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From Total Equational to Partial First Order Logic
, 1998
"... The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to pa ..."
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Cited by 19 (8 self)
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The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to partiality, like (variants of) error algebras and ordersortedness are also discussed, showing their uses and limitations. Moreover, both the total and the partial (positive) conditional fragment are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved. Some more powerful algebraic frameworks are sketched at the end. Equational specifications introduced in last chapter, are a powerful tool to represent the most common data types used in programming languages and their semantics. Indeed, Bergstra and Tucker have shown in a series of papers (see [BT87] for a complete exposition of results) that a data type is semicompu...
Polymorphic Syntax Definition
 THEOR. COMPUT. SCI
, 1997
"... Contextfree grammars are used in several algebraic specification formalisms instead of firstorder signatures for the definition of the structure of algebras, because grammars provide better notation than signatures. The rigidity of these firstorder structures enforces a choice between strongly ty ..."
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Cited by 3 (0 self)
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Contextfree grammars are used in several algebraic specification formalisms instead of firstorder signatures for the definition of the structure of algebras, because grammars provide better notation than signatures. The rigidity of these firstorder structures enforces a choice between strongly typed structures with little genericity or generic operations over untyped structures. In twolevel signatures level 1 defines the algebra of types used at level 0 providing the possibility to define polymorphic abstract data types. Twolevel grammars are the grammatical counterpart of twolevel signatures. This paper discusses the correspondence between contextfree grammars and firstorder signatures, the extension of this correspondence to twolevel grammars and signatures, examples of the usage of twolevel grammars for polymorphic syntax definition, a restriction of the class of twolevel grammars for which the parsing problem is decidable, a parsing algorithm that yields a minimal and ...
SecondOrder Algebraic Specifiation of . . .
 CENTRUM VOOR WISKUNDE EN INFORMATICA (CWI
, 1992
"... Higherorder algebraic specification is a synthesis of firstorder algebraic specification and higherorder functional programming which is both logically appealing as well as considerably more expressive than its two predecessors. To illustrate this, we describe the static semantics of a simple ..."
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Higherorder algebraic specification is a synthesis of firstorder algebraic specification and higherorder functional programming which is both logically appealing as well as considerably more expressive than its two predecessors. To illustrate this, we describe the static semantics of a simple blockstructured programming language using secondorder equations in addition to firstorder ones. The specification has a highly nondeterministic character and does not use a type environment. Furthermore, it supports error recovery and early detection of errors in incomplete programs.
Algebraic System Specification and Development: Survey and Annotated Bibliography  Second Edition 
, 1997
"... Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . ..."
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Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.2 Action Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.1 Early Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.2 Recent Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . 55 4.7.3 The Common Framework Initiative. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Methodology 57 5.1 Development Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Applica...
Solving Type Equations in MultiLevel Specifications
 LANGUAGE PROTOTYPING. AN ALGEBRAIC SPECIFICATION APPROACH, VOLUME 5 OF AMAST SERIES IN COMPUTING. WORLD SCIENTIFIC PUBLISHING INC
, 1996
"... In firstorder algebraic specification functions have types of the form s1 \Theta \Delta \Delta \Delta \Theta sn ! s0 , where the s i are type constants. Such types exclude higherorder and polymorphic functions. In multilevel algebraic specification the structure of types used in function declara ..."
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In firstorder algebraic specification functions have types of the form s1 \Theta \Delta \Delta \Delta \Theta sn ! s0 , where the s i are type constants. Such types exclude higherorder and polymorphic functions. In multilevel algebraic specification the structure of types used in function declarations is specified as an algebraic data type. If only free constructors are used in the types used in function declarations, type assignment is an extension of the Hindley /Milner algorithm to multiple levels of types. By means of equations over types, sophisticated type systems can be modeled in a simple and uniform language. The type assignment for arbitrary multilevel specifications requires Eunification. Although this is undecidable in general, it is decidable for restricted sets of equations. In an earlier paper, the modular applicative multilevel equational specification formalism MLS is defined. The typechecker supports only free type constructors. In this paper we introduce multi...