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FUNDIO: A LambdaCalculus with a letrec, case, Constructors, and an IOInterface: Approaching a Theory of unsafePerformIO. Frank report 16, Institut für
 Informatik, J.W. GoetheUniversität Frankfurt, September 2003. SSSS04. Manfred SchmidtSchauß, Marko Schütz, and
"... Abstract. A nondeterministic callbyneed lambdacalculus λndlr with case, constructors, letrec and a (nondeterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of leftmost outermost reduction. The semantics is defined by contextual e ..."
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Abstract. A nondeterministic callbyneed lambdacalculus λndlr with case, constructors, letrec and a (nondeterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of leftmost outermost reduction. The semantics is defined by contextual equivalence of expressions instead of using αβ(η)equivalence. It is shown that several program transformations are correct, for example all (deterministic) rules of the calculus, and in addition the rules for garbage collection, removing indirections and unique copy. This shows that the combination of a context lemma and a metarewriting on reductions using complete sets of commuting (forking, resp.) diagrams is a useful and successful method for providing a semantics of a functional programming language and proving correctness of program transformations. 1
Unique Fixed Point Induction for McCarthy's Amb
 IN: PROCEEDINGS OF THE 24TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE, ”LNCS” 1672
, 1999
"... We develop an operational theory of higherorder functions, recursion, and fair nondeterminism for a nontrivial, higherorder, callbyname functional programming language extended with McCarthy's amb. Implemented via fair parallel evaluation, functional programming with amb is very expres ..."
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We develop an operational theory of higherorder functions, recursion, and fair nondeterminism for a nontrivial, higherorder, callbyname functional programming language extended with McCarthy's amb. Implemented via fair parallel evaluation, functional programming with amb is very expressive. However, conventional semantic fixed point principles for reasoning about recursion fail in the presence of fairness. Instead, we adapt higherorder operational methods to deal with fair nondeterminism. We present two natural semantics, describing mayand mustconvergence, and define a notion of contextual equivalence over these two modalities. The presence of amb raises special difficulties when reasoning about contextual equivalence. In particular, we report on a challenging open problem with regard to the validity of bisimulation proof methods. We develop two sound and useful reasoning methods which, in combination, enable us to prove a rich collection of laws for contextual...
Imprecise Exceptions, CoInductively
"... In a recent paper, Peyton Jones et al. proposed a design for imprecise exceptions in the lazy functional programming language Haskell [PJRH + 99]. The main contribution of the design was that it allowed the language to continue to enjoy its current rich algebra of transformations. However, the den ..."
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In a recent paper, Peyton Jones et al. proposed a design for imprecise exceptions in the lazy functional programming language Haskell [PJRH + 99]. The main contribution of the design was that it allowed the language to continue to enjoy its current rich algebra of transformations. However, the denotational semantics used to formalise the design does not combine easily with other extensions, most notably that of concurrency. We present an alternative semantics for a lazy functional language with imprecise exceptions which is entirely operational in nature, and combines well with other extensions, such as I/O and concurrency. The semantics is based upon a convergence relation, which describes evaluation, and an exceptional convergence relation, which describes the raising of exceptions. Convergence and exceptional convergence lead naturally to a simple notion of renement, where a term M is re ned by N whenever they have identical convergent behaviour, and any exception raised by N c...
Games for Verification: Algorithmic Issues
, 2000
"... This dissertation deals with a number of algorithmic problems motivated by computer aided formal verification of finite state systems. The goal of formal verification is to enhance the design and development of complex systems by providing methods and tools for specifying and verifying correctness o ..."
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This dissertation deals with a number of algorithmic problems motivated by computer aided formal verification of finite state systems. The goal of formal verification is to enhance the design and development of complex systems by providing methods and tools for specifying and verifying correctness of designs. The success of formal methods in practice depends heavily on the degree of automation of development and verification process. This motivates development of efficient algorithms for problems underlying many verification tasks. Two
A Generic Operational Metatheory for Algebraic Effects ∗
"... We provide a syntactic analysis of contextual preorder and equivalence for a polymorphic programming language with effects. Our approach applies uniformly to arbitrary algebraic effects, and thus incorporates, as instances: errors, input/output, global state, nondeterminism, probabilistic choice, an ..."
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We provide a syntactic analysis of contextual preorder and equivalence for a polymorphic programming language with effects. Our approach applies uniformly to arbitrary algebraic effects, and thus incorporates, as instances: errors, input/output, global state, nondeterminism, probabilistic choice, and combinations thereof. Our approach is to extend Plotkin and Power’s structural operational semantics for algebraic effects (FoSSaCS 2001) with a primitive “basic preorder ” on ground type computation trees. The basic preorder is used to derive notions of contextual preorder and equivalence on program terms. Under mild assumptions on this relation, we prove fundamental properties of contextual preorder (hence equivalence) including extensionality properties, a characterisation via applicative contexts, and machinery for reasoning about polymorphism using relational parametricity. 1.
Characteristic Formulae for FixedPoint Semantics: A General Framework
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... The literature on concurrency theory offers a wealth of examples of characteristicformula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed points of suitable functions. Such constructions and their proof ..."
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The literature on concurrency theory offers a wealth of examples of characteristicformula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed points of suitable functions. Such constructions and their proofs of correctness have been developed independently, but have a common underlying structure. This study provides a general view of characteristic formulae that are expressed in terms of logics with a facility for the recursive definition of formulae. It is shown how several examples of characteristicformula constructions from the literature can be recovered as instances of the proposed general framework, and how the framework can be used to yield novel constructions. The paper also offers general results pertaining to the definition of cocharacteristic formulae and of characteristic formulae expressed in terms of infinitary modal logics.
HigherOrder Program Generation
, 2001
"... This dissertation addresses the challenges of embedding programming languages, specializing generic programs to specific parameters, and generating specialized instances of programs directly as executable code. Our main tools are higherorder programming techniques and automatic program generation. ..."
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This dissertation addresses the challenges of embedding programming languages, specializing generic programs to specific parameters, and generating specialized instances of programs directly as executable code. Our main tools are higherorder programming techniques and automatic program generation. It is our thesis that they synergize well in the development of customizable software. Recent
Algorithms in Computational Biology
, 1999
"... In this thesis we are concerned with the construction of algorithms that address problems of biological relevance. This activity is part of a broader... ..."
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In this thesis we are concerned with the construction of algorithms that address problems of biological relevance. This activity is part of a broader...
StepIndexed Relational Reasoning for Countable Nondeterminism
"... Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces noncontinuous behaviour, it is wellknown that developing semantic models for program ..."
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Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces noncontinuous behaviour, it is wellknown that developing semantic models for programming languages with countable nondeterminism is challenging. We present a stepindexed logical relations model of a higherorder functional programming language with countable nondeterminism and demonstrate how it can be used to reason about contextually defined may and mustequivalence. In earlier stepindexed models, the indices have been drawn from ω. Here the stepindexed relations for mustequivalence are indexed over an ordinal greater than ω.
Reasoning about Contextual Equivalence: From Untyped to Polymorphically Typed Calculi
"... Abstract: This paper describes a syntactical method for contextual equivalence in polymorphically typed lambdacalculi. Our specific calculus has letrec as cyclic let, data constructors, caseexpressions, seq, and recursive types. The typed language is a subset of the untyped language. Normalorder ..."
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Abstract: This paper describes a syntactical method for contextual equivalence in polymorphically typed lambdacalculi. Our specific calculus has letrec as cyclic let, data constructors, caseexpressions, seq, and recursive types. The typed language is a subset of the untyped language. Normalorder reduction is defined for the untyped language. Since there are less typed contexts the typed contextual preorder and equivalence are coarser than the untyped ones. We use typelabels for all subexpressions of the typed expressions, and prove a context lemma for the typelabeled calculus. We show how to reason about correctness of program transformations in the typed language, and how to easily transfer the methods and results from untyped program calculi to polymorphically typed ones. 1