M. Hofmann. Semantical analysis of higher-order abstract syntax. In Proceedings of LICS'99, pages 204213. IEEE, 1999. Home/Search Document Not in Database Summary Related Articles Check |
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A New Approach to Abstract Syntax with Variable Binding - Gabbay, Pitts (2001) (33 citations) (Correct)
.... given by the inclusion functor I , Set, and the shift functor : Set Set , given by X(n) X(n 1) These ingredients also occur in subsequent work on modelling calculus names in Set [FMS96, Sta96b] and, most relevantly, recent work on modelling variable binding abstract syntax [FPT99, Hof99], where other presheaf categories besides Set are considered. Now, a somewhat overlooked model of the calculus, mentioned in [PiS93b, Examples 4.3] is the full subcategory of Set whose objects are the pullback preserving functors. This is equivalent to a well known topos, sometimes ....
....of sets) on the other hand, the Schanuel topos is a sheaf subtopos of the presheaf category Set , with the inclusion sending the FM set of atoms A to the object of names I , Set and the abstraction operator [A ] to the shift functor ( mentioned above. Both the presheaf toposes used in [FPT99, Hof99] and the Schanuel topos (and indeed many other categories equipped with a faithful functor to Set ) support an initial algebra semantics for signatures with binding. So does the Schanuel topos, and its associated FM set theory, have any advantage over these other, related categories It is ....
Hofmann, M.: Semantical analysis of higher-order abstract syntax. In 14th Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, Washington, DC, 1999, pp. 204-213.
Basic Category Theory for Models of Syntax - Crole (2002) (2 citations) (Correct)
....which this is possible. For further work see [16] and the references therein. There is a wealth of literature on so called Higher Order Abstract Syntax. This is another methodology for encoding syntax with binders. For an introduction, see [15, 14] although the ideas go back to Church. The paper [10] provides links between Higher Order Abstract Syntax, and the presheaf models described in these notes. For material on implementation, see [4, 5] A more recent approach, which combines de Bruijn notation and ordinary calculus in a hybrid syntax, is described in [1] If you are interested in ....
M. Hofmann. Semantical analysis for higher-order abstract syntax. In G. Longo, editor, Proceedings of the 14th Annual Symposium on Logic in Computer Science (LICS'99), pages 204--213, Trento, Italy, July 1999. IEEE Computer Society Press.
TOSCA 2001 Preliminary Version - The Theory Of (Correct)
....algebra. Thus, most proof editors give no induction principles, case analysis, inversion predicates and similar tools for reasoning on terms of type Var tm, i.e. contexts. Nevertheless, it is possible to prove that types of the form Var . Var tm do have recursion and induction principles [10,2,11,5]. Hence, beside the simple Axioms of the Theory of Contexts above, we can safely assume higher order induction and recursion principles as needed (provided that Var is constructorless) like the following induction over Var tm (notice that there are two base cases) Axiom tm ind1 : ....
....algorithm fails to give the right inversion predicate when the datatype, which we have to discriminate over, is higher order, because usual inductive type theories do not recognize a higher order type as inductive. Nevertheless, we know that types of the form Var tm do have recursion principles [10, 2, 11]. Hence, we can consistently 13 Honsell et al. introduce these principles (as Axioms) for the definition of the recursive map needed in the inversion predicate: Parameter subst inv fun : tm (Var tm) tm Prop. Axiom subst inv fun var0 : N,M:tm) subst inv fun N var M) N=M) Axiom ....
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M. Hofmann. Semantical analysis of higher-order abstract syntax. In Longo
Isabelle/Isar - a versatile environment for human-readable formal .. - Wenzel (2002) (2 citations) (Correct)
....would enable the full range of meta theoretical studies (including completeness issues etc. leaving behind the handsome approach of higher order abstract syntax. There has been ongoing work on combining higher order abstract syntax directly with induction principles [Despeyroux et al. 1997] [Hofmann, 1999], although the resulting systems do have their own complexities, both in theory and practice. 8.2 Extensional equality The axiomatic base of minimal logic is now extended by a particular kind of equality. The following declarations introduce = as an extensional equivalence relation that ....
M. Hofmann. Semantical analysis of higher-order abstract syntax. In 14th Annual IEEE Symposium on Logic in Computer Science (LICS'99), volume 158. IEEE Computer Society, 1999.
A Framework for Typed HOAS and Semantics - Miculan, Scagnetto (2003) (2 citations) (Correct)
....the semantic aspects on a par. The metamodel should enlighten the interactions and dependencies between these two abstraction levels. The aim of this paper is indeed to define and investigate such a framework. Our setting is inspired by previous work by Fiore, Hofmann, Plotkin, Turi, among others [2 4, 7, 8]. Like in these works, we advocate the use of presheaf categories for a satisfactory representation of the abstract syntax of (typed) languages with variables and binding operators. But moreover, it turns out that the same presheaf categories can be used to address the semantic aspects as well. ....
....classes of) terms of type # at # by S# (#) # t : # . 2. ALGEBRAIC TYPED HOAS In this section we give an abstract algebraic presentation of typed abstract syntax with bindings. The term calculus of Figure 1 stratify sets of terms according to the typing contexts. As pointed out in [4, 7], an adequate universe for reflecting this situation is some functor category of the form C , where the index category is a suitable category of contexts. In the case of typed syntax [3] the category of contexts turns out to be the free cocartesian category over the category of variable ....
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M. Hofmann. Semantical analysis of higher-order abstract syntax. In Longo [12], pages 204--213.
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M. Hofmann. Semantical analysis of higher-order abstract syntax. In Proceedings of LICS'99, pages 204213. IEEE, 1999.
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Martin Hofmann. Semantical analysis of higher-order abstract syntax. In Proc. 14th Symp. on Logic in Computer Science, pages 204--213. IEEE, July 1999.
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M. Hofmann, Semantical analysis of higher-order abstract syntax, in: G. Longo, editor, Logic in Computer Science (1999), pp. 204--213. REFERENCES 23
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Martin Hofmann. Semantical analysis of higher-order abstract syntax. In Proc. of 14th Ann. IEEE Symp. on Logic in Computer Science, LICS'99, Trento, Italy, 2--5 July 1999, pages 204--213. IEEE Computer Society Press, Los Alamitos, CA, 1999.
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