## Higher-Order Algebra, Logic, and Term Rewriting: First International Workshop, HOA '93, Amsterdam, The Netherlands, September 23 - 24, 1993. Selected PapersThis volume contains the final revised versions of the best papers presented at the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting (HOA '93), held in Amsterdam in September 1993. Higher-Order methods are increasingly applied in functional and logic programming languages, as well as in specification and verification of programs and hardware. The 15 full papers in this volume are devoted to the algebra and model theory of higher-order languages, computational logic techniques including resolution and term rewriting, and specification and verification case studies; in total they provide a competently written overview of current research and suggest new research directions in this vigourous area. |

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### Contents

Interaction Systems | 1 |

Strong Normalization of Typeable Rewrite Systems | 20 |

A Transformation System Combining Partial Evaluation with Term Rewriting | 40 |

Prototyping Relational Specifications Using HigherOrder Objects | 56 |

Origin Tracking for HigherOrder Term Rewriting Systems | 76 |

Theory Interpretation in Simple Type Theory | 96 |

The Semantics of SPECTRUM | 124 |

A TYPED LANGUAGE FOR ALGEBRAIC SPECIFICATION | 146 |

Compilation of Combinatory Reduction Systems | 169 |

A CASE STUDY OF CONVOLUTION | 189 |

Ordered and Continuous Models of HigherOrder Specifications | 223 |

Rewriting Properties of Combinators for Rudimentary Linear Logic | 256 |

Comparing Combinatory Reduction Systems and Higherorder Rewrite Systems | 276 |

Termination Proofs for Higherorder Rewrite Systems | 305 |

Extensions of Initial Models and their SecondOrder Proof Systems | 326 |

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### Common terms and phrases

abstract algebra algorithm application assignment associated axioms bound calculus called closed combinators completion Computer Science condition consider constant construction contains context continuous corresponding CRSs defined Definition denoted derivation described direct domain elements environment equal equational example exists expression extended extensional first-order formula free variables function give given hand higher order higher-order induction initial Interaction interpretation introduced kind language Lemma linear logic means metavariables minimal monotonic natural normal Note notion obtain occurrence operator origins pair partial predicate present proof Proposition prove recursive reduction relation replacement respect restriction result rewrite rules rewrite system satisfies semantics side signature simple sort specification standard step strict structure substitution subterm symbol term termination Theorem theory tion translation University variables