## Data Types, Infinity and Equality in System AF2 (1995)

Venue: | In CSL ’93, volume 832 of LNCS |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Raffalli95datatypes,,

author = {Christophe Raffalli},

title = {Data Types, Infinity and Equality in System AF2},

booktitle = {In CSL ’93, volume 832 of LNCS},

year = {1995},

pages = {280--294},

publisher = {Springer}

}

### OpenURL

### Abstract

This work presents an extension of system AF 2 to allow the use of infinite data types. We extend the logic with inductive and coinductive types, and show that the "programming method" is still correct. Unlike previous work in other type-systems, we only use the pure -calculus. Propositions about normalization and unicity of the representation of data have no equivalent in other systems. Moreover, the class of data types we consider is very large with some unusual ones. 1 Introduction Since the work of Curry, a lot of type-systems have been created (e.g., De Bruijn's Automath [4]; Girard's system F [5]; Martin-Lof's type theory [10]; Coquand-Huet's Calculus of construction [3]; etc). One of their purposes is program extraction via the CurryHoward isomorphism [6], which establishes a correspondence between programs and proofs of specifications. One of these systems is AF 2 (second order functional arithmetic) due to Leivant and Krivine [9, 7, 8]. It uses equations as algorithmic specif...

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Citation Context ...duction Since the work of Curry, a lot of type-systems have been created (e.g., De Bruijn's Automath [4]; Girard's system F [5]; Martin-Lof's type theory [10]; Coquand-Huet's Calculus of construction =-=[3]-=-; etc). One of their purposes is program extraction via the CurryHoward isomorphism [6], which establishes a correspondence between programs and proofs of specifications. One of these systems is AF 2 ... |

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Citation Context ...ystems. Moreover, the class of data types we consider is very large with some unusual ones. 1 Introduction Since the work of Curry, a lot of type-systems have been created (e.g., De Bruijn's Automath =-=[4]-=-; Girard's system F [5]; Martin-Lof's type theory [10]; Coquand-Huet's Calculus of construction [3]; etc). One of their purposes is program extraction via the CurryHoward isomorphism [6], which establ... |

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Citation Context ...still correct. The particulars of this work come from those of AF 2 , including data types encoded in pure -calculus, equational axioms, and second order logic. Moreover, in most of the previous work =-=[11, 13, 15]-=-, infinite data types are added through a categorical duality, 1 defined by their destructors (except for [15]), and use the coinduction principle. In our work, finite and infinite data types are adde... |

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Citation Context ...yHoward isomorphism [6], which establishes a correspondence between programs and proofs of specifications. One of these systems is AF 2 (second order functional arithmetic) due to Leivant and Krivine =-=[9, 7, 8]. It uses -=-equations as algorithmic specifications, and its "programming method" ensures the correctness of programs extracted from proofs of function totality. However, the efficiency of these extract... |

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Citation Context ...jn's Automath [4]; Girard's system F [5]; Martin-Lof's type theory [10]; Coquand-Huet's Calculus of construction [3]; etc). One of their purposes is program extraction via the CurryHoward isomorphism =-=[6]-=-, which establishes a correspondence between programs and proofs of specifications. One of these systems is AF 2 (second order functional arithmetic) due to Leivant and Krivine [9, 7, 8]. It uses equa... |

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Citation Context ... is very large with some unusual ones. 1 Introduction Since the work of Curry, a lot of type-systems have been created (e.g., De Bruijn's Automath [4]; Girard's system F [5]; Martin-Lof's type theory =-=[10]-=-; Coquand-Huet's Calculus of construction [3]; etc). One of their purposes is program extraction via the CurryHoward isomorphism [6], which establishes a correspondence between programs and proofs of ... |

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Citation Context ...still correct. The particulars of this work come from those of AF 2 , including data types encoded in pure -calculus, equational axioms, and second order logic. Moreover, in most of the previous work =-=[11, 13, 15]-=-, infinite data types are added through a categorical duality, 1 defined by their destructors (except for [15]), and use the coinduction principle. In our work, finite and infinite data types are adde... |

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Citation Context ...still correct. The particulars of this work come from those of AF 2 , including data types encoded in pure -calculus, equational axioms, and second order logic. Moreover, in most of the previous work =-=[11, 13, 15]-=-, infinite data types are added through a categorical duality, 1 defined by their destructors (except for [15]), and use the coinduction principle. In our work, finite and infinite data types are adde... |

1 | Le syst`eme AF 2 avec points fixes - Raffalli - 1994 |