### Abstract

We investigate the possibility of a semantic account of the execution time (i.e. the number of β_{v}-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin’s call-by-value λ-calculus. For this purpose, we use a linear logic based denotational model that can be seen as a non-idempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name λ-calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name λ-calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

Original language | English |
---|---|

Pages (from-to) | 57-72 |

Number of pages | 16 |

Journal | Electronic Proceedings in Theoretical Computer Science, EPTCS |

Volume | 293 |

DOIs | |

Publication status | Published - 2019 |

Event | 12th Workshop on Developments in Computational Models, DCM 2018 and 9th Workshop on Intersection Types and Related Systems, ITRS 2018 - Oxford, UK United Kingdom Duration: 8 Jul 2018 → 8 Jul 2018 |

### ASJC Scopus subject areas

- Software

### Cite this

**Towards a semantic measure of the execution time in call-by-value lambda-calculus.** / Guerrieri, Giulio.

Research output: Contribution to journal › Conference article

}

TY - JOUR

T1 - Towards a semantic measure of the execution time in call-by-value lambda-calculus

AU - Guerrieri, Giulio

PY - 2019

Y1 - 2019

N2 - We investigate the possibility of a semantic account of the execution time (i.e. the number of βv-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin’s call-by-value λ-calculus. For this purpose, we use a linear logic based denotational model that can be seen as a non-idempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name λ-calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name λ-calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

AB - We investigate the possibility of a semantic account of the execution time (i.e. the number of βv-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin’s call-by-value λ-calculus. For this purpose, we use a linear logic based denotational model that can be seen as a non-idempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name λ-calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name λ-calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

UR - http://www.scopus.com/inward/record.url?scp=85066074836&partnerID=8YFLogxK

U2 - 10.4204/EPTCS.293.5

DO - 10.4204/EPTCS.293.5

M3 - Conference article

VL - 293

SP - 57

EP - 72

JO - Electronic Proceedings in Theoretical Computer Science

JF - Electronic Proceedings in Theoretical Computer Science

SN - 2075-2180

ER -