Refinement Calculus
A Systematic Introduction
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60 Result(s)
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Chapter
Enforcing behavior with contracts
Contracts have been introduced earlier as a way of modeling a collection of agents that work within the limits set by the contract. We have analyzed the question of when an agent or a coalition of agents can r...
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Chapter and Conference Paper
SFI: A Refinement Based Layered Software Architecture
Refinement calculus [1,5] is a formal framework for reasoning about program correctness and correctness preserving program refinements. It serves as the foundation for an object-oriented software architecture and...
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Chapter and Conference Paper
Software Construction by Stepwise Feature Introduction
We study a method for software construction that is based on introducing new features to an evolving system one by one. A layered software architecture is proposed to support this method. We show how to descri...
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Article
Encoding, Decoding and Data Refinement
Data refinement is the systematic replacement of a data structure with another one in program development. Data refinement between program statements can on an abstract level be described as a commutativity p...
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Article
Class Refinement as Semantics of Correct Object Substitutability
Subtype polymorphism, based on syntactic conformance of objects' methods and used for substituting subtype objects for supertype objects, is a characteristic feature of the object-oriented programming style. ...
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Chapter and Conference Paper
Analysing UML Use Cases as Contracts
The Unified Modeling Language (UML) consists in a set of diagrams that describe a system under development. A use case diagram specifies the required functionality of the system, showing the collaboration among a...
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Article
Fusion and simultaneous execution in the refinement calculus
In the refinement calculus, program statements are modelled as predicate transformers. A product operator for predicate transformers was introduced by Martin [18] and Naumann [25] using category theoretic con...
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Book
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Chapter
Iteration of Conjunctive Statements
In our preceding treatment of iteration, we have considered the situation where the body of the iteration is either monotonic or continuous. In this chapter, we look at some of the additional properties that i...
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Chapter
Types and Data Structures
So far, we have assumed a fixed collection of types, type operators, constants and axioms in the logic. We next consider how to extend our theories to model new domains of discourse by defining new types with ...
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Chapter
The Refinement Calculus Hierarchy
The predicate transformers that we use to model contracts are constructed from other predicate transformers or from simpler elements, like state predicates, state transformers, or state relations. The predicat...
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Chapter
Functions
We start our overview of the basic axioms and inference of higher-order logic by studying the rules for reasoning about functions. These are essentially the rules of simply typed lambda calculus. A method of exte...
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Chapter
Statements as Games
In the previous chapter we showed that contract statements can be interpreted as (monotonic) predicate transformers. But predicate transformers are pure mathematical entities, functions from predicates (sets) ...
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Chapter
Truth Values
In previous chapters we have introduced higher-order logic and described the constants and inference rules that are used for reasoning about functions. In this chapter we present the constants and inference ru...
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Chapter
Subclasses of Statements
Not only monotonicity, but also other homomorphism properties of predicate transformers turn out to be important in modeling programming constructs. In this chapter we study homomorphic predicate transformers,...
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Chapter
Recursion
We now apply fixed-point theory to recursively defined statements, interpreting a recursive statement as the least fixed point of a monotonic function on predicate transformers. We show how to construct recurs...
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Chapter
Boolean Expressions and Conditionals
In the previous chapter we showed how to reason about predicates and sets in general. In programming, predicates arise in two different disguises. First, they are used to describe control structures with branc...
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Chapter
Well-founded Sets and Ordinals
So far, we have looked at lattices as a special kind of posets. In this chapter, we focus on another important special kind of posets: well-founded sets and well-ordered sets. Well-founded sets are partially orde...
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Chapter
Continuity and Executable Statements
In Chapter 19, we used ordinals to express fixed points as limits. In practice, the natural numbers are sufficient as long as all statements involved are continuous. In this chapter we will study the notion of...
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Chapter
The N-Queens Problem
The n-queens problem is to place n queens (where n > 0) on an n -by-n chessboard so that no queen is threatened by another one. According to the rules of chess, this is equivalent to the requirement that no two q...
