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PolynomialTime Inverse Computation for Accumulative Functions with Multiple Data Traversals
"... Inverse computation has many applications such as serialization/deserialization, providing support for undo, and testcase generation for software testing. In this paper, we propose an inverse computation method that always terminates for a class of functions known as parameterlinear macro tree tra ..."
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Inverse computation has many applications such as serialization/deserialization, providing support for undo, and testcase generation for software testing. In this paper, we propose an inverse computation method that always terminates for a class of functions known as parameterlinear macro tree transducers, which involve multiple data traversals and the use of accumulations. The key to our method is the observation that a function in the class can be regarded as a nonaccumulative contextgenerating transformation without multiple data traversals. Accordingly, we demonstrate that it is easy to achieve terminating inverse computation for the class by contextwise memoization of the inverse computation results. We also show that when we use a tree automaton to express the inverse computation results, the inverse computation runs in time polynomial to the size of the original output and the textual program size.
The expression lemma ⋆
"... Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of objec ..."
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Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of object types with virtual methods play a central role for the same reason. There is a semantical correspondence between these two situations which we reveal and formalize categorically. To this end, we assume a coalgebraic model of OO programming with functional objects. The development may be helpful in deriving refactorings that turn sufficiently disciplined functional programs into OO programs of a designated shape and vice versa. Key words: expression lemma, expression problem, functional object, catamorphism, fold, the composite design pattern, program calculation, distributive law, free monad, cofree comonad. 1
Three Complementary Approaches to Bidirectional Programming
"... Abstract. This paper surveys three distinct approaches to bidirectional programming. The first approach, syntactic bidirectionalization, takes a program describing the forward transformation as input and calculates a wellbehaved reverse transformation. The second approach, semantic bidirectionaliza ..."
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Abstract. This paper surveys three distinct approaches to bidirectional programming. The first approach, syntactic bidirectionalization, takes a program describing the forward transformation as input and calculates a wellbehaved reverse transformation. The second approach, semantic bidirectionalization, is similar, but takes the forward transformation itself as input rather than a program describing it. It requires the transformation to be a polymorphic function and uses parametricity and free theorems in the proof of wellbehavedness. The third approach, based on bidirectional combinators, focuses on the use of types to ensure wellbehavedness and special constructs for dealing with alignment problems. In presenting these approaches, we pay particular attention to use of complements, which are structures that represent the information discarded by the transformation in the forward direction. 1
A TypeBased Approach to Parallelization
 National University of Singapore
, 2003
"... Parallel programs can be synthesized from sequential functional programs via a technique known as context preservation [6]. This technique has significantly broadened the set of sequential programs eligible for parallelization. However, the ability to automatically detect functions which admit conte ..."
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Parallel programs can be synthesized from sequential functional programs via a technique known as context preservation [6]. This technique has significantly broadened the set of sequential programs eligible for parallelization. However, the ability to automatically detect functions which admit contextpreservation property has not been investigated. In this paper, we propose a typebased approach to automatically detect a class of functions with contextpreservation property. In essence, our type system aims to detect an extendedring property of the subject program, from which context preservation is guaranteed. Through this type system, a sequential program can be automatically transformed to fit into a skeletal form, which can then be parallelized.
A Type System for Parallelization
"... Parallel programming is becoming an important cornerstone of general computing. In addition, type systems have significant impact on program analysis. In this paper, we demonstrate an automated typebased system that soundly synthesizes parallel programs from sequential functional programs. Our t ..."
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Parallel programming is becoming an important cornerstone of general computing. In addition, type systems have significant impact on program analysis. In this paper, we demonstrate an automated typebased system that soundly synthesizes parallel programs from sequential functional programs. Our type inference system discovers the parallelizability property of a sequential program in a modular fashion, by exploring a ring structure among the program's operators. It handles selfrecursive functions with accumulating parameters, as well as a class of nonlinear mutualrecursive functions. We automatically generates parallel code in a mutumorphic form  a succint model for parallel computation. Transforming into
Hiroshi Unno
"... We introduce higherorder, multiparameter, tree transducers (HMTTs, for short), which are kinds of higherorder tree transducers that take input trees and output a (possibly infinite) tree. We study the problem of checking whether the tree generated by a given HMTT conforms to a given output speci ..."
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We introduce higherorder, multiparameter, tree transducers (HMTTs, for short), which are kinds of higherorder tree transducers that take input trees and output a (possibly infinite) tree. We study the problem of checking whether the tree generated by a given HMTT conforms to a given output specification, provided that the input trees conform to input specifications (where both input/output specifications are regular tree languages). HMTTs subsume higherorder recursion schemes and ordinary tree transducers, so that their verification has a number of potential applications to verification of functional programs using recursive data structures, including resource usage verification, string analysis, and exact typechecking of XMLprocessing programs. We propose a sound but incomplete verification algorithm for the HMTT verification problem: the algorithm reduces the verification problem to a modelchecking problem for higherorder recursion schemes extended with finite data domains, and then uses (an extension of) Kobayashi’s algorithm for modelchecking recursion schemes. While the algorithm is incomplete (indeed, as we show in the paper, the verification problem is undecidable in general), it is sound and complete for a subclass of HMTTs called linear HMTTs. We have applied our HMTT verification algorithm to various program verification problems and obtained promising results.
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"... ABSTRACT Parallel programs can be synthesized from sequential functional programs via a technique known as context preservation[6]. This technique has significantly broadened the set of sequential programs eligible for parallelization. However, the ability to automatically detect functions which adm ..."
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ABSTRACT Parallel programs can be synthesized from sequential functional programs via a technique known as context preservation[6]. This technique has significantly broadened the set of sequential programs eligible for parallelization. However, the ability to automatically detect functions which admit contextpreservation property has not been investigated. In this paper, we propose a typebased approach to automatically detect a class of functions with contextpreservation property. In essence, our type system aims to detect an extendedring property of the subject program, from which context preservation is guaranteed. Through this type system, a sequential program can be automatically transformed to fit into a skeletal form, which can then be parallelized. In contrast to the usual type system that are constructed from the evaluation rules of the underlying language, our type system is constructed from a set of metarules that are used to transform programs into skeletal forms suitable for parallelization. 1. INTRODUCTION Systematic parallelization of sequential programs remains a major challenge in parallel computing. Particularly challenging are programs which make use of distributive and associative properties in order to restructure into divideandconquer style parallelism.
Sliced bananas on opaque data ⋆ The expression lemma
"... Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of objec ..."
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Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of object types with virtual methods play a central role for the same reason. There is a semantical correspondence between these two situations which we reveal and formalize categorically. To this end, we assume a coalgebraic model of OO programming with functional objects. In practical terms, the development prepares for refactorings that turn sufficiently disciplined functional folds into OO programs of a designated shape (and v.v.). Key words: expression lemma, expression problem, functional object, catamorphism, fold, composite, program calculation, distributive law, free monad, cofree comonad. 1
B[count++] = A[i];
"... / * copy all bigger elements from A[1..n] into B[] */ count = 0; for (i=0; i<n; i++) { sumAfter = 0; for (j=i+1; j<n; j++) { sumAfter + = A[j]; if (A[i]> sumAfter) ..."
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/ * copy all bigger elements from A[1..n] into B[] */ count = 0; for (i=0; i<n; i++) { sumAfter = 0; for (j=i+1; j<n; j++) { sumAfter + = A[j]; if (A[i]> sumAfter)