Martin-L of, P. 1975. An intuitionistic theory of types: Predicative part. In Proceedings of the Logic Colloquium, 1973. Studies in Logic and the Foundations of Mathematics, vol. 80. North-Holland, 73--118.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are convertible by computing their normal forms and comparing them. This approach bypasses the traditional notion of reduction, formalized as a binary relation, and is therefore sometimes referred to as reduction free normalization . Normalization by evaluation was invented by Martin L of [ML75b] In the original presentation it just appears as a special way of presenting an ordinary normalization proof. Instead of proving that every term has a normal form, one writes a function which returns the normal form, together with a proof that it actually is a normal form. This way of writing a ....

....( meta language: hence normalization by evaluation . If instead we work in a classical meta language, then some extra work would be needed to implement the meta language function in a programming language. Martin L of s early work on NBE dealt with normalization for intuitionistic type theory [ML75b] This version of type theory had a weak notion of reduction, where no reduction under the sign was allowed. This kind of reduction is closely related to reduction of terms in combinatory logic, and we shall present this case in Section 2. Normalization by evaluation for typed lambda calculus ....

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Per Martin-Lof. An intuitionistic theory of types: Predicative part. In H. E. Rose and J. C. Shepherdson, editors, Logic Colloquium `73, pages 73-118. North-Holland, 1975.

....: U i depends on the arguments a of C. Indexed inductive de nitions (IID) subsume inductively de ned relations, such as the identity relation understood as the least re exive relation. The identity relation was indeed the only example of an IID in the early versions of Martin L of type theory [13]. Theoretically, this is not very limiting since one can de ne many other families of sets (predicates) using the identity together with the other set formers of type theory. But from a more practical point of view it became desirable to extend Martin L of type theory with a general notion of ....

P. Martin-Lof. An intuitionistic theory of types: Predicative part. In H. E. Rose and J. C. Shepherdson, editors, Logic Colloquium `73, pages 73-118. North-Holland, 1975.

....inherits types from the parame ters, it is necessary to change the sense of the quantification and universally quantify the shared type variable over the functional type of the module. These ideas are closely related to the dependent type structures of Per Martin L6f s intuitionistic type theory [MAR75], and recent work by John Mitchell, Gordon Plotkin, and the author to explain type abstraction in terms of the quantification theory of types. 5. Conclusion The design described here is the latest in a long series of approximations to the ideal of a module facility that is an organic ....

P. Martin-L6f, An intuitionistic theory of types: predicative part, Logic Colloquium 73, ed. H. E. Rose and J. C. Shepherdson, North-Holland, Amsterdam, 1975, pp. 73-118.

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P. Martin-Lof. An intuitionistic theory of types: predicative part. In H.E. Rose and J. Shepherdson, editors, logic Colloquium '73. North Holland, 1975.

No context found.

Martin-L of, P. 1975. An intuitionistic theory of types: Predicative part. In Proceedings of the Logic Colloquium, 1973. Studies in Logic and the Foundations of Mathematics, vol. 80. North-Holland, 73--118.

No context found.

P. Martin-L of. An intuitionistic theory of types: Predicative part. In H. Rose and J. Shepherdson, editors, Logic Colloquium. Elsevier, 1975.

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