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Initial algebra semantics is enough
 Proceedings, Typed Lambda Calculus and Applications
, 2007
"... Abstract. Initial algebra semantics is a cornerstone of the theory of modern functional programming languages. For each inductive data type, it provides a fold combinator encapsulating structured recursion over data of that type, a Church encoding, a build combinator which constructs data of that ty ..."
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Cited by 16 (6 self)
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Abstract. Initial algebra semantics is a cornerstone of the theory of modern functional programming languages. For each inductive data type, it provides a fold combinator encapsulating structured recursion over data of that type, a Church encoding, a build combinator which constructs data
Inductionrecursion and initial algebras
 Annals of Pure and Applied Logic
, 2003
"... 1 Introduction Inductionrecursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and MartinL"of [17, 18, 19]. The first occurrence of formal inductionrecursion is MartinL"of's definition ..."
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Cited by 34 (12 self)
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1 Introduction Inductionrecursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and MartinL"of [17, 18, 19]. The first occurrence of formal inductionrecursion is MartinL"of's definition of a universe `a la Tarski [19], which consists of a set U
Initial Algebra, Final Coalgebra and Datatype
, 2011
"... Induction ” in which they provided a brief introduction to initial algebras and final coalgebras[1]. Induction is used both as a definition principle, and as a proof principle for algebraic structures. But there are also important dual “coalgebraic” ..."
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Induction ” in which they provided a brief introduction to initial algebras and final coalgebras[1]. Induction is used both as a definition principle, and as a proof principle for algebraic structures. But there are also important dual “coalgebraic”
Strong Dinaturality and Initial Algebras
, 2000
"... this paper, we wish to show that one simple trick that works is using Mulry's notion of strong dinaturality [1]. Let C, E be categories, E with pullbacks, and let H,K : C op C # E be two bifunctors. A strong dinatural transformation between H and K is a collection of # of morphisms #A ..."
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this paper, we wish to show that one simple trick that works is using Mulry's notion of strong dinaturality [1]. Let C, E be categories, E with pullbacks, and let H,K : C op C # E be two bifunctors. A strong dinatural transformation between H and K is a collection of # of morphisms #A : H (A, A)#K (A, A) in E , one for each object A # C, such that, for any two objects A, B # C and any morphism g : A#B in C, K (id A , g) # #A # pL = K (g, id B ) #<F12.1
GRÖBNER BASES, INITIAL IDEALS AND INITIAL ALGEBRAS
, 2003
"... We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties. ..."
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Cited by 3 (0 self)
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We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties.
Specifying Data Objects with Initial Algebras
, 909
"... Chris PrestonThis study presents a systematic approach to specifying data objects with the help of initial algebras. The primary aim is to describe the setup to be found in modern functional programming languages such as Haskell and ML, although it can also be applied to more general situations. Th ..."
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Chris PrestonThis study presents a systematic approach to specifying data objects with the help of initial algebras. The primary aim is to describe the setup to be found in modern functional programming languages such as Haskell and ML, although it can also be applied to more general situations
Fibrational Induction Rules for Initial Algebras ⋆
"... Abstract. This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs ’ elegant algebraic formulation of inductio ..."
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Cited by 6 (1 self)
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Abstract. This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs ’ elegant algebraic formulation
Initial Algebra and Final Coalgebra Semantics for Concurrency
, 1994
"... The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial ..."
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Cited by 55 (8 self)
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The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial
An InitialAlgebra Approach to Directed Acyclic Graphs
, 1995
"... The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying different ways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive ..."
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Cited by 6 (0 self)
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The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying different ways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a
Results 1  10
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319,109