### Abstract

We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the expression's evaluation derivation in a standard big-step operational semantics. The latter is a measure of the "future" cost of using the value of that expression. A translation function maps target expressions to complexities. Our main result is the following Soundness Theorem: If t is a term in the target language, then the cost component of ktk is an upper bound on the cost of evaluating t. The proof of the Soundness Theorem is formalized in Coq, providing certified upper bounds on the cost of any expression in the target language.

Original language | English (US) |
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Title of host publication | PLPV 2013 - Proceedings of the 2013 ACM SIGPLAN Workshop on Programming Languages Meets Program Verification, Co-located with POPL 2013 |

Pages | 25-34 |

Number of pages | 10 |

DOIs | |

State | Published - 2013 |

Event | 2013 7th ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, PEPM 2013 - Co-located with POPL 2013 - Rome, Italy Duration: Jan 22 2013 → Jan 22 2013 |

### Publication series

Name | PLPV 2013 - Proceedings of the 2013 ACM SIGPLAN Workshop on Programming Languages Meets Program Verification, Co-located with POPL 2013 |
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### Other

Other | 2013 7th ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, PEPM 2013 - Co-located with POPL 2013 |
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Country | Italy |

City | Rome |

Period | 1/22/13 → 1/22/13 |

### Keywords

- Automated theorem proving
- Certified bounds
- Higher-order complexity

### ASJC Scopus subject areas

- Software

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## Cite this

*PLPV 2013 - Proceedings of the 2013 ACM SIGPLAN Workshop on Programming Languages Meets Program Verification, Co-located with POPL 2013*(pp. 25-34). (PLPV 2013 - Proceedings of the 2013 ACM SIGPLAN Workshop on Programming Languages Meets Program Verification, Co-located with POPL 2013). https://doi.org/10.1145/2428116.2428123