Technical report Frank / JohannWolfgangGoetheUniversität, Fachbereich Informatik und Mathematik, Institut für Informatik
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Computing overlappings by unification in the deterministic lambda calculus LR with letrec, case, constructors, seq and variable chains
(2011)

Conrad Rau
Manfred SchmidtSchauß
 Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules.The method is similar to the computation of critical pairs for the completion of term rewriting systems. We describe an effective unification algorithm to determine all overlaps of transformations with reduction rules for the lambda calculus LR which comprises a recursive letexpressions, constructor applications, case expressions and a seq construct for strict evaluation. The unification algorithm employs manysorted terms, the equational theory of leftcommutativity modeling multisets, context variables of different kinds and a mechanism for compactly representing binding chains in recursive letexpressions. As a result the algorithm computes a finite set of overlappings for the reduction rules of the calculus LR that serve as a starting point to the automatization of the analysis of program transformations.