Refine
Year of publication
- 2018 (3) (remove)
Document Type
- Working Paper (3) (remove)
Language
- English (3) (remove)
Has Fulltext
- yes (3)
Is part of the Bibliography
- no (3)
Keywords
- automated deduction (1)
- contextual equivalence (1)
- correctness (1)
- deduction (1)
- functional programming (1)
- lambda calculus (1)
- nominal unification (1)
- observational equivalence (1)
- program transformation (1)
- semantics (1)
Institute
- Informatik (3) (remove)
Our recently developed LRSX Tool implements a technique to automatically prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program transformation is correct if it preserves the observational semantics of programs- In our tool the so-called diagram method is automated by combining unification, matching, and reasoning on alpha-renamings on the higher-order metalanguage, and automating induction proofs via an encoding into termination problems of term rewrite systems. We explain the techniques, we illustrate the usage of the tool, and we report on experiments.
Automated deduction in higher-order program calculi, where properties of transformation rules are demanded, or confluence or other equational properties are requested, can often be done by syntactically computing overlaps (critical pairs) of reduction rules and transformation rules. Since higher-order calculi have alpha-equivalence as fundamental equivalence, the reasoning procedure must deal with it. We define ASD1-unification problems, which are higher-order equational unification problems employing variables for atoms, expressions and contexts, with additional distinct-variable constraints, and which have to be solved w.r.t. alpha-equivalence. Our proposal is to extend nominal unification to solve these unification problems. We succeeded in constructing the nominal unification algorithm NomUnifyASC. We show that NomUnifyASC is sound and complete for these problem class, and outputs a set of unifiers with constraints in nondeterministic polynomial time if the final constraints are satisfiable. We also show that solvability of the output constraints can be decided in NEXPTIME, and for a fixed number of context-variables in NP time. For terms without context-variables and atom-variables, NomUnifyASC runs in polynomial time, is unitary, and extends the classical problem by permitting distinct-variable constraints.
1998 ACM Subject Classification F.4.1 Mathematical Logic
We explore space improvements in LRP, a polymorphically typed call-by-need functional core language. A relaxed space measure is chosen for the maximal size usage during an evaluation. It Abstracts from the details of the implementation via abstract machines, but it takes garbage collection into account and thus can be seen as a realistic approximation of space usage. The results are: a context lemma for space improving translations and for space equivalences; all but one reduction rule of the calculus are shown to be space improvements, and the exceptional one, the copy-rule, is shown to increase space only moderately.
Several further program transformations are shown to be space improvements or space equivalences, in particular the translation into machine expressions is a space equivalence. These results are a step Forward in making predictions about the change in runtime space behavior of optimizing transformations in callbyneed functional languages.