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16
Efficient optimistic parallel simulations using reverse computation
 ACM Transactions on Modeling and Computer Simulation
, 1999
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The Universal Resolving Algorithm: Inverse Computation in a Functional Language
 in Mathematics of Program Construction. Proceedings
, 2000
"... We present an algorithm for inverse computation in a firstorder functional language based on the notion of a perfect process tree. The Universal Resolving Algorithm (URA) introduced in this paper is sound and complete, and computes each solution, if it exists, in finite time. The algorithm has been ..."
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Cited by 22 (3 self)
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We present an algorithm for inverse computation in a firstorder functional language based on the notion of a perfect process tree. The Universal Resolving Algorithm (URA) introduced in this paper is sound and complete, and computes each solution, if it exists, in finite time. The algorithm has been implemented for TSG, a typed dialect of SGraph, and shows some remarkable results for the inverse computation of functional programs such as pattern matching and the inverse interpretation of Whileprograms.
NREVERSAL of Fortune  The Thermodynamics of Garbage Collection
 In ACM Sigplan Notices
, 1977
"... The need to reverse a computation arises in many contextsdebugging, editor undoing, optimistic concurrency undoing, speculative computation undoing, trace scheduling, exception handling undoing, database recovery, optimistic discrete event simulations, subjunctive computing, etc. The need to anal ..."
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Cited by 14 (0 self)
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The need to reverse a computation arises in many contextsdebugging, editor undoing, optimistic concurrency undoing, speculative computation undoing, trace scheduling, exception handling undoing, database recovery, optimistic discrete event simulations, subjunctive computing, etc. The need to analyze a reversed computation arises in the context of static analysisliveness analysis, strictness analysis, type inference, etc. Traditional means for restoring a computation to a previous state involve checkpoints; checkpoints require time to copy, as well as space to store, the copied material. Traditional reverse abstract interpretation produces relatively poor information due to its inability to guess the previous values of assignedto variables. We propose an abstract computer model and a programming languageYLispwhose primitive operations are injective and hence reversible, thus allowing arbitrary undoing without the overheads of checkpointing. Such a computer can be built from reversible conservative logic circuits, with the serendipitous advantage of dissipating far less heat than traditional Boolean AND/OR/NOT circuits. Unlike functional languages, which have one &quot;state &quot; for all times, YLisp has at all times one &quot;state&quot;, with unique predecessor and successor states. Compiling into a reversible pseudocode can have benefits even when targeting a traditional computer. Certain optimizations, e.g., updateinplace, and compiletime garbage collection may be more easily performed, because the
Running Programs Backwards: the Logical Inversion of Imperative
, 2003
"... Imperative programs can be inverted directly from their forwarddirected program code with the use of logical inference. The relational semantics of imperative computations treats programs as logical relations over the observable state of the environment, which is taken to be the state of the variab ..."
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Cited by 13 (0 self)
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Imperative programs can be inverted directly from their forwarddirected program code with the use of logical inference. The relational semantics of imperative computations treats programs as logical relations over the observable state of the environment, which is taken to be the state of the variables in memory. Program relations denote both forward and backward computations, and the direction of the computation depends upon the instantiation pattern of arguments in the relation. This view of inversion has practical applications when the relational semantics is treated as a logic program. Depending on the logic programming inference scheme used, execution of this relational program can compute the inverse of the imperative program. A number of nontrivial imperative computations can be inverted with minimal logic programming tools.
Principles of Inverse Computation and the Universal Resolving Algorithm
 IN THE ESSENCE OF COMPUTATION: COMPLEXITY, ANALYSIS, TRANSFORMATION
, 2002
"... We survey fundamental concept in inverse programming and present the Universal Resolving Algorithm (URA), an algorithm for inverse computation in a firstorder, functional programming language. We discusst he principles behind the algorithm, including a threestep approach based on the notion of a p ..."
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Cited by 13 (2 self)
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We survey fundamental concept in inverse programming and present the Universal Resolving Algorithm (URA), an algorithm for inverse computation in a firstorder, functional programming language. We discusst he principles behind the algorithm, including a threestep approach based on the notion of a perfect process tree, and demonstrate our implementation with several examples. We explaint he idea of a semantics modifier for inverse computation which allows us to perform inverse computation in other programming languages via interpreters.
From Kleene Algebra to Refinement Algebra
, 2002
"... KAT (Kleene Algebra with Tests) have proved to be useful for reasoning about programs in a partial correctness framework. We describe DRA (demonic Refinement Algebra), a variation of KAT for total correctness and illustrate its modeling and reasoning power with a number of applications and examples. ..."
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Cited by 12 (0 self)
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KAT (Kleene Algebra with Tests) have proved to be useful for reasoning about programs in a partial correctness framework. We describe DRA (demonic Refinement Algebra), a variation of KAT for total correctness and illustrate its modeling and reasoning power with a number of applications and examples.
Compositional Analysis of Dynamical Systems using Predicate Transformers (Summary).
, 1993
"... Introduction We propose a complementary approach to discrete dynamical systems, using predicate transformers. We present general concepts like invariance and attraction, and we propose properties to characterize the structure of invariants. Then we present the concept of composition of dynamical sy ..."
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Cited by 11 (7 self)
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Introduction We propose a complementary approach to discrete dynamical systems, using predicate transformers. We present general concepts like invariance and attraction, and we propose properties to characterize the structure of invariants. Then we present the concept of composition of dynamical systems. We define algebraic operators on systems and we try to discover how dynamical properties of small systems are preserved or transformed when these are composed into more complex systems. Finally, we illustrate this approach on an example. We work with a space E (e.g. N, or R), and extend functions from E to E into functions PE ! PE, which are invertible. Any subset of E can be described by a predicate. For example, an interval [a; b] ` R is defined by the predicate P (x) =
There and back again: arrows for invertible programming
 In Proceedings of the 2005 ACM SIGPLAN workshop on Haskell
, 2006
"... Invertible programming occurs in the area of data conversion where it is required that the conversion in one direction is the inverse of the other. For that purpose, we introduce bidirectional arrows (biarrows). The biarrow class is an extension of Haskell’s arrow class with an extra combinator tha ..."
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Cited by 8 (0 self)
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Invertible programming occurs in the area of data conversion where it is required that the conversion in one direction is the inverse of the other. For that purpose, we introduce bidirectional arrows (biarrows). The biarrow class is an extension of Haskell’s arrow class with an extra combinator that changes the direction of computation. The advantage of the use of biarrows for invertible programming is the preservation of invertibility properties using the biarrow combinators. Programming with biarrows in a polytypic or generic way exploits this the most. Besides bidirectional polytypic examples, including invertible serialization, we give the definition of a monadic biarrow transformer, which we use to construct a bidirectional parser/pretty printer.
Statement inversion and strongest postcondition
 Science of Computer Programming
, 1993
"... A notion of inverse commands is de ned for a language with a weakest precondition semantics, permitting both demonic and angelic nondeterminism as well as miracles and nontermination. Every conjunctive and terminating command is invertible, the inverse being nonmiraculous and disjunctive. A simulat ..."
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Cited by 8 (2 self)
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A notion of inverse commands is de ned for a language with a weakest precondition semantics, permitting both demonic and angelic nondeterminism as well as miracles and nontermination. Every conjunctive and terminating command is invertible, the inverse being nonmiraculous and disjunctive. A simulation relation between commands is described using inverse commands. A generalized form of inverse is de ned for arbitrary conjunctive commands. The generalized inverses are shown to be closely related to strongest postconditions. 1
Program Inversion in the Refinement Calculus
 Information Processing letters
, 1990
"... We present a calculational method for inverting programs by inverting the components separately. This is made possible by using assertions as commands and by permitting constructs that exhibit angelic nondeterminism. Rules are given for transforming inverted programs so that the angelic constructs a ..."
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Cited by 6 (1 self)
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We present a calculational method for inverting programs by inverting the components separately. This is made possible by using assertions as commands and by permitting constructs that exhibit angelic nondeterminism. Rules are given for transforming inverted programs so that the angelic constructs are removed. A simple example illustrates the method. 1 Introduction The idea of program inversion goes back to Dijkstra [8]. Informally speaking, inverting a program S means constructing a program T that works like the reverse of S . Thus T , supplied with some output of S , will calculate the corresponding input to S . Intuitively based rules for program inversion by calculation are given by Gries [9]. A formal definition of the concept of inverse program together with proof rules for inverting programs is given by Chen and Udding [6], who demonstrate the use of program inversion in formal program development. Both Dijkstra and Gries consider programs to be invertible only if they are func...