This paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of inductive-inductive definitions, Hofmann-style quotient types, and Abel's size types. The latter, which provide a convenient constructive abstraction of what classically would be accomplished with transfinite ordinals, are used to prove termination of the recursive definitions of the elimination and computation properties of our encoding of QW-types. The development is formalized using the Agda theorem-prover.
This paper introduces an expressive class of indexed quotient-inductive types, called QWI types, within the framework of constructive type theory. They are initial algebras for indexed families of equational theories with possibly infinitary operators and equations. We prove that QWI types can be derived from quotient types and inductive types in the type theory of toposes with natural number object and universes, provided those universes satisfy the Weakly Initial Set of Covers (WISC) axiom. We do so by constructing QWI types as colimits of a family of approximations to them defined by well-founded recursion over a suitable notion of size, whose definition involves the WISC axiom. We developed the proof and checked it using the Agda theorem prover.
This paper introduces an expressive class of indexed quotient-inductive types, called QWI types, within the framework of constructive type theory. They are initial algebras for indexed families of equational theories with possibly infinitary operators and equations. We prove that QWI types can be derived from quotient types and inductive types in the type theory of toposes with natural number object and universes, provided those universes satisfy the Weakly Initial Set of Covers (WISC) axiom. We do so by constructing QWI types as colimits of a family of approximations to them defined by well-founded recursion over a suitable notion of size, whose definition involves the WISC axiom. We developed the proof and checked it using the Agda theorem prover.
Purpose This paper aims to investigate if the more stringent requirements of AASB 138, effective 1 January 2005, regarding capitalising research and development (R&D) spending could have been a catalyst for changes in managerial decisions that consequently resulted in reduced R&D spending in Australian companies. Design/methodology/approach Financial data of 31 Australian listed firms for financial years from 2001 to 2010 were used. Companies were classified as either capitalisers or non-capitalisers. A regression model was used to ascertain whether managers reduced R&D spending to manage earnings to attain short-term goals. Also, the research intensity ratios were calculated to determine trends in R&D spending of the two groups. Findings The pursuit of choosing short-term earnings targets to the detriment of long-term returns is referred to as short-termism. This study found a marked increase in the significance of short-termism in explaining changes in R&D of capitalisers before 2005. Furthermore, the median research intensity ratio of capitalisers declined almost three times that of non-capitalisers after the introduction of AASB 138. These findings suggest that AASB 138 could have been a catalyst for changes in managerial decisions in pursuit of short-termism, resulting in reduced R&D spending as a means to manage earnings. Originality/value This study is useful to standard setters and board of directors as it alerts them about the potential adverse effect AASB 138 might have on the survivability and competitiveness of Australian companies and hence the Australian economy.
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