Matching with multiplication and exponentiation (extended abstract)

  title={Matching with multiplication and exponentiation (extended abstract)},
  author={Bernard Lang},
  journal={Mathematical Structures in Computer Science},
  pages={959 - 968}
  • Bernard Lang
  • Published 1 October 2005
  • Mathematics
  • Mathematical Structures in Computer Science
We develop a matching algorithm for an equational theory with multiplication, exponentiation and a unit element. The algorithm is proved consistent, complete and minimal using techniques based on initial algebras. 


A Complete Unification Algorithm for Associative-Commutative Functions
An algorithm which unifies terms whose function is associativa and commutative is presented here and returns a complete set of unifiers without recourse to the indefinite generation of vurianU and instances of the terms being unified required by previous solutions to the problem.
Linear unification
A unification algorithm is described which tests a set of expressions for unifiability and which requires time and space which are only linear in the size of the input.
A Unification Algorithm for Typed lambda-Calculus
  • G. Huet
  • Computer Science
    Theor. Comput. Sci.
  • 1975
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
An approach is presented for taking advantage of the structure of some special theories with simplifiers, commutativity, and associativity, which are valuable concepts to build in by means of a “natural” notation and/or new inference rules.
Proving and applying program transformations expressed with second-order patterns
A complete second-order matching algorithm is presented that allows effective use of these rules and it is shown how to formally prove the correctness of the rules using a denotational semantics for the programming language.
Unification of Idempotent Functions
The main results are that the unification problem for idempotence is decidable, and the set of all uni-fiers is finite, but not a singleton in general.
A Machine-Oriented Logic Based on the Resolution Principle
The paper concludes with a discussion of several principles which are applicable to the design of efficient proof-procedures employing resolution as the basle logical process.
A system which automatically improves programs
Methods of mechanically converting programs that are easy to understand into more efficient ones, converting recursion equations using high level operations into lower level flowchart programs are given.
Building - in equational theories
  • 1972
String unification. Essex University Memo CSM-7
  • Slagle, J. R
  • 1975