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Firstclass Polymorphism with Type Inference
"... Languages like ML and Haskell encourage the view of values as firstclass entities that can be passed as arguments or results of functions, or stored as components of data structures. The same languages o#er parametric polymorphism, which allows the use of values that behave uniformly over a range ..."
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Cited by 53 (0 self)
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Languages like ML and Haskell encourage the view of values as firstclass entities that can be passed as arguments or results of functions, or stored as components of data structures. The same languages o#er parametric polymorphism, which allows the use of values that behave uniformly over a range of di#erent types. But the combination of these features is not supported polymorphic values are not firstclass. This restriction is sometimes attributed to the dependence of such languages on type inference, in contrast to more expressive, explicitly typed languages, like System F, that do support firstclass polymorphism. This paper uses relationships between types and logic to develop a type system, FCP, that supports firstclass polymorphism, type inference, and also firstclass abstract datatypes. The immediate result is a more expressive language, but there are also long term implications for language design. 1
Merging Monads and Folds for Functional Programming
 In Advanced Functional Programming, LNCS 925
, 1995
"... . These notes discuss the simultaneous use of generalised fold operators and monads to structure functional programs. Generalised fold operators structure programs after the decomposition of the value they consume. Monads structure programs after the computation of the value they produce. Our progra ..."
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Cited by 51 (2 self)
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. These notes discuss the simultaneous use of generalised fold operators and monads to structure functional programs. Generalised fold operators structure programs after the decomposition of the value they consume. Monads structure programs after the computation of the value they produce. Our programs abstract both from the recursive processing of their input as well as from the sideeffects in computing their output. We show how generalised monadic folds aid in calculating an efficient graph reduction engine from an inefficient specification. 1 Introduction Should I structure my program after the decomposition of the value it consumes or after the computation of the value it produces? Some [Bir89, Mee86, Mal90, Jeu90, MFP91] argue in favour of structuring programs after the decomposition of the value they consume. Such syntax directed programs are written using a limited set of recursion functionals. These functionals, called catamorphisms or generalised fold operators are naturally ...
Deriving Structural Hylomorphisms From Recursive Definitions
 In ACM SIGPLAN International Conference on Functional Programming
, 1996
"... this paper, we propose an algorithm which can automatically turn all practical recursive definitions into structural hylomorphisms making program fusion be easily applied. 1 Introduction ..."
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Cited by 49 (17 self)
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this paper, we propose an algorithm which can automatically turn all practical recursive definitions into structural hylomorphisms making program fusion be easily applied. 1 Introduction
Shortcut Fusion for Accumulating Parameters Ziplike Functions
, 2002
"... We present an alternative approach to shortcut fusion based on the function unfoldr. Despite its simplicity the technique can remove intermediate lists in examples which are known to be difficult. We show that it can remove all lists from definitions involving ziplike functions and functions using ..."
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Cited by 47 (0 self)
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We present an alternative approach to shortcut fusion based on the function unfoldr. Despite its simplicity the technique can remove intermediate lists in examples which are known to be difficult. We show that it can remove all lists from definitions involving ziplike functions and functions using accumulating parameters.
Compilation by Transformation in NonStrict Functional Languages
, 1995
"... In this thesis we present and analyse a set of automatic sourcetosource program transformations that are suitable for incorporation in optimising compilers for lazy functional languages. These transformations improve the quality of code in many different respects, such as execution time and memory ..."
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Cited by 44 (1 self)
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In this thesis we present and analyse a set of automatic sourcetosource program transformations that are suitable for incorporation in optimising compilers for lazy functional languages. These transformations improve the quality of code in many different respects, such as execution time and memory usage. The transformations presented are divided in two sets: global transformations, which are performed once (or sometimes twice) during the compilation process; and a set of local transformations, which are performed before and after each of the global transformations, so that they can simplify the code before applying the global transformations and also take advantage of them afterwards. Many of the local transformations are simple, well known, and do not have major effects on their own. They become important as they interact with each other and with global transformations, sometimes in nonobvious ways. We present how and why they improve the code, and perform extensive experiments wit...
Foundations for structured programming with GADTs
 Conference record of the ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2008
"... GADTs are at the cutting edge of functional programming and become more widely used every day. Nevertheless, the semantic foundations underlying GADTs are not well understood. In this paper we solve this problem by showing that the standard theory of data types as carriers of initial algebras of fun ..."
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Cited by 40 (5 self)
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GADTs are at the cutting edge of functional programming and become more widely used every day. Nevertheless, the semantic foundations underlying GADTs are not well understood. In this paper we solve this problem by showing that the standard theory of data types as carriers of initial algebras of functors can be extended from algebraic and nested data types to GADTs. We then use this observation to derive an initial algebra semantics for GADTs, thus ensuring that all of the accumulated knowledge about initial algebras can be brought to bear on them. Next, we use our initial algebra semantics for GADTs to derive expressive and principled tools — analogous to the wellknown and widelyused ones for algebraic and nested data types — for reasoning about, programming with, and improving the performance of programs involving, GADTs; we christen such a collection of tools for a GADT an initial algebra package. Along the way, we give a constructive demonstration that every GADT can be reduced to one which uses only the equality GADT and existential quantification. Although other such reductions exist in the literature, ours is entirely local, is independent of any particular syntactic presentation of GADTs, and can be implemented in the host language, rather than existing solely as a metatheoretical artifact. The main technical ideas underlying our approach are (i) to modify the notion of a higherorder functor so that GADTs can be seen as carriers of initial algebras of higherorder functors, and (ii) to use left Kan extensions to trade arbitrary GADTs for simplerbutequivalent ones for which initial algebra semantics can be derived.
Free Theorems in the Presence of seq
, 2004
"... Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, the standard parametricity theorem fails for nonstrict languages supporting a polymorph ..."
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Cited by 39 (12 self)
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Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, the standard parametricity theorem fails for nonstrict languages supporting a polymorphic strict evaluation primitive like Haskell's $\mathit{seq}$. Contrary to the folklore surrounding $\mathit{seq}$ and parametricity, we show that not even quantifying only over strict and bottomreflecting relations in the $\forall$clause of the underlying logical relation  and thus restricting the choice of functions with which such relations are instantiated to obtain free theorems to strict and total ones  is sufficient to recover from this failure. By addressing the subtle issues that arise when propagating up the type hierarchy restrictions imposed on a logical relation in order to accommodate the strictness primitive, we provide a parametricity theorem for the subset of Haskell corresponding to a GirardReynoldsstyle calculus with fixpoints, algebraic datatypes, and $\mathit{seq}$. A crucial ingredient of our approach is the use of an asymmetric logical relation, which leads to ``inequational'' versions of free theorems enriched by preconditions guaranteeing their validity in the described setting. Besides the potential to obtain corresponding preconditions for standard equational free theorems by combining some new inequational ones, the latter also have value in their own right, as is exemplified with a careful analysis of $\mathit{seq}$'s impact on familiar program transformations.
Tupling Calculation Eliminates Multiple Data Traversals
 In ACM SIGPLAN International Conference on Functional Programming
, 1997
"... Tupling is a wellknown transformation tactic to obtain new efficient recursive functions by grouping some recursive functions into a tuple. It may be applied to eliminate multiple traversals over the common data structure. The major difficulty in tupling transformation is to find what functions are ..."
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Cited by 38 (20 self)
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Tupling is a wellknown transformation tactic to obtain new efficient recursive functions by grouping some recursive functions into a tuple. It may be applied to eliminate multiple traversals over the common data structure. The major difficulty in tupling transformation is to find what functions are to be tupled and how to transform the tupled function into an efficient one. Previous approaches to tupling transformation are essentially based on fold/unfold transformation. Though general, they suffer from the high cost of keeping track of function calls to avoid infinite unfolding, which prevents them from being used in a compiler. To remedy this situation, we propose a new method to expose recursive structures in recursive definitions and show how this structural information can be explored for calculating out efficient programs by means of tupling. Our new tupling calculation algorithm can eliminate most of multiple data traversals and is easy to be implemented. 1 Introduction Tupli...
Microprocessor Specification in Hawk
 In Proceedings of the 1998 International Conference on Computer Languages
, 1998
"... Modern microprocessors require an immense investment of time and effort to create and verify, from the highlevel architectural design downwards. We are exploring ways to increase the productivity of design engineers by creating a domainspecific language for specifying and simulating processor arch ..."
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Cited by 38 (3 self)
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Modern microprocessors require an immense investment of time and effort to create and verify, from the highlevel architectural design downwards. We are exploring ways to increase the productivity of design engineers by creating a domainspecific language for specifying and simulating processor architectures. We believe that the structuring principles used in modern functional programming languages, such as static typing, parametric polymorphism, firstclass functions, and lazy evaluation provide a good formalism for such a domainspecific language, and have made initial progress by creating a library on top of the functional language Haskell. We have specified the integer subset of an outoforder, superscalar DLX microprocessor, with registerrenaming, a reorder buffer, a global reservation station, multiple execution units, and speculative branch execution. Two key abstractions of this library are the signal abstract data type (ADT), which models the simulation history of a wire, and the transaction ADT, which models the state of an entire instruction as it travels through the microprocessor. 1
Proving the Correctness of RecursionBased Automatic Program Transformations
 Theoretical Computer Science
, 1996
"... This paper shows how the Improvement Theorema semantic condition ..."
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Cited by 37 (4 self)
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This paper shows how the Improvement Theorema semantic condition