Results 1 
8 of
8
Combining Symbolic Constraint Solvers on Algebraic Domains
 Journal of Symbolic Computation
, 1994
"... ion An atomic constraint p ? (t 1 ; : : : ; t m ) is decomposed into a conjunction of pure atomic constraints by introducing new equations of the form (x = ? t), where t is an alien subterm in the constraint and x is a variable that does not appear in p ? (t 1 ; : : : ; t m ). This is formalized tha ..."
Abstract

Cited by 28 (7 self)
 Add to MetaCart
ion An atomic constraint p ? (t 1 ; : : : ; t m ) is decomposed into a conjunction of pure atomic constraints by introducing new equations of the form (x = ? t), where t is an alien subterm in the constraint and x is a variable that does not appear in p ? (t 1 ; : : : ; t m ). This is formalized thanks to the notion of abstraction. Definition 4.2. Let T be a set of terms such that 8t 2 T ; 8u 2 X [ SC; t 6= E1[E2 u: A variable abstraction of the set of terms T is a surjective mapping \Pi from T to a set of variables included in X such that 8s; t 2 T ; \Pi(s) = \Pi(t) if and only if s =E1[E2 t: \Pi \Gamma1 denotes any substitution (with possibly infinite domain) such that \Pi(\Pi \Gamma1 (x)) = x for any variable x in the range of \Pi. It is important to note that building a variable abstraction relies on the decidability of E 1 [ E 2 equality in order to abstract equal alien subterms by the same variable. Let T = fu #R j u 2 T (F [ X ) and u #R2 T (F [ X )n(X [ SC)g...
A Complete Transformational Toolkit for Compilers
 ACM Transactions on Programming Languages and Systems
, 1996
"... . In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program sl ..."
Abstract

Cited by 23 (9 self)
 Add to MetaCart
. In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIM t , under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starti...
A Propositional Logic With 4 Values: True, False, Divergent and Meaningless
"... In this paper, we survey 3valued logics and their complete axiomatizations, one of which may be new. We then propose a 4valued, functionally complete logic that incorporates these 3valued systems and provide notations for interesting operators and subsystems. ..."
Abstract

Cited by 15 (12 self)
 Add to MetaCart
In this paper, we survey 3valued logics and their complete axiomatizations, one of which may be new. We then propose a 4valued, functionally complete logic that incorporates these 3valued systems and provide notations for interesting operators and subsystems.
Undecidability and Completeness Results for Process Algebras With Alternative Quantification Over Data
, 1998
"... We define a class of process algebras with a generalised operation P that allows explicit treatment of alternative quantification over data, and investigate the specific subclass formed by the algebras of finite processes modulo strong bisimulation. We prove that, in such algebras, equality bet ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
We define a class of process algebras with a generalised operation P that allows explicit treatment of alternative quantification over data, and investigate the specific subclass formed by the algebras of finite processes modulo strong bisimulation. We prove that, in such algebras, equality between process terms is definable by means of a firstorder data formula, and that, if the data is computable and has a builtin equality predicate, any \Pi 0 4 data formula is definable as an equation between ground process terms. From these results we work to the conclusion that equality in strong bisimulation algebras with a computable data part is \Pi 0 4 hard. We also investigate a restricted version of alternative quantification: the input prefix mechanism of Parrow and Sangiorgi (1995) and Hennessy and Lin (1996). We show that this restriction yields a less expressive formalism if the data is computable and has a builtin equality predicate: equality between input prefix proc...
"Generating Tools from Algebraic Specifications" Abstracts of the papers from the ASF+SDF'95 Workshop CWI, Amsterdam, May 11 12, 1995
"... s of the papers from the ASF+SDF'95 Workshop CWI, Amsterdam, May 11 & 12, 1995 [1] J. Heering and P. Klint. The prehistory of ASF+SDF (19801984). pages 14. [2] P. Klint. The evolution of implementation techniques in the ASF+SDF metaenvironment. pages 526. Abstract: The ASF+SDF Metaenvironment ..."
Abstract
 Add to MetaCart
s of the papers from the ASF+SDF'95 Workshop CWI, Amsterdam, May 11 & 12, 1995 [1] J. Heering and P. Klint. The prehistory of ASF+SDF (19801984). pages 14. [2] P. Klint. The evolution of implementation techniques in the ASF+SDF metaenvironment. pages 526. Abstract: The ASF+SDF Metaenvironment is an interactive development environment for formal language definitions. It is both a metaenvironment supporting fully interactive editing of modular language definitions written in the formalism ASF+SDF and a generator for dedicated environments for defined languages. The actual development of this system started in 1985 as part of the GIPE (Generation of Interactive Programming Environments) projects [HKKL86]. Now, ten years later, it is worthwhile to assess what has been achieved and, more importantly, which problems are still to be addressed. A historical and at times methodological perspective is necessary in such an assessment. However, rather than evaluating all aspects of the sys...
J. Heering
 ACM Transactions on Programming Languages and Systems
, 1996
"... In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slic ..."
Abstract
 Add to MetaCart
In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a "transformational toolkit" to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of the untyped lambda calculus extended with an algebraic rewriting system that characterizes the behavior of lazy stores and generalized conditionals. A major question left open in the earlier paper was whether there existed a complete equational axiomatization of PIM's semantics. In this paper, we answer this question in the affirmative for PIM's core algebraic component, PIM t , under the assumption of certain reasonable restrictions on term formation. We systematically derive the complete PIM logic as the culmination of a sequence of increasingly powerful equational systems starting f...
Homomorphism Preserving . . .
, 1993
"... Although every computable data type has an initial algebra specification with hidden functions, it may happen that some of the homomorphic images of the data type are not models of the specification. The latter are reducts of algebras that would be models of the specification if all its function ..."
Abstract
 Add to MetaCart
Although every computable data type has an initial algebra specification with hidden functions, it may happen that some of the homomorphic images of the data type are not models of the specification. The latter are reducts of algebras that would be models of the specification if all its functions were visible, whereas the homomorphic images of the data type are independent of the specification and need not be compatible with the hidden functions used in it. A hidden function specification that does not exclude any of the homomorphic images of its initial model from its model class will be called homomorphism preserving. It turns out that, unlike unrestricted initial algebra specification, homomorphism preserving initial algebra specification of computable data types requires both hidden sorts and hidden functions.