The geometry of linear higher-order recursion

Abstract

Linearity and ramification constraints have been widely used to weaken higher-order (primitive)

Context semantics, linear logic, and computational complexity

“…The usual measure based on the length of regular paths cannot be used, since there are proof-nets which can be normalized in polynomial time but whose regular paths have exponential length (as we are going to show in the following). Context semantics has been recently exploited by the author in the quantitative analysis of linear lambda calculi with higher-order recursion [4]. Noticeably, context semantics is powerful enough to induce bounds on the algebraic potential size of terms, a parameter which itself bounds normalization time (up to a polynomial overhead).…”

Semantically linear programming languages

“…In other words, linear functions between two coherence spaces are less than stable functions between the same domains. Since the syntactical constraints of S PCF forbid useless duplications of redexes, we are utterly convinced that S PCF can be fruitfully exploited in research fields like optimal evaluation (see for instance [2,31,34]), implicit computational complexity (see for instance [4,5,14]), linear computation (see for instance [1,13]). Further motivations are theoretical.…”

Linearity and recursion in a typed Lambda-calculus

“…Other work that is currently being investigated includes the relationship with calculi for computational complexity. For instance, closed construction in System L gives PR functions [16], but closed construction does not affect Lrec (the encoding of µ is closed).…”

“…In particular, a linear version of Gödel's System T which we call System L captures exactly the class of primitive recursive functions (PR) if iterators use only closed linear functions [16], whereas the same system with a closed reduction strategy [19] has all the computation power of System T [4]. The latter result shows some redundancy regarding duplication in System T , which can be achieved through iteration or through non-linear occurrences of the bound variable in the body of a function.…”