we prove the soundness of our model with respect to the equational theory of f cardelli et al internat conf on theoretical aspects of computer software lecture notes in computer science vol 526 springer berlin 1991 pp 750 770 and show coherence our model is of independent interest because it integrates ad hoc and parametric polymorphism in an elegant fashion admits nontrivial records and record update operations and formalizes an order faithfulness criterion for well behaved multiple subtyping

set theoretical and other elementary models of the l calculus abstract part i pp 351 373 of this paper is the previously unpublished 1972 memorandum plotkin 1972 with editorial changes and some minor corrections part ii pp 373 409 presents what happened next together with some further development of the material the first part begins with an elementary set theoretical model of the calculus functions are modelled in a similar way to that normally employed in set theory by their graphs difficulties are caused in this enterprise by the axiom of foundation next based on that model a model of the calculus is constructed by means of a natural deduction method finally a theorem is proved giving some general properties of those nontrivial models of the calculus which are continuous complete lattices the second part begins with a brief discussion of models of the calculus in set theories with anti foundation axioms next the model of the calculus of part i and also the closely related but different models of scott 1976 1980 and of engeler 1981 1988 are reviewed then general frameworks in which elementary constructions of models can be given are discussed following longo 1982 one can employ certain scott engeler algebras following coppo et al 1983 one can obtain filter models from their extended applicative type structures an extended discussion is given of various ways of constructing models of the calculus and the connections between them finally an extension of the theorem to complete partial orders is given the theme of the paper is the consideration of means of constructing models there is hardly any analysis of their properties there is no discussion of their application

recycling krylov subspaces for efficient large scale electrical impedance tomography electrical impedance tomography eit captures images of internal features of a body electrodes are attached to the boundary of the body low intensity alternating currents are applied and the resulting electric potentials are measured then based on the measurements an estimation algorithm obtains the three dimensional internal admittivity distribution that corresponds to the image one of the main goals of medical eit is to achieve high resolution and an accurate result at low computational cost however when the finite element method fem is employed and the corresponding mesh is refined to increase resolution and accuracy the computational cost increases substantially especially in the estimation of absolute admittivity distributions therefore we consider in this work a fast iterative solver for the forward problem which was previously reported in the context of structural optimization we propose several improvements to this solver to increase its performance in the eit context the solver is based on the recycling of approximate invariant subspaces and it is applied to reduce the eit computation time for a constant and high resolution finite element mesh in addition we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver the numerical results show the effectiveness of our approach the proposed algorithm is faster than the preconditioned conjugate gradient cg algorithm the results also show that even on a standard pc without parallelization a high mesh resolution more than 150 000 degrees of freedom can be used for image estimation at a relatively low computational cost

on functions preserving levels of approximation a refined model construction for various lambda calculi abstract in this paper di domains are enriched by a family of projections which assign to each point a sequence of canonical approximations the morphisms are stable maps that preserve the levels of approximation generated by the projections for the computation of an approximation of a given level of the output they require in addition only information about the input of at most the same level of approximation it is shown that the category of these domains and maps is cartesian closed the set of morphisms between two such domains is a domain of the same kind but turns out not to be an exponent in the category domains d are constructed which are isomorphic to the exponent d d moreover it is proved that the space of retractions in an exponent d d is a retract of this both results together provide new models of amadio longo s extension p of the calculus as has been shown by amadio and longo strong type theories which incorporate the type type assumption can be syntactically interpreted in this calculus

the genericity theorem and parametricity in the polymorphic l calculus abstract this paper focuses on how terms of the polymorphic calculus which may take types as inputs depend on types these terms are generally understood in all models to have an essentially constant meaning on input types we show the proof theory of polymorphic calculus suggests a clear syntactic description of this phenomenon namely under a reasonable condition we show that if two polymorphic functions agree on a single type then they agree on all types equivalently types are generic inputs

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

the category theoretic solution of recursive metric space equations it is well known that one can use an adaptation of the inverse limit construction to solve recursive equations in the category of complete ultrametric spaces we show that this construction generalizes to a large class of categories with metric space structure on each set of morphisms the exact nature of the objects is less important in particular the construction immediately applies to categories where the objects are ultrametric spaces with extra structure and where the morphisms preserve this extra structure the generalization is inspired by classical domain theoretic work by smyth and plotkin for many of the categories we consider there is a natural subcategory in which each set of morphisms is required to be a compact metric space our setting allows for a proof that such a subcategory always inherits solutions of recursive equations from the full category as another application we present a construction that relates solutions of generalized domain equations in the sense of smyth and plotkin to solutions of equations in our class of categories our primary motivation for solving generalized recursive metric space equations comes from recent and ongoing work on kripke style models in which the sets of worlds must be recursively defined we show a series of examples motivated by this line of work

co induction in relational semantics abstract an application of the mathematical theory of maximum fixed points of monotonic set operators to relational semantics is presented it is shown how an important proof method which we call co induction a variant of park s 1969 principle of fixpoint induction can be used to prove the consistency of the static and the dynamic relational semantics of a small functional programming language with recursive functions

simulations in coalgebra a new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive such an order forms a basic building block for a lax relation lifting or relator as used by other authors simulations appear as coalgebras of this lifted functor and similarity as greatest simulation two way similarity is then similarity in both directions in general it is different from bisimilarity in the usual coalgebraic sense but a sufficient condition is formulated and illustrated to ensure that bisimilarity and two way similarity coincide also suitable conditions are identified which ensures that similarity on a final coalgebra forms an algebraic dcpo structure this involves a close investigation of the iterated applications fn 0 and fn 1 of a functor f with an order to the initial algebras and final objects

complete restrictions of the intersection type discipline abstract in this paper the intersection type discipline as defined in barendregt 1983 is studied we will present two different and independent complete restrictions of the intersection type discipline the first restricted system the strict type assignment system is presented in section 2 its major feature is the absence of the derivation rule and it is based on a set of strict types we will show that these together give rise to a strict filter lambda model that is essentially different from the one presented in barendregt we will show that the strict type assignment system is the nucleus of the full system i e for every derivation in the intersection type discipline there is a derivation in which is used only at the very end finally we will prove that strict type assignment is complete for inference semantics the second restricted system is presented in section 3 its major feature is the absence of the type we will show that this system gives rise to a filter i model and that type assignment without is complete for the i calculus finally we will prove that a lambda term is typeable in this system if and only if it is strongly normalizable

a particular solution trefftz method for non linear poisson problems in heat and mass transfer this paper proposes a computational procedure based on the trefftz method for the solution of non linear poisson problems the problem is solved by finding an approximate particular solution to the poisson equation and using boundary collocation to solve the resulting laplace equation this method results in a global collocation and hence eliminates the need for discretization of the domain in both two and three dimensions the solution procedure proposed earlier in the literature based upon the above method has been reformulated for increased computational efficiency a quasi newton iteration method along with a new heuristic for source point location is used for efficient convergence of the numerical scheme the efficacy of the new formulation has been demonstrated for two classes of problems viz the thermal explosion problem and the diffusion reaction problem in a partially wetted catalyst pellet a brief error analysis of the method as well as future research directions is presented

on final coalgebras of continuous functors continuous endofunctors f of locally finitely presentable categories carry a natural metric on their final coalgebra whenever f 0 has an element this metric is proved to be a cauchy completion of the initial algebra of f this is illustrated on the poset of real numbers represented as a final coalgebra of an endofunctor of pos by pavlovic and pratt under additional assumptions on the locally finitely presentable category all finitary endofunctors are proved to have a final coalgebra constructed in steps of the natural iteration construction

infinite hypergraphs i basic properties abstract basic properties of the category of infinite directed hyperedge labelled hypergraphs are studied an algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions it is then shown that two expressions define the same hypergraphs if and only if they are congruent with respect to some rewriting system these results will be used in the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions

an irregular filter model in this paper we introduce a new filter model which is of a kind that has escaped investigation up to now it is induced by an intersection type theory generated in a non standard way by a preorder which puts into relation an atom with an arrow type without equating them we study the domain theoretic implications of this choice that are not trivial in order to describe this filter model a new category is introduced and a special purpose functor defined the filter model is then characterized as the initial algebra of the functor

the mixed powerdomain this paper introduces an operator m called the mixed powerdomain which generalizes the convex plotkin powerdomain the construction is based on the idea of representing partial information about a set of data items using a pair of sets one representing partial information in the manner of the upper smyth powerdomain and the other in the manner of the lower hoare powerdomain where the components of such pairs are required to satisfy a consistency condition this provides a richer family of meaningful partial descriptions than are available in the convex powerdomain and also makes it possible to include the empty set in a satisfactory way the new construct is given a rigorous mathematical treatment like that which has been applied to the known powerdomains it is proved that m is a continuous functor on bifinite domains which is left adjoint to the forgetful functor from a category of continuous structures called mix algebras for a domain d with a coherent scott topology elements of md can be represented as pairs u v where u d is a compact upper set v d is a closed set and the downward closure of u v is equal to v a stone dual characterization of m is also provided

equational logic of circular data type specification abstract iteration theories introduced by bloom elgot and wright in 1980 formalize the equational properties of the strong behaviors of flowchart algorithms we show that the same equational properties are shared by the functors used to specify circular data types lehmann and smyth 1981 have shown how to specify circular data types such as stacks as fixed points of certain functors the called gw functors for example the set of stacks of elements in the set a is a solution to the equation in the variable x x f a x where f x x 1 a x is the functor on set taking the pair a x to the disjoint union of the singleton set 1 and the product a x such equations have initial solutions f a which in turn determine a solution functor f the equational properties of the operation f f are precisely captured by the axioms for iteration theories more precisely we show how the structure th c of all functors c n c p n p 0 on the category c forms an iteration theory and conversely any identity valid in all such structures is valid in the class of all iteration theories

a simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials in this paper a numerical multiscale method is proposed for computing the response of structures made of linearly non aging viscoelastic and highly heterogeneous materials in contrast with most of the approaches reported in the literature the present one operates directly in the time domain and avoids both defining macroscopic internal variables and concurrent computations at micro and macro scales the macroscopic constitutive law takes the form of a convolution integral containing an effective relaxation tensor to numerically identify this tensor a representative volume element rve for the microstructure is first chosen relaxation tests are then numerically performed on the rve correspondingly the components of the effective relaxation tensor are determined and stored for different snapshots in time at the macroscopic scale a continuous representation of the effective relaxation tensor is obtained in the time domain by interpolating the data with the help of spline functions the convolution integral characterizing the time dependent macroscopic stress strain relation is evaluated numerically arbitrary local linear viscoelastic laws and microstructure morphologies can be dealt with implicit algorithms are provided to compute the time dependent response of a structure at the macroscopic scale by the finite element method accuracy and efficiency of the proposed approach are demonstrated through 2d and 3d numerical examples and applied to estimate the creep of structures made of concrete

tail recursion through universal invariants abstract tail recursive constructions suggest a new semantics for datatypes which allows a direct match between specifications and tail recursive programs the semantics focuses on loops their fixpoints invariants and convergence convergent models of the natural numbers and lists are examined in detail and under very mild conditions are shown to be equivalent to the corresponding initial algebra models

bi simulations up to characterise process semantics we define bi simulations up to a preorder and show how we can use them to provide a coinductive bi simulation like characterisation of semantic equivalences preorders for processes in particular we can apply our results to all the semantics in the linear time branching time spectrum that are defined by preorders coarser than the ready simulation preorder the relation between bisimulations up to and simulations up to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders in particular we have shown that the simulation up to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation since all of these canonical preorders are defined in an homogeneous way we can prove properties for them in a generic way as an illustrative example of this technique we generate an axiomatic characterisation of each of these canonical preorders that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time branching time spectrum whose correctness and completeness can be proved once and for all although we first prove by induction our results for finite processes then we see by using continuity arguments that they are also valid for infinite finitary processes

micromechanical modeling of coupled viscoelastic viscoplastic composites based on an incrementally affine formulation this study proposes a micromechanical modeling of inclusion reinforced viscoelastic viscoplastic composites based on mean field approaches for this we have generalized the so called incrementally affine linearization method which was proposed by doghri et al 2010a for elasto viscoplastic materials the proposal provides an affine relation between stress and strain increments via an algorithmic tangent operator in order to find the incrementally affine expression we start by the linearization of evolution equations at the beginning of a time step around the end time of the step next a numerical integration of the linearized equations is required using a fully implicit backward euler scheme the obtained algebraic equations lead to an incrementally affine formulation which is form similar to linear thermoelasticity therefore known homogenization models for linear thermoelastic composites can be applied the proposed method can deal with general viscoelastic viscoplastic constitutive models with an arbitrary number of internal variables the semi analytical predictions are validated against finite element simulations and experimental results

an adaptive greedy technique for inverse boundary determination problem in this paper the method of fundamental solutions mfs is employed for determining an unknown portion of the boundary from the cauchy data specified on parts of the boundary we propose a new numerical method with adaptive placement of source points in the mfs to solve the inverse boundary determination problem since the mfs source points placement here is not trivial due to the unknown boundary we employ an adaptive technique to choose a sub optimal arrangement of source points on various fictitious boundaries afterwards the standard tikhonov regularization method is used to solve ill conditional matrix equation while the regularization parameter is chosen by the l curve criterion the numerical studies of both open and closed fictitious boundaries are considered it is shown that the proposed method is effective and stable even for data with relatively high noise levels

universal homogeneous event structures and domains abstract in the theory of denotational semantics of programming languages several authors established the existence of particular kinds of universal domains here we use a general model theoretic result to show that there exists a unique countable universal homogeneous event structure from this we deduce that the category of all event domains with stable embedding projection pairs as morphisms contains a universal object similarly we also obtain a universal di domain we also show that the category of all event domains is closed under inverse limits similar results are derived for kahn and plotkin s concrete data structures and concrete domains

open maps behavioural equivalences and congruences abstract spans of open maps have been proposed by joyal nielsen and winskel as a way of adjoining an abstract equivalence bisimilarity to a category of models of computation ms where is an arbitrary subcategory of observations part of the motivation was to recast and generalise milner s well known strong bisimulation in this categorical setting an issue left open was the congruence properties of bisimilarity we address the following fundamental question given a category of models of computation ms and a category of observations are there any conditions under which algebraic constructs viewed as functors preserve bisimilarity we define the notion of functors being factorisable show how this ensures that bisimilarity is a congruence with respect to such functors guided by the definition of factorisability we show how it is possible to parametrise proofs of functors being factorisable with respect to the category of observations i e with respect to a behavioural equivalence

coinductive big step operational semantics using a call by value functional language as an example this article illustrates the use of coinductive definitions and proofs in big step operational semantics enabling it to describe diverging evaluations in addition to terminating evaluations we formalize the connections between the coinductive big step semantics and the standard small step semantics proving that both semantics are equivalent we then study the use of coinductive big step semantics in proofs of type soundness and proofs of semantic preservation for compilers a methodological originality of this paper is that all results have been proved using the coq proof assistant we explain the proof theoretic presentation of coinductive definitions and proofs offered by coq and show that it facilitates the discovery and the presentation of the results

a 2 categorical pasting theorem in order to facilitate the study of 2 categories with structure we state and prove an n categorical pasting theorem this is based upon a new definition of n pasting scheme that generalises johnson s definition of a well formed loop free pasting scheme by weakening his no direct loops condition we define n pasting prove the theorem and show that for n 3 it incorporates all possible composites of n cells we show that that is not true for higher n we define the horizontal n category of an n 1 category to generalise that of a 2 category we define horizontal and vertical composition for an n 1 category and we state and prove an interchange law we also study further conditions on a pasting diagram and their impact upon how one may evaluate a composite and we express street s free n categories in terms of left adjoints

a theory of communicating processes with value passing a semantic theory of process algebras which allows processes to communicate values is described a behavioural theory of testing is given for such processes and is modelled by an extension of acceptance trees a proof system is also given for this model and is shown to be both sound and complete finally the model is shown to be fully abstract with respect to the behavioural theory

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

a coalgebraic presentation of structured transition systems this paper relates labelled transition systems and coalgebras with the motivation of comparingand combiningtheir complementary contributions to the theory of concurrent systems the well known mismatch between these two notions concerningthe morphisms is resolved by extendingthe coalg ebraic framework by lax cohomomorphisms enriching both labelled transition systems and coalgebras with algebraic structure for an algebraic speci cation the correspondence is lost again this motivates the introduction of lax coalgebras where the coalgebra structure is given by a lax homomorphism the resulting category of lax coalgebras and lax cohomomorphisms for a suitable endofunctor is shown to be isomorphic to the category of structured transition systems where both states and transitions form algebras the framework is also presented on a more abstract categorical level using monads and comonads extendingthe bialgebraic approach introduced by turi and plotkin c 2001 elsevier science b v all rights reserved

quantitative domains and infinitary algebras abstract we describe a class of models of the lambda calculus that generalize and simplify the quantitative domains of girard 1988 their salient feature is that these domains do not have enough points in the sense that a map of domains is not entirely determined by its value on the points i e the morphisms from the terminal object of the category we construct a universal domain whose structure is particularly simple and describe some of the features of the untyped lambda calculus associated to it finally we show how linear logic can be interpreted in these domains and construct another category of domains that supports linear logic

the comparison of a cpo based semantics with cms based semantics for csp we study two semantics for csp both semantics are compositional and interleaving the first uses the concept of complete partial orders cpo for the handling of repetitive constructs and for the creation of suitable semantic domains the second uses the concept of complete metric spaces cms for the same purposes our results show that the cms semantics gives more detailed information about a program and that we can obtain the cpo semantics from it from this investigation we can draw conclusions concerning the influence of the mathematical discipline on the kind of semantics obtained

on proving limiting completeness we give two proofs of wadsworth s classic approximation theorem for the pure lambda calculus one of these illustrates a new method utilising a certain kind of intermediate semantics for proving correspondences between denotational and operational semantics the other illustrates a direct technique of milne employing recursively specified inclusive relations

quantitative simulations by matrices abstract we introduce notions of simulation between semiring weighted automata as models of quantitative systems our simulations are instances of the categorical coalgebraic notions previously studied by hasuo hence soundness against language inclusion comes for free but are concretely presented as matrices that are subject to linear inequality constraints pervasiveness of these formalisms allows us to exploit existing algorithms in searching for a simulation and hence verifying quantitative correctness that is formulated as language inclusion transformations of automata that aid search for simulations are introduced too this verification workflow is implemented for the plus times and max plus semirings furthermore an extension to weighted tree automata is presented and implemented

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

completeness of rewrite rules and rewrite strategies for fp this paper treats languages whose operational semantics is given by a set of rewrite rules for such languages it is important to be able to determine that there are enough rules to be able to compute the correct meaning of all expressions but not so many that the system of rules is inconsistent a formal framework is developed in which to give a precise treatment of these completeness and soundness issues which are then investigated in the context of an extended version of the functional programming language fp the rewrite rules of fp are shown to be sound and complete with respect to three different notions of completeness the latter half of the paper considers rewrite strategies in order to implement a language based on rewrite rules it does not suffice to know that there are enough rules in the language a good strategy for determining the order in which to apply them is also needed but what is good corresponding to each notion of completeness there is a notion of a good rewrite strategy these notions of goodness are examined and characterized and examples of a number of natural good strategies are given although these results are presented in the context of fp the techniques some of which are nontrivial extensions of techniques first used in the context of calculus should apply well beyond the realm of fp rewriting systems

trees and semantics abstract several types of trees are proposed in the literature to model the behaviour of nondeterministic processes the purpose of this paper is to clarify the distinction between the various types of trees and to discuss their use as semantic domains trees in the sense of milner s derivation trees and bisimulation equivalence classes of trees are considered in three different settings in the category of sets in the metric setting and in the partial order setting each type of tree is characterized by a domain equation special attention is given to the use of trees as models for processes which allow for unbounded nondeterminism as for instance milners ccs processes in this case one has to deal with infinitely branching trees which cause problems to give denotational semantics that are fully abstract w r t a transition system based operational semantics

non well founded sets modeled as ideal fixed points abstract motivated by ideas from the study of abstract data types we show how to interpret non well founded sets as fixed points of continuous transformations of an initial continuous algebra we conisder a preordered structure closely related to the set hf of well founded hereditarily finite sets by taking its ideal completion we obtain an initial continuous algebra in which we are able to solve all of the usual systems of equations that characterize hereditarily finite non well founded sets in this way we are able to obtain a structure which is isomorphic to hf 1 the non well founded analog of hf

boundary identification for a 3d laplace equation using a genetic algorithm in this paper we consider the identification of the geometric structure of the boundary of the solution domain for the three dimensional laplace equation we investigate the determination of the shape of an unknown portion of the boundary of a solution domain from cauchy data on the remaining portion of the boundary this problem arises in the study of quantitative non destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion the domain identification problem is considered as a variational problem to minimize a defect functional which utilises some additional data on certain known parts of the boundary a real coded genetic algorithm rcga is used in order to minimise the objective functional the unknown boundary is parameterized using b splines the laplace equation is discretised using the method of fundamental solutions mfs numerical results are presented and discussed for several test examples

a new class of micro macro models for elastic viscoplastic heterogeneous materials abstract the determination of the effective behavior of heterogeneous materials from the properties of the components and the microstructure constitutes a major task in the design of new materials and the modeling of their mechanical behavior in real heterogeneous materials the simultaneous presence of instantaneous mechanisms elasticity and time dependent ones non linear viscoplasticity leads to a complex space time coupling between the mechanical fields difficult to represent in a simple and efficient way in this work a new self consistent model is proposed starting from the integral equation for a translated strain rate field the chosen translated field is the compatible viscoplastic strain rate of the fictitious viscoplastic heterogeneous medium submitted to a uniform unknown boundary condition the self consistency condition allows to define these boundary conditions so that a relative simple and compact strain rate concentration equation is obtained this equation is explained in terms of interactions between an inclusion and a matrix which lead to interesting conclusions the model is first applied to the case of two phase composites with isotropic linear and incompressible viscoelastic properties in that case an exact self consistent solution using the laplace carson transform is available the agreement between both approaches appears quite good results for elastic viscoplastic bcc polycrystals are also presented and compared with results obtained from kroner weng s and paquin et al arch appl mech 69 1999 14 s model

strong categorical datatypes ii a term logic for categorical programming abstract this paper lifts earlier category theoretic results on datatypes to the level of an abstract language suitable for categorical programming language implementation the earlier work built a strongly normalizing categorical combinator reduction system based entirely on functorial strength which allows the distribution of context to the interior of datatypes here we declare inductive initial and coinductive final datatypes in a hagino wraith style to provide an expressive computing environment an inductive resp coinductive datatype consists of a strong type forming functor accompanied by 1 a collection of constructors resp destructors and 2 a fold resp unfold which is parametrized by state transformations to realize the appropriate universal property the high complexity of programming exclusively in categorical notation combinators warrants the development of a friendlier language isomorphic to the distributive categorical setting in this paper such a term logic which is also the programming language of the charity programming system is described this logic is first order and is dictated directly by the underlying categorical semantics it embodies primitive inductive and coinductive principles which reflect the uniqueness properties of the fold and unfold combinators several basic progam equivalences are demonstrated to illustrate how these inductive and coinductive principles can be used

fixpoint semantics and simulation abstract a general functorial framework for recursive definitions is presented in which simulation of a definition scheme by another one implies an ordering between the values defined by these schemes in an arbitrary model under mild conditions on the functor involved the converse implication also holds a model is constructed such that if the values defined are ordered there is a simulation between the definition schemes the theory is illustrated by applications to context free grammars recursive procedures in imperative languages and simulation and bisimulation of processes

notions of computation and monads abstract the calculus is considered a useful mathematical tool in the study of programming languages since programs can be identified with terms however if one goes further and uses conversion to prove equivalence of programs then a gross simplification is introduced programs are identified with total functions from values to values that may jeopardise the applicability of theoretical results in this paper we introduce calculi based on a categorical semantics for computations that provide a correct basis for proving equivalence of programs for a wide range of notions of computation

strictness analysis via abstract interpretation for recursively defined types abstract in this paper we consider a functional language with recursively defined types and a weak form of polymorphism for this language a strictness analysis is developed based on abstract interpretation in a category of complete algebraic lattices

a type theoretical alternative to iswim cuch owhy abstract the paper first written in 1969 and circulated privately concerns the definition axiomatization and applications of the hereditarily monotone and continuous functionals generated from the integers and the booleans plus undefined elements the system is formulated as a typed system of combinators or as a typed calculus with a recursion operator the least fixed point operator and its proof rules are contrasted to a certain extent with those of the untyped calculus for publication 1993 a new preface has been added and many bibliographical references and comments in footnotes have been appended

on the greatest fixed point of a set functor abstract the greatest fixed point of a set functor is proved to be a a metric completion and b a cpo completion of finite iterations for each possibly infinitary signature the terminal coalgebra is thus proved to be the coalgebra of all labelled trees this is the completion of the set of all such trees of finite depth a set functor is presented which has a fixed point but does not have a greatest fixed point a sufficient condition for the existence of a greatest fixed point is proved the existence of two fixed points of successor cardinalities

processes as formal power series a coinductive approach to denotational semantics we characterize must testing equivalence on csp in terms of the unique homomorphism from the moore automaton of csp processes to the final moore automaton of partial formal power series over a certain semiring the final automaton is then turned into a csp algebra operators and fixpoints are defined respectively via behavioural differential equations and simulation relations this structure is then shown to be preserved by the final homomorphism as a result we obtain a fully abstract compositional model of csp phrased in purely set theoretical terms

a co induction principle for recursively defined domains abstract this paper establishes a new property of predomains recursively defined using the cartesian product disjoint union partial function space and convex powerdomain constructors we prove that the partial order on such a recursive predomain d is the greatest fixed point of a certain monotone operator associated to d this provides a structurally defined family of proof principles for these recursive predomains to show that one element of d approximates another it suffices to find a binary relation containing the two elements that is a post fixed point for the associated monotone operator the statement of the proof principles is independent of any of the various methods available for explicit construction of recursive predomains following milner and tofte 1991 the method of proof is called co induction it closely resembles the way bisimulations are used in concurrent process calculi milner 1989 two specific instances of the co induction principle already occur in the work of abramsky 1990 1991 in the form of internal full abstraction theorems for denotational semantics of sccs and lazy lambda calculus in the first case post fixed binary relations are precisely abramsky s partial bisimulations whereas in the second case they are his applicative bisimulations the co induction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in strict or lazy higher order functional programming languages

the largest cartesian closed category of domains the main result of this paper provides a necessary and sufficient condition that the function space d d of a domain algebraic cpo d be again a domain the condition confirming a conjecture of plotkin is that d be strongly algebraic sfp the importance of this is that it enables us to conclude that sfp is the largest category of domains that is closed under the constructions of interest in semantics in the final section we briefly consider how our results may need to be extended if our admittedly rather restrictive notion of category of domains is relaxed in certain ways

universal profinite domains abstract we introduce a bicartesian closed category of what we call profinite domains study of these domains is carried out through the use of an equivalent category of pre orders in a manner similar to the information systems approach advocated by dana scott and others a class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators as a special instance of this construction a universal domain for the category sfp is demonstrated necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations a new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points