Related papers: On counting untyped lambda terms
Infinite types and formulas are known to have really curious and unsound behaviors. For instance, they allow to type {\Omega}, the auto- autoapplication and they thus do not ensure any form of normalization/productivity. Moreover, in most…
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating…
In various situations one is given only the predictions of multiple classifiers over a large unlabeled test data. This scenario raises the following questions: Without any labeled data and without any a-priori knowledge about the…
We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…
As a consequence of identifying the principle described in the title, we prove that for any uncountable cardinal lambda, if there is a lambda-free Whitehead group of cardinality lambda which is not free, then there are many ``nice''…
We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
We study the number of non-zero terms in two specific families of ternary cyclotomic polynomial, we find formulas for the number of terms by writing the cyclotomic polynomial as a sum of smaller sub-polynomials and study the properties of…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
Word embedding, specially with its recent developments, promises a quantification of the similarity between terms. However, it is not clear to which extent this similarity value can be genuinely meaningful and useful for subsequent tasks.…
The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed $\lambda$-calculus, i.e. to solve the equation a = b where a and b are simply typed $\lambda$-terms and b is…
We propose an efficient method to estimate the accuracy of classifiers using only unlabeled data. We consider a setting with multiple classification problems where the target classes may be tied together through logical constraints. For…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.