69 research outputs found
Functional programming with bananas, lenses, envelopes and barbed wire
We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example functions in Bird and Wadler's Introduction to Functional Programming can be expressed using these operators
Z-style notation for Probabilities
A notation for probabilities is proposed that differs from the traditional, conventional notation by making explicit the domains and bound variables involved. The notation borrows from the Z notation, and lends itself well to calculational manipulations, with a smooth transition back and forth to set and predicate notation
Introducing a Calculus of Effects and Handlers for Natural Language Semantics
In compositional model-theoretic semantics, researchers assemble
truth-conditions or other kinds of denotations using the lambda calculus. It
was previously observed that the lambda terms and/or the denotations studied
tend to follow the same pattern: they are instances of a monad. In this paper,
we present an extension of the simply-typed lambda calculus that exploits this
uniformity using the recently discovered technique of effect handlers. We prove
that our calculus exhibits some of the key formal properties of the lambda
calculus and we use it to construct a modular semantics for a small fragment
that involves multiple distinct semantic phenomena
Visual programming with recursion patterns in interaction nets
In this paper we propose to use Interaction Nets as a formalism for Visual Functional Programming. We consider the use of recursion patterns as a programming idiom, and introduce a suitable archetype/instantiation mechanism for interaction agents, which allows one to define agents whose behaviour is based on recursion patterns.Fundação para a Ciência e a Tecnologia (FCT
Towards modular compilers for effects
Compilers are traditionally factorised into a number of separate phases, such as parsing, type checking, code generation, etc. However, there is another potential factorisation that has received comparatively little attention: the treatment of separate language features, such as mutable state, input/output, exceptions, concurrency and so forth. In this article we focus on the problem of modular compilation, in which the aim is to develop compilers for separate language features independently, which can then be combined as required. We summarise our progress to date, issues that have arisen, and further wor
The Sketch of a Polymorphic Symphony
In previous work, we have introduced functional strategies, that is,
first-class generic functions that can traverse into terms of any type while
mixing uniform and type-specific behaviour. In the present paper, we give a
detailed description of one particular Haskell-based model of functional
strategies. This model is characterised as follows. Firstly, we employ
first-class polymorphism as a form of second-order polymorphism as for the mere
types of functional strategies. Secondly, we use an encoding scheme of run-time
type case for mixing uniform and type-specific behaviour. Thirdly, we base all
traversal on a fundamental combinator for folding over constructor
applications.
Using this model, we capture common strategic traversal schemes in a highly
parameterised style. We study two original forms of parameterisation. Firstly,
we design parameters for the specific control-flow, data-flow and traversal
characteristics of more concrete traversal schemes. Secondly, we use
overloading to postpone commitment to a specific type scheme of traversal. The
resulting portfolio of traversal schemes can be regarded as a challenging
benchmark for setups for typed generic programming.
The way we develop the model and the suite of traversal schemes, it becomes
clear that parameterised + typed strategic programming is best viewed as a
potent combination of certain bits of parametric, intensional, polytypic, and
ad-hoc polymorphism
- …