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On proving the correctness of program transformations based on free theorems for higher-order polymorphic calculi

PATRICIA JOHANN
2005 Mathematical Structures in Computer Science  
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doi:10.1017/s0960129504004578 fatcat:rzo52ydjwfflzfersxd2y3rwvu

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
The Journal of Functional Programming would like to change that!  ...  The abstracts are made freely available on the JFP website, i.e. not behind any paywall, and do not require any transfer for copyright, merely a license from the author.  ...  The latter investigation exemplifies the main application of our theory: free theorems may not only ensure semantic correctness of program transformations, they may also ensure that a program transformation  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

Page 4858 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
in languages supporting higher-order polymorphic functions and fixpoint recursion.  ...  We use this specification to prove the correctness of a lambda lifting algorithm similar to the one pro- posed by Johnsson.  ... 

Short Cut Fusion: Proved and Improved [chapter]

Patricia Johann
2001 Lecture Notes in Computer Science  
Arguments that short cut fusion is correct typically appeal either to intuition or to "free theorems" -even though the latter have not been known to hold for the languages supporting higher-order polymorphic  ...  Together with the well-known generalization cata of foldr to arbitrary algebraic data types, this allows us to formulate and prove correct for each a contextual equivalence-preserving cata-augment fusion  ...  I am grateful to Olaf Chitil, Graham Hutton, and Andrew Pitts for helpful discussions on the topic of this paper. I also thank the volume  ... 
doi:10.1007/3-540-44806-3_4 fatcat:qa7f2ults5d7xgl5niuphnhus4

Programming and Proving with Classical Types [chapter]

Cristina Matache, Victor B. F. Gomes, Dominic P. Mulligan
2017 Lecture Notes in Computer Science  
In this work, we use the λµ-calculus as the foundation for a system of proof terms for classical first-order logic.  ...  We extend the language with polymorphic types, add a host of data types in 'direct style', and prove several metatheoretical properties.  ...  Gomes and Mulligan acknowledge funding from EPSRC grant EP/K008528 ('REMS: Rigorous Engineering for Mainstream Systems'). We thank the anonymous referees and Peter Sewell for their helpful comments.  ... 
doi:10.1007/978-3-319-71237-6_11 fatcat:2dz6qias4vbmpp3qggznclk3ee

A Two-Valued Logic for Properties of Strict Functional Programs Allowing Partial Functions

David Sabel, Manfred Schmidt-Schauß
2012 Journal of automated reasoning  
The semantics is based on a contextual (observational) semantics, which gives a consistent presentation of higher-order functions.  ...  Our analysis also sheds new light on the the role of partial functions and loose specifications. It is also an analysis of influence of extensions of programs on the tautologies.  ...  We thank Peter Schauß for discussions on proof traces of VeriFun. We also thank the anonymous referees for remarks that improved the paper.  ... 
doi:10.1007/s10817-012-9253-6 fatcat:juyveq7eabel7ktibjmhpzgkrq

Integrating Automated and Interactive Theorem Proving [chapter]

Ahrendt, Beckert, Hähnle, Menzel, Reif, Schellhorn, Schmitt
1998 Applied Logic Series  
For a discussion of some of the issues that have to be solved for higher-order logic (polymorphism, currying, problems arising from the identification of boolean terms with formulas) see (Archer et al  ...  Such orders are used in many refinements of calculi in theorem proving, hence our results are of general interest.  ... 
doi:10.1007/978-94-017-0435-9_4 fatcat:nsfxar65jbhybcrsdvi2stys6u

Extending Abramsky's Lazy Lambda Calculus: (Non)-Conservativity of Embeddings

Manfred Schmidt-Schauß, Elena Machkasova, David Sabel, Marc Herbstritt
2013 International Conference on Rewriting Techniques and Applications  
In addition to untyped calculi, we study their monomorphically and polymorphically typed versions. For most of the extensions we obtain non-conservativity which we prove by providing counterexamples.  ...  are an adequate model for semantic equivalences in real-world purely functional programming languages, in particular for a pure core language of Haskell.  ...  We now show correctness of program transformations.  ... 
doi:10.4230/lipics.rta.2013.239 dblp:conf/rta/Schmidt-SchaussMS13 fatcat:73fcc2qtcngmlneqa2eo62bvia

Some aspects of categories in computer science [chapter]

P.J. Scott
2000 Handbook of Algebra  
He developed formal calculi of variable types, the so-called polymorphic lambda calculi, which correspond to proofs in higher-order logics.  ...  Thus inductive proof techniques based on the complexity of subformulas are not available in higher-order logic. This is the essence of the problem of impredicativity in polymorphism.  ...  (iii) Although Manes and Arbib use the Limit Axiom to prove existence of Elgot-style iteration (see below), Kuro s did not have it. And for many aspects of the theory below, it is not needed.  ... 
doi:10.1016/s1570-7954(00)80027-3 fatcat:oeaqbcqgzjhuzl2ddangzergr4

A General Framework For Lazy Functional Logic Programming With Algebraic Polymorphic Types [article]

Puri Arenas-Sanchez, Mario Rodriguez-Artalejo
2004 arXiv   pre-print
On top of a given C, we specify a program as a set R of C-based conditional rewriting rules for defined functions.  ...  We get soundness and completeness for C-based rewriting w.r.t. models, existence of free models for all programs, and type preservation results.  ...  Acknowledgments: The authors are indebted to their colleagues A. Gil-Luezas and F.J. López-Fraguas for their support to the development of this work.  ... 
arXiv:cs/0404050v1 fatcat:b6gy7hhesjevfiv5bv4udmm3rm

Introduction [chapter]

Bernhard Möller, Helmut A. Partsch, Stephen A. Schuman
1993 Lecture Notes in Computer Science  
BIRD/DE MOOR introduce a calculus based on a categorical setting and involving relational concepts and the theory of free inductive data types.  ...  ., the speed and storage costs of higher-order functions and the lack of selective updating. It has been used to derive a large number of realistic programs, several of which are in everyday use.  ...  The KIDS system provides knowledge-based support for the derivation of correct and efficient programs from specifications.  ... 
doi:10.1007/3-540-57499-9_14 fatcat:eztaayoch5crzf76amxx6q7r3i

On the Versatility of Open Logical Relations [chapter]

Gilles Barthe, Raphaëlle Crubillé, Ugo Dal Lago, Francesco Gavazzo
2020 Lecture Notes in Computer Science  
Logical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi.  ...  However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued  ...  Introduction Logical relations have been extremely successful as a way of proving equivalence between concrete programs as well as correctness of program transformations.  ... 
doi:10.1007/978-3-030-44914-8_3 fatcat:k6qdai3k5vdkrnhayohebr6ygi

Free theorems in the presence of seq

Patricia Johann, Janis Voigtländer
2004 Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '04  
We use these results to derive criteria ensuring that both equational and inequational versions of short cut fusion and related program transformations based on free theorems hold in the presence of seq  ...  Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free.  ...  Acknowledgments We would like to thank the anonymous referees for their useful suggestions regarding the presentation of the paper.  ... 
doi:10.1145/964001.964010 dblp:conf/popl/JohannV04 fatcat:rfmupwerljgrzluvumyt2in3km

Free theorems in the presence of seq

Patricia Johann, Janis Voigtländer
2004 SIGPLAN notices  
We use these results to derive criteria ensuring that both equational and inequational versions of short cut fusion and related program transformations based on free theorems hold in the presence of seq  ...  Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free.  ...  Acknowledgments We would like to thank the anonymous referees for their useful suggestions regarding the presentation of the paper.  ... 
doi:10.1145/982962.964010 fatcat:st2ill6zkjdrhgcr7lniyriapq

Concatenate, reverse and map vanish for free

Janis Voigtländer
2002 SIGPLAN notices  
The correctness of transformations is proved by using the free theorems derivable from parametric polymorphic types.  ...  The general idea is to uniformly abstract from data constructors and manipulating operations by means of rank-2 polymorphic combinators that exploit algebraic properties of these operations to provide  ...  of such models for lambda calculi with higher-order polymorphic functions and fixpoint recursion justifies this assumption.  ... 
doi:10.1145/583852.581481 fatcat:4edosbwk5jakjbn6i4sgqlcavq
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