## A correctness proof for Warren's HO into FO translation (1993)

Venue: | In Proc. GULP' 93 |

Citations: | 12 - 1 self |

### BibTeX

@INPROCEEDINGS{Gonzalez-Moreno93acorrectness,

author = {Juan Carlos Gonzalez-Moreno and Juan Carlos Gonz'alez-moreno},

title = {A correctness proof for Warren's HO into FO translation},

booktitle = {In Proc. GULP' 93},

year = {1993},

pages = {569--585}

}

### Years of Citing Articles

### OpenURL

### Abstract

In [16], Warren suggested a method for embedding higher-order (HO) programming constructs into Prolog, that can be viewed as a kind of higher-order into first-order (FO) translation. This method has been used in different settings as a tool for the combination of functional and logic programming [3, 2, 1], or even for the reduction of the former to the later [4]. The present paper was motivated by our feeling that the semantic correctness of Warren's translation is not yet sufficiently well understood. We give a formulation of the method in the framework of the HO functional logic language SFL [6, 7], which uses conditional narrowing as operational semantics and has also a well defined declarative semantics. We show that HO SFL programs can be translated into FO SFL programs in such a way that both the declarative and the narrowing semantics are preserved. As a consequence, narrowing strategies which are sound and complete for FO SFL programs can be automatically transferred to HO SFL programs, via the translation.

### Citations

346 | An Efficient Unification Algorithm
- Martelli, Montanari
- 1982
(Show Context)
Citation Context ...e that ! C ? can be narrowed to a pair !s, t? of unifiable patterns. We are going to use as notion of most general unifier those dued to Robinson [13] and Martelli and Montanari unification algorithm =-=[12]-=- to unify FO terms. In the case of HO expressions we modify the algorithm to avoid unification of HO variable applications with constructions. This is dued to technical reasons that are not treated in... |

106 |
Kernel Leaf: A Logic plus Functional Language
- Giovannetti, Levi, et al.
(Show Context)
Citation Context ... K, I combinators. In [3, 2] the translation is used to define a semantics for the HO functional-logic language IDEAL by means of the well defined semantics of the FO functional-logic language K-LEAF =-=[10, 11]-=-. In fact, the meaning of any IDEAL program is defined as the meaning of its translation into K-LEAF. More recently [4], recovering the original purpose of Warren, uses the translation to reduce funct... |

21 | On the completeness of narrowing as the operational semantics of functional logic programming
- González-Moreno, Hortalá-González, et al.
- 1992
(Show Context)
Citation Context ...t 0 ffi A t 1 = (t 0 t 1 ), whenever (t 0 t 1 ) is a partial pattern; t 0 ffi A t 1 = ?, whenever (t 0 t 1 ) is neither a partial pattern nor of the form (f s 1 .. s n ), f 2 FS n \Sigma , n ? 0. See =-=[6, 7]-=- for a more precise definition. The collection HCAA Sigma of all Herbrand algebras of signature \Sigma is a Scott domain under the ordering under the ordering v HCAA \Sigma defined by H vHCAA \Sigma H... |

14 |
IDEAL: An Ideal Deductive Applicative Language
- Bosco, Giovannetti
- 1986
(Show Context)
Citation Context ...olog, that can be viewed as a kind of higher-order into first-order (FO) translation. This method has been used in different settings as a tool for the combination of functional and logic programming =-=[3, 2, 1]-=-, or even for the reduction of the former to the later [4]. The present paper was motivated by our feeling that the semantic correctness of Warren's translation is not yet sufficiently well understood... |

7 |
Denotational versus Declarative Semantics for Functional
- Gonz\’alez-Moreno, Hortal\’a-Gonz\’alez, et al.
- 1992
(Show Context)
Citation Context ...our feeling that the semantic correctness of Warren's translation is not yet sufficiently well understood. We give a formulation of the method in the framework of the HO functional logic language SFL =-=[6, 7]-=-, which uses conditional narrowing as operational semantics and has also a well defined declarative semantics. We show that HO SFL programs can be translated into FO SFL programs in such a way that bo... |

5 |
On Warren's Method for Functional Programming
- Cheng, Emden, et al.
- 1990
(Show Context)
Citation Context ...der (FO) translation. This method has been used in different settings as a tool for the combination of functional and logic programming [3, 2, 1], or even for the reduction of the former to the later =-=[4]-=-. The present paper was motivated by our feeling that the semantic correctness of Warren's translation is not yet sufficiently well understood. We give a formulation of the method in the framework of ... |

4 |
C.Moiso, C.Palamidessi: A two-level approach to logic and functional programming
- Bellia, Giovannetti
- 1987
(Show Context)
Citation Context ...olog, that can be viewed as a kind of higher-order into first-order (FO) translation. This method has been used in different settings as a tool for the combination of functional and logic programming =-=[3, 2, 1]-=-, or even for the reduction of the former to the later [4]. The present paper was motivated by our feeling that the semantic correctness of Warren's translation is not yet sufficiently well understood... |

3 | J.B.Wright: On Initial Algebra Semantics and Continuous Algebras - Goguen, Wagner - 1977 |

2 |
E.Giovannetti, C.Moiso: Complete semantic caracterization of K-LEAF, a logic language with partial functions
- Levi, Bosco
- 1987
(Show Context)
Citation Context ... K, I combinators. In [3, 2] the translation is used to define a semantics for the HO functional-logic language IDEAL by means of the well defined semantics of the FO functional-logic language K-LEAF =-=[10, 11]-=-. In fact, the meaning of any IDEAL program is defined as the meaning of its translation into K-LEAF. More recently [4], recovering the original purpose of Warren, uses the translation to reduce funct... |