Results 11 - 20
of
23
From Reduction-Based to Reduction-Free Normalization
, 2004
"... We present a systematic construction of a reduction-free normalization function. Starting from ..."
Abstract
-
Cited by 10 (7 self)
- Add to MetaCart
We present a systematic construction of a reduction-free normalization function. Starting from
Types as graphs: Continuations in type logical grammar
- JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
"... Using the programming-language concept of CONTINUATIONS, we propose a new, multimodal analysis of quantification in Type Logical Grammar. Our approach provides a geometric view of in-situ quantification in terms of graphs, and motivates the limited use of empty antecedents in derivations. Just as ..."
Abstract
-
Cited by 9 (7 self)
- Add to MetaCart
Using the programming-language concept of CONTINUATIONS, we propose a new, multimodal analysis of quantification in Type Logical Grammar. Our approach provides a geometric view of in-situ quantification in terms of graphs, and motivates the limited use of empty antecedents in derivations. Just as continuations are the tool of choice for reasoning about evaluation order and side effects in programming languages, our system provides a principled, type-logical way to model evaluation order and side effects in natural language. We illustrate with an improved account of quantificational binding, weak crossover, wh-questions, superiority, and polarity licensing.
Refocusing in Reduction Semantics
, 2004
"... The evaluation function of a reduction semantics (i.e., a small-step operational semantics with an explicit representation of the reduction context) is canonically defined as the transitive closure of (1) decomposing a term into a reduction context and a redex, (2) contracting this redex, and (3) ..."
Abstract
-
Cited by 6 (3 self)
- Add to MetaCart
The evaluation function of a reduction semantics (i.e., a small-step operational semantics with an explicit representation of the reduction context) is canonically defined as the transitive closure of (1) decomposing a term into a reduction context and a redex, (2) contracting this redex, and (3) plugging the contractum in the context. Directly implementing this evaluation function therefore yields an interpreter with a worst-case overhead, for each step, that is linear in the size of the input term. We present
On the equivalence between small-step and big-step abstract machines: a simple application of lightweight fusion
, 2007
"... ..."
About Classical Logic and Imperative Programming
- Annals of mathematics and Articial Intelligence
, 1996
"... Introduction In this lecture, we shall consider a very well known typed #-calculus system, which is the second order #-calculus (also called "system F") of Girard [2], rediscovered by Reynolds [16] in a computer science frame. We shall extend it in two ways: . Types will be formulas of second orde ..."
Abstract
-
Cited by 3 (0 self)
- Add to MetaCart
Introduction In this lecture, we shall consider a very well known typed #-calculus system, which is the second order #-calculus (also called "system F") of Girard [2], rediscovered by Reynolds [16] in a computer science frame. We shall extend it in two ways: . Types will be formulas of second order predicate calculus, and not only, as in system F, second order propositional calculus [5, 6]. In a certain sense, this is a harmless extension, since the #-terms which are typable are the same. This kind of extension has already been considered by D. Leivant [11]. . A much more serious extension is the following: the underlying logic will be classical logic, and not only, as in system F, intuitionistic logic. Extraction of programs from classical proofs has been considered, since two or three years by several people (C. Murthy [12], J.Y. Girardapproach has the following features: 1. We
