R. Backhouse. On the meaning and construction of the rules in Martin-L#f's theory of types. In Workshop on General Logic, LFCS-88-52, Edinburgh, February 1987. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Program Development in Constructive Type Theory - Galmiche (1992) (1 citation) (Correct)
....de ned types in terms of wellorderings and for adding new rules for such types. The problem to add new rules for inductively de ned types is solved by a general scheme meant to introduce new type operators by giving formation and introduction rules and deriving elimination and equality rules [1]. Another approach based on a xed point operator is also possible. We discuss the problem of representation as wellorderings and show that all inductively de ned type can be represented as well orderings [23] In this case, we have to assume extensional equality relation on types as given in ....
.... representation for a structure is the iterative and the recursive ones [15] Dioeerent approaches to the introduction of inductive sets in type theory have been proposed using the well order set constructor, introducing a xed point set constructor [7] or introducing a method to add new rules [1]. The rst is not general enough to express all inductive sets. The second is quite complicated and the third is not suOEcient for the purpose because it is not formalized inside the theory formalism and we want to have set constructor for inductive sets with reasoning about it using theory rules. ....
R. Backhouse. On the meaning and construction of the rules in Martin-L#f's theory of types. In Workshop on General Logic, LFCS-88-52, Edinburgh, February 1987.
Martin-Löf's Type Theory - Nordström, Petersson, Smith (Correct)
....for the selector is called the elimination rule and the de ning equations are called equality rules. Given the introduction rules, it is possible to mechanically derive the elimination rule and the equality rules for a set; how this can be done have been investigated by Martin L#f [29] Backhouse [2], Coquand and Paulin [9] and Dybjer[14] 5.1 The set of Boolean values The set of Boolean values is an example of an enumeration set. The values of an enumeration set are exactly the same as the constructors of the set and all constructors yield dioeerent elements. For the Booleans this means ....
Roland Backhouse. On the meaning and construction of the rules in Martin-L#f's theory of types. In Proceedings of the Workshop on General Logic, Edinburgh. Laboratory for the Foundations of Computer Science, University of Edinburgh, February 1987.
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