DeepAI AI Chat
Log In Sign Up

Non-idempotent types for classical calculi in natural deduction style

by   Delia Kesner, et al.

In the first part of this paper, we define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments --based on decreasing measures of type derivations-- to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the lengths of the head-reduction and the maximal reduction sequences to normal-form. In the second part of this paper, the λμ-calculus is refined to a resource aware interpretation called λμr, which is inspired by the substitution at a distance paradigm. The small-step λμr-calculus turns out to be compatible with a natural extension of the non-idempotent interpretations of λμ, i.e. λμr-reduction preserves and decreases typing derivations in an extended appropriate typing system. We thus derive a simple arithmetical characterization of strongly λμr-normalizing terms by means of typing.


page 1

page 2

page 3

page 4


A Quantitative Understanding of Pattern Matching

This paper shows that the recent approach to quantitative typing systems...

Sequence Types and Infinitary Semantics

We introduce a new representation of non-idempotent intersection types, ...

Two Decreasing Measures for Simply Typed Lambda-Terms (Extended Version)

This paper defines two decreasing measures for terms of the simply typed...

Observability = Typability + Inhabitation

We define an observability property for a calculus with pattern matching...

The Bang Calculus Revisited

Call-by-Push-Value (CBPV) is a programming paradigm subsuming both Call-...

Intersection Type Distributors

Building on previous works, we present a general method to define proof ...

Call-by-need, neededness and all that

We show that call-by-need is observationally equivalent to weak-head nee...