منابع مشابه
Formal neighbourhoods, combinatory Böhm trees, and untyped normalization by evaluation
We prove the correctness of an algorithm for normalizing untyped combinator terms by evaluation. The algorithm is written in the functional programming language Haskell, and we prove that it lazily computes the combinatory Böhm tree of the term. The notion of combinatory Böhm tree is analogous to the usual notion of Böhm tree for the untyped lambda calculus. It is defined operationally by repea...
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We show the existence of an infinitary confluent and normalising extension of the finite extensional lambda calculus with beta and eta. Besides infinite beta reductions also infinite eta reductions are possible in this extension, and terms without head normal form can be reduced to bottom. As corollaries we obtain a simple, syntax based construction of an extensional Böhm model of the finite la...
متن کاملNormalization by evaluation with typed abstract syntax
We present a simple way to implement typed abstract syntax for the lambda calculus in Haskell, using phantom types, and we specify normalization by evaluation (i.e., type-directed partial evaluation) to yield this typed abstract syntax. Proving that normalization by evaluation preserves types and yields normal forms then reduces to type-checking the specification.
متن کاملRegular Böhm trees
Böhm trees are the natural infinite generalisations of normal forms in pure λ-calculus. They arose from the work of Böhm on separability (Böhm 1968), and were first identified by Barendregt, who devotes chapter 10 of his book (Barendregt 1980) to their study, and relates denotational models such as D∞ to appropriate quotients over Böhm trees. There is however no generally agreed presentation of...
متن کاملComputing with Böhm Trees
This paper develops a general technique to analyze the head reduction of a term in a context. This technique is used to give a direct proof of the theorem of Hyland and Wadsworth : two -terms that have the same Böhm trees, up to (possibly infinite) -equivalence, are operationally equivalent. It is also used to prove a conjecture of R. Kerth : Every unsolvable -term has a decoration. This syntac...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2002
ISSN: 1571-0661
DOI: 10.1016/s1571-0661(04)80603-0