
Types by Need (Extended Version)
A cornerstone of the theory of lambdacalculus is that intersection type...
read it

Factoring Derivation Spaces via Intersection Types (Extended Version)
In typical nonidempotent intersection type systems, proof normalization...
read it

On sets of terms with a given intersection type
We are interested in how much of the structure of a strongly normalizabl...
read it

Modular Termination for SecondOrder Computation Rules and Application to Algebraic Effect Handlers
We present a new modular proof method of termination for secondorder co...
read it

Intersection Types for Unboundedness Problems
Intersection types have been originally developed as an extension of sim...
read it

On Probabilistic Term Rewriting
We study the termination problem for probabilistic term rewrite systems....
read it

From Linear Term Rewriting to Graph Rewriting with Preservation of Termination
Encodings of term rewriting systems (TRSs) into graph rewriting systems ...
read it
Intersection Types and (Positive) AlmostSure Termination
Randomized higherorder computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of obtaining any given result, rather than the possibility or the necessity of obtaining it, like in (non)deterministic computation. Termination, arguably the simplest kind of reachability problem, can be spelled out in at least two ways, depending on whether it talks about the probability of convergence or about the expected evaluation time, the second one providing a stronger guarantee. In this paper, we show that intersection types are capable of precisely characterizing both notions of termination inside a single system of types: the probability of convergence of any lambdaterm can be underapproximated by its type, while the underlying derivation's weight gives a lower bound to the term's expected number of steps to normal form. Noticeably, both approximations are tight – not only soundness but also completeness holds. The crucial ingredient is nonidempotency, without which it would be impossible to reason on the expected number of reduction steps which are necessary to completely evaluate any term. Besides, the kind of approximation we obtain is proved to be optimal recursion theoretically: no recursively enumerable formal system can do better than that.
READ FULL TEXT
Comments
There are no comments yet.