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doi:10.1093/comjnl/bxn029 Enumerating Proofs of Positive Formulae
, 2007
"... We provide a semigrammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This method is complete in the sense that each normal proofterm ..."
Abstract

Cited by 3 (1 self)
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We provide a semigrammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This method is complete in the sense that each normal proofterm of the formula is produced by some scheme generated by the grammar. As a corollary, we get a similar description of the set of normal proofs of positive formulae for a large class of theories including simple type theory and System F.
Counting a Type's Principal Inhabitants
 Fundamenta Informaticae
, 1998
"... We present a Counting Algorithm that computes the number of terms in normal form that have a given type as a principal type and produces a list of these terms. The design of the algorithm follows the lines of BenYelles' algorithm for counting normal (not necessarily principal) inhabitants o ..."
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Cited by 3 (2 self)
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We present a Counting Algorithm that computes the number of terms in normal form that have a given type as a principal type and produces a list of these terms. The design of the algorithm follows the lines of BenYelles' algorithm for counting normal (not necessarily principal) inhabitants of a type . 1 Introduction In [2], BenYelles presented a Counting Algorithm, also described in [3], which given a type computes the number of terms in normal form that can receive type in TA . For each type the algorithm decides in a nite number of steps whether the number of closed normal forms with type is nite or innite, computes this number in the nite case, and lists all relevant terms in both cases. Related to this is the problem of counting the number of normal forms that have a given type as a principal type. As pointed out in ([3], p. 127), this problem is still open and in this paper we present a Counting Algorithm which solves this case. Analogous to BenY...