Interactive programming in Agda – Objects and graphical user interfaces

Abstract

We develop a methodology for writing interactive and object-based programs (in the sense of Wegner) in dependently typed functional programming languages. The methodology is implemented in the ooAgda library. ooAgda provides a syntax similar to the one used in object-oriented programming languages, thanks to Agda's copattern matching facility. The library allows for the development of graphical user interfaces (GUIs), including the use of action listeners.Our notion of interactive programs is based on the IO monad defined by Hancock and Setzer, which is a coinductive data type. We use a sized coinductive type which allows us to write corecursive programs in a modular way. Objects are server-side interactive programs that respond to method calls by giving answers and changing their state. We introduce two kinds of objects: simple objects and IO objects. Methods in simple objects are pure, while method calls in IO objects allow for interactions before returning their result. Our approach also allows us to extend interfaces and objects by additional methods.We refine our approach to state-dependent interactive programs and objects through which we can avoid exceptions. For example, with a state-dependent stack object, we can statically disable the pop method for empty stacks. As an example, we develop the implementation of recursive functions using a safe stack. Using a coinductive notion of object bisimilarity, we verify basic correctness properties of stack objects and show the equivalence of different stack implementations. Finally, we give a proof of concept that our interaction model allows to write GUI programs in a natural way: we present a simple drawing program, and a program which allows the users to move a small spaceship using a button.

Intrinsically-Typed Mechanized Semantics for Session Types

“…To extend our model to recursive sessions, we revise the type structure following Abel et al [2017]. Session types are modeled as the greatest fixed point of a functor STF, which models the different session type constructors.…”

Declarative GUIs

“…GUI events are handled by objects, which we have defined in our previous work [1], where they are described in detail. As in other object-oriented frameworks, an object receives methods and in response returns a result and updates its internal state.…”

“…In our previous article [1], we introduced an Agda library for developing state-dependent, interactive, object-based programs. We demonstrated its use for the development of basic GUIs.…”

“…State-Dependent IO In previous work [1], which was based on work of the second author [69], we gave a detailed introduction to interactive programs and objects, and to statedependent interactive programs and objects in dependent type theory. The theory of objects in dependent type theory is based on the IO monad in dependent type theory, developed by Hancock and Setzer [29][30][31]70].…”

“…This allows for monadic composition of programs, that is, sequencing one program with another program, where the second program depends on the return value of the first program. In the state-dependent version [1], both the set of available commands and the form of responses can depend on a state, and commands may modify the state.…”