Order Theory for Big-Step Semantics

We show that tools from order theory, such as Kleene fixpoint theorem, can be used to define bigstep semantics that simultaneously account for both converging and diverging behaviors of programs. These semantics remain very concrete. In particular, values are defined syntactically: the semantics of a function abstraction is a function closure rather than some abstract continuous function

Call-by-Value Is Dual to Call-by-Name – Reloaded

Abstract. We consider the relation of the dual calculus of Wadler (2003) to the λµ-calculus of Parigot (1992). We give translations from the λµ-calculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, translating from λµ to dual and then ‘reloading ’ from dual back into λµ yields a term equal to the original term. Composing the translations with duality on the dual calculus yields an involutive notion of duality on the λµ-calculus. A previous notion of duality on the λµ-calculus has been suggested by Selinger (2001), but it is not involutive. Note This paper uses color to clarify the relation of types and terms, and of source and target calculi. If the URL below is not in blue please download the color version fro

Lagois Connections - a Counterpart to Galois Connections -

In this paper we define a Lagois connection, which is a generalization of a special type of Galois connection. We begin by introducing two examples of Lagois connections. We then recall the definition of Galois connection and some of its properties; next we define Lagois connection, establish some of its properties, and compare these with properties of Galois connections; and then we (further) develop examples of Lagois connections. Via these examples it is shown that, as is the case of Galois connections, there is a plethora of Lagois connections. Also it is shown that several fundamental situations in computer science and mathematics that cannot be interpreted in terms of Galois connections naturally fit into the theory of Lagois connections. key words: Galois connection, Galois insertion, Lagois connection, quasiinverse, poset system, closure operator, interior operator AMS subject classification: Primary: 06A15, 06A10 Secondary: 68F05, 68F99, 54B99 The authors were p..