# A Resource Aware Computational Interpretation for Herbelin's Syntax

@inproceedings{Kesner2015ARA, title={A Resource Aware Computational Interpretation for Herbelin's Syntax}, author={Delia Kesner and Daniel Lima Ventura}, booktitle={ICTAC}, year={2015} }

We investigate a new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics. For that, we associate to Herbelin's syntax a type system based on non-idempotent intersection types, together with a set of reduction rules ---inspired from the substitution at a distance paradigm--- that preserves and decreases the size of typing derivations. The non-idempotent approach allows us to use very simple combinatorial arguments, only…

## 13 Citations

### A resource aware semantics for a focused intuitionistic calculus

- Computer ScienceMathematical Structures in Computer Science
- 2017

A new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics is investigated and a type system based on non-idempotent intersection types is associated to Herbelin's syntax.

### 32 : 2 Types as Resources for Classical Natural Deduction

- Mathematics
- 2017

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…

### Types as Resources for Classical Natural Deduction

- MathematicsFSCD
- 2017

Two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types are defined and typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences.

### Non-idempotent types for classical calculi in natural deduction style

- MathematicsLog. Methods Comput. Sci.
- 2020

A simple arithmetical characterization of strongly $\lambda\mu$r-normalizing terms by means of typing is derived, which preserves and decreases typing derivations in an extended appropriate typing system.

### Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

- Computer ScienceDCM/ITRS
- 2018

This work investigates the possibility of a semantic account of the execution time for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus, using a linear logic based denotational model that can be seen as a non-idempotent intersection type system: relational semantics.

### Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus (Long Version)

- Computer Science
- 2018

This work investigates the possibility of a semantic account of the execution time for the shuffling calculus, an extension of Plotkin’s call-by-value λ -calculus, using a linear logic based denotational model that can be seen as a nonidempotent intersection type system: relational semantics.

### A Quantitative Understanding of Pattern Matching

- Computer ScienceTYPES
- 2019

This paper shows that the recent approach to quantitative typing systems for programming languages can be extended to pattern matching features. Indeed, we define two resource aware type systems,…

### Tight typings and split bounds

- Computer ScienceProc. ACM Program. Lang.
- 2018

The two main novelties are exact split bounds for the leftmost strategy—the only known strategy that evaluates terms to full normal forms and provides a reasonable complexity measure—and the observation that the computing device hidden behind multi types is the notion of substitution at a distance, as implemented by the linear substitution calculus.

### Tight typings and split bounds, fully developed

- Computer ScienceJournal of Functional Programming
- 2020

This work unifies de Carvalho and Bernadet & Graham-Lengrand via a uniform technique and a complexity-based perspective and provides exact bounds for four evaluation strategies, both in the λ-calculus (head, leftmost-outermost, and maximal evaluation) and in the linear substitution calculus (linear head evaluation).

## References

SHOWING 1-10 OF 54 REFERENCES

### Quantitative Types for Intuitionistic Calculi

- Mathematics
- 2014

We define quantitative type systems for two intuitionistic term languages. While the first language in natural deduction style is already known in the literature, the second one is one of the…

### Strong Normalization of Herbelin's Explicit Substitution Calculus with Substitution Propagation

- MathematicsJ. Log. Comput.
- 2003

This paper proves the implicit conjecture that the addition of a cut permutation rule breaks the proof of strong normalization, thus showing how to model beta-reduction in Herbelin's calculus (extended with rules to allow cut permutations).

### Quantitative Types for the Linear Substitution Calculus

- Computer Science, MathematicsIFIP TCS
- 2014

We define two non-idempotent intersection type systems for the linear substitution calculus, a calculus with partial substitutions acting at a distance that is a computational interpretation of…

### An elementary proof of strong normalization for intersection types

- Mathematics, Computer ScienceArch. Math. Log.
- 2001

A new and elementary proof of strong normalization for the lambda calculus of intersection types is provided, and it is shown that not only the set of strongly normalizing terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize theSet of weakly normalization terms.

### Solvability in Resource Lambda-Calculus

- Computer ScienceFoSSaCS
- 2010

This work defines a term solvable whenever there is a simple head context reducing the term into a sum where at least one addend is the identity, and gives a syntactical, operational and logical characterization of this kind of solvability.

### A Filter Lambda Model and the Completeness of Type Assignment

- PhilosophyJ. Symb. Log.
- 1983

In [6, p. 317] Curry described a formal system assigning types to terms of the type-free λ-calculus. In [11] Scott gave a natural semantics for this type assignment and asked whether a completeness…

### Characterising Strongly Normalising Intuitionistic Terms

- MathematicsFundam. Informaticae
- 2012

A characterisation, via intersection types, of the strongly normalising proof-terms of an intuitionistic sequent calculus where LJ easily embeds, and explains why the type systems in the natural deduction format for ΛJ and λx known from the literature contain extra, exceptional rules for typing generalised application or substitution.

### Non-idempotent intersection types and strong normalisation

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2013

A typing system with non-idempotent intersection types, typing a term syntax covering three different calculi, and the instance based on filters is shown to be better at proving strong normalisation results for {\ lambda}S and {\lambda}lxr.

### Intersection Types for the Resource Control Lambda Calculi

- MathematicsICTAC
- 2011

It is proved that typability implies strong normalisation in λ® by adapting the reducibility method and that strongnormalisation implies typability in both systems using head subject expansion.