Abstract

We introduce the motivations, history, technical approach, and design choices behind DARWARS Ambush!, a game-based, convoy operations trainer that was heavily used by the U.S. Army and Marines for five years. We discuss a number of the practical deployment concerns we addressed and discuss how we cultivated relationships to build a community of committed users. As one of the first large-scale, successful serious games for learning, DARWARS Ambush! broke new ground and led to many lessons learned on how to best design, develop, and deploy a serious game. We discuss some of our experiences, decisions, and lessons learned, and conclude with some recommendations that may help new efforts attain success as well.

Introduction

In late 2004, DARPA Program Manager Dr. Ralph Chatham asked BBN Technologies, who was already under contract on his DARWARS Training Superiority Program, whether we could quickly – within six months – deploy a training system to help soldiers better respond to convoy ambushes then prevalent in Iraq. At that time, convoy ambushes involving small arms, rocket-propelled grenades (RPGs), or improvised explosive devices (IEDs) were a leading cause of casualties. The U.S. military had recognized the need for increased training for convoy operations and aggressively pursued a variety of training solutions, including live-fire training exercises, marksmanship trainers, and driver training systems (see Steele, 2004; Tiron, 2004 for examples). Dr. Chatham recognized the need for a squad-level team trainer that would focus on situational awareness, communication, and coordination.

Abstract

The Virtual Dental Implant Trainer (VDIT) is a 3-D simulation environment for dental students to practice dental implant surgery procedures. It provides a highly authentic surgery experience for trainees looking to practice techniques learned elsewhere, or for experienced dentists looking to refresh their skills. Because of its focus on being a practice environment, VDIT does not contain many of the instructional design techniques often found in many other training simulations. Furthermore, there is limited use of game elements found in many other serious games. However, given the tasks and emphasis on practice, this is acceptable. With additional effort VDIT could be transitioned into a more effective and engaging instructional environment.

Introduction

The Virtual Dental Implant Trainer (VDIT) is a highly accurate procedural training simulation environment for dentists. VDIT is not intended to be a stand-alone learning experience for those i rst learning how to perform dental implant surgery. Rather, it was specii cally designed to be used in conjunction with other training, or for those seeking a practice environment. These decisions on use greatly affected the game’s design. The remaining sections of this chapter look at the effectiveness of these decisions on VDIT.

Abstract

The Computer-based Corpsman Training System (CBCTS) was developed by ECS, Inc. for the U.S. Army Research, Development and Engineering Command. Game design elements complement the instructional design elements to produce an award-winning learning game. Notable design features include a well-designed tutorial, opportunities for decision making, time to reflect and replay a scenario, and implicit and explicit feedback. While game and instructional elements work very well together in CBCTS, suggestions are made in this chapter to increase instructional guidance to gain learning efficiencies without jeopardizing gameplay. These suggestions will benefit all learning game designers striving to improve their own games. Game designers are cautioned that additional elements may increase the design and development resource requirements, and instructional and gameplay trade-offs have to be considered. Some of these trade-offs are briefly addressed.

Introduction

The Computer-based Corpsman Training System (CBCTS) is a learning game that provides combat corpsmen realistic training to prepare them to apply their skills in a combat situation. CBCTS was developed by ECS, Inc. for the U.S. Army Research, Development and Engineering Command (RDECOM). The game supports training for Navy combat medics who are assigned to the U.S. Marine Corps. CBCTS is used at the Army Medical Department (AMEDD) Center and School as part of the curriculum to prepare combat medics.

Extension of λC to the system λD0

In the present chapter we investigate the formal aspects of adding definitions to a type system. In this we follow the pioneering work of N.G. de Bruijn (cf. de Bruijn, 1970). As the basic system we take λC, the most powerful system in the λ-cube. System λC is suitable for the PAT-interpretation, because it encapsulates λP. But it also covers the nice second order aspects of λ2. Therefore, λC appears to be enough for the purpose of ‘coding’ mathematics and mathematical reasonings and is an excellent candidate for the natural extension we want, being almost inevitable for practical applications: the addition of definitions.

We start with an extension leading from λC to a system called λD0. This system contains a formal version of definitions in the usual sense, the so-called descriptive definitions, so it can be used for a great amount of applications in the realm of logic and mathematics. But λD0 does not yet allow a satisfactory representation of axioms and axiomatic notions; these will be considered in the following chapter, in which a small, further extension of λD0 leads to our final system λD. (We have noticed before that we do not consider inductive and recursive definitions, since we can do without them; see Section 8.2.)

In order to give a proper description of λD0, we first extend our set of expressions, as given in Definition 6.3.1 for λC.

Aim and scope

The aim of the book is, firstly, to give an introduction to type theory, an evolving scientific field at the crossroads of logic, computer science and mathematics. Secondly, the book explains how type theory can be used for the verification of mathematical expressions and reasonings.

Type theory enables one to provide a ‘coded’ version – i.e. a full formalisation – of many mathematical topics. The formal system underlying type theory forces the user to work in a very precise manner. The real power of type theory is that well-formedness of the formalised expressions implies logical and mathematical correctness of the original content.

An attractive property of type theory is that it becomes possible and feasible to do the encoding in a ‘natural’ manner, such that one follows (and recognises) the way in which these subjects were presented originally. Another important feature of type theory is that proofs are treated as first-class citizens, in the sense that proofs do not remain meta-objects, but are coded as expressions (terms) of the same form as the rest of the formalisation.

The authors intend to address a broad audience, ranging from university students to professionals. The exposition is gentle and gradual, developing the material at a steady pace, with ample examples and comments, cross-references and motivations. Theoretical issues relevant for logic and computer science alternate with practical applications in the area of fundamental mathematical subjects.

This book, Type Theory and Formal Proof: An Introduction, is a gentle, yet profound, introduction to systems of types and their inhabiting lambda-terms. The book appears shortly after Lambda Calculus with Types (Barendregt et al., 2013). Although these books have a partial overlap, they have very different goals. The latter book studies the mathematical properties of some formalisms of types and lambda-terms. The book in your hands is focused on the use of types and lambda-terms for the complete formalisation of mathematics. For this reason it also treats higher order and dependent types. The act of defining new concepts, essential for mathematical reasoning, forms an integral part of the book. Formalising makes it possible that arbitrary mathematical concepts and proofs be represented on a computer and enables a machine verification of the well-formedness of definitions and of the correctness of proofs. The resulting technology elevates the subject of mathematics and its applications to its maximally complete and reliable form.

The endeavour to reach this level of precision was started by Aristotle, by his introduction of the axiomatic method and quest for logical rules. For classical logic Frege completed this quest (and Heyting for the intuitionistic logic of Brouwer). Frege did not get far with his intended formalisation of mathematics: he used an inconsistent foundation. In 1910 Whitehead and Russell introduced types to remedy this. These authors made proofs largely formal, except that substitutions still had to be understood and performed by the reader.

Type constructors

In the previous chapter we introduced the possibility of constructing generalised terms, by abstracting a term from a type variable. For example, the term λx : σ · x (which is the identity on the fixed type σ) can be generalised to the term λα : * · λ x : α · x (the ‘polymorphic’ identity, i.e. the identity on variable type α, abstracted from this α).

In a similar manner, there is a natural wish to construct generalised types. For example, types like β → β, γ → γ, (γ → β) → (γ → β), …, all have the general structure ◇ → ◇, with the same type both left and right of the arrow. Abstracting over ◇ makes it possible to describe the whole family of types with this structure.

In order to handle this, we introduce a generalised expression that embodies the essence of this structure: λα : * · α → α. This is itself not a type, but a function with a type as a value. It is therefore called a type constructor. Only when we ‘feed’ it with e.g. β, γ or (γ → β), we obtain types:

(λα : * · α → α) β → β β → β,

(λα : * · α → α) γ → β γ → γ,

(λα : * · α → α) (γ → β) → β (γ → β) → (γ → β).