Results 1 
5 of
5
Comprehending Monads
 Mathematical Structures in Computer Science
, 1992
"... Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised to an arbit ..."
Abstract

Cited by 455 (13 self)
 Add to MetaCart
Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised to an arbitrary monad, and how the resulting programming feature can concisely express in a pure functional language some programs that manipulate state, handle exceptions, parse text, or invoke continuations. A new solution to the old problem of destructive array update is also presented. No knowledge of category theory is assumed.
Linear Types Can Change the World!
 PROGRAMMING CONCEPTS AND METHODS
, 1990
"... The linear logic of J.Y. Girard suggests a new type system for functional languages, one which supports operations that "change the world". Values belonging to a linear type must be used exactly once: like the world, they cannot be duplicated or destroyed. Such values require no reference counti ..."
Abstract

Cited by 134 (9 self)
 Add to MetaCart
The linear logic of J.Y. Girard suggests a new type system for functional languages, one which supports operations that "change the world". Values belonging to a linear type must be used exactly once: like the world, they cannot be duplicated or destroyed. Such values require no reference counting or garbage collection, and safely admit destructive array update. Linear types extend Schmidt's notion of single threading; provide an alternative to Hudak and Bloss' update analysis; and offer a practical complement to Lafont and HolmstrÃ¶m's elegant linear languages.
The complexity of type inference for higherorder typed lambda calculi
 In. Proc. 18th ACM Symposium on the Principles of Programming Languages
, 1991
"... We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential ..."
Abstract

Cited by 28 (11 self)
 Add to MetaCart
We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential time, and for Fa the problem is nonelementary. We show as well a sequence of lower bounds on recognising the i^typable terms, where the bound for Fk+1 is exponentially larger than that for Fk. The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Nonaccepting computations are mapped to nonnormalising reduction sequences, and hence nontypable terms. The accepting computations are mapped to typable terms, where higherorder types encode reduction sequences, and firstorder types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. A primary technical tool in this reduction is the composition of polymorphic functions having different domains and ranges. These results are the first nontrivial lower bounds on type inference for the Girard/Reynolds
How to Make Destructive Updates Less Destructive
 IN PROC. 18TH ACM SYMP. ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1991
"... We present a safe embedding of mutable data structures in functional languages. With safety we mean that confluence and (in some sense) referential transparency are maintained. We develop a static criterion based on abstract interpretation which checks that any sideeffect which a function may exert ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
We present a safe embedding of mutable data structures in functional languages. With safety we mean that confluence and (in some sense) referential transparency are maintained. We develop a static criterion based on abstract interpretation which checks that any sideeffect which a function may exert via a destructive update remains invisible. The technique opens up the possibility of designing safe and efficient widespectrum languages which combine functional and imperative language constructs.
Quantifier Elimination and Parametric Polymorphism in Programming Languages
 J. Functional Programming
, 1992
"... We present a simple and easy to understand explanation of ML type inference and parametric polymorphism within the framework of type monomorphism, as in the first order typed lambda calculus. We prove the equivalence of this system with the standard interpretation using type polymorphism, and extend ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We present a simple and easy to understand explanation of ML type inference and parametric polymorphism within the framework of type monomorphism, as in the first order typed lambda calculus. We prove the equivalence of this system with the standard interpretation using type polymorphism, and extend the equivalence to include polymorphic fixpoints. The monomorphic interpretation gives a purely combinatorial understanding of the type inference problem, and is a classic instance of quantifier elimination, as well as an example of Gentzenstyle cut elimination in the framework of the CurryHoward propositionsastypes analogy. Supported by NSF Grant CCR9017125, and grants from Texas Instruments and from the Tyson Foundation. 1 Introduction In his influential paper, "A theory of type polymorphism in programming," Robin Milner proposed an extension to the first order typed calculus which has become known as the core of the ML programming language [Mil78, HMT90]. The extension augment...