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Theorems for free!
 FUNCTIONAL PROGRAMMING LANGUAGES AND COMPUTER ARCHITECTURE
, 1989
"... From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus. ..."
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Cited by 330 (6 self)
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From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.
Projections for Polymorphic FirstOrder Strictness Analysis
 Math. Struct. in Comp. Science
, 1991
"... this paper, that results from this kind of analysis are, in a sense, polymorphic. This confirms an earlier conjecture [19], and shows how the technique can be applied to firstorder polymorphic functions. The paper is organised as follows. In the next section, we review projectionbased strictness a ..."
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Cited by 6 (1 self)
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this paper, that results from this kind of analysis are, in a sense, polymorphic. This confirms an earlier conjecture [19], and shows how the technique can be applied to firstorder polymorphic functions. The paper is organised as follows. In the next section, we review projectionbased strictness analysis very briefly. In Section 3 we introduce the types we will be working with: they are the objects of a category. We show that parameterised types are functors, with certain cancellation properties. In Section 4 we define strong and weak polymorphism: polymorphic functions in programming languages are strongly polymorphic, but we will need to use projections with a slightly weaker property. We prove that, under certain conditions, weakly polymorphic functions are characterised by any nontrivial instance. We can therefore analyse one monomorphic instance of a polymorphic function using existing techniques, and apply the results to every instance. In Section 5 we choose a finite set of projections for each type, suitable for use in a practical compiler. We call these specially chosen projections contexts, and we show examples of factorising contexts for compound types in order to facilitate application of the results of Section 4. We give a number of examples of polymorphic strictness analysis. Finally, in Section 6 we discuss related work and draw some conclusions. 2. Projections for Strictness Analysis
Logic of Build Fusion
, 2000
"... The starting point of this work is the observation that the CurryHoward isomorphism, relating types ! propositions programs ! proofs composition ! cut extends to the correspondence of program fusion ! cut elimination This simple idea suggests logical interpretations of some of the basic methods of ..."
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The starting point of this work is the observation that the CurryHoward isomorphism, relating types ! propositions programs ! proofs composition ! cut extends to the correspondence of program fusion ! cut elimination This simple idea suggests logical interpretations of some of the basic methods of generic and transformational programming. In the present paper, we provide a logical analysis of the general form of build fusion, also known as deforestation, over the inductive and the coinductive datatypes, regular or nested. The analysis is based on a novel logical interpretation of parametricity in terms of the paranatural transformations, introduced in the paper. 1 Introduction 1.1 Fusion and cut The CurryHoward isomorphism is one of the conceptual building blocks of type theory, built deep into the foundation of computer science and functional programming [6, ch. 3]. The fact that it is an isomorphism means that the type and the term constructors on one side obey the same laws as ...