Verification of Ptime Reducibility for System F Terms Via Dual Light Affine Logic

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BT04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial time and all Ptime functions can be represented. In the present work we address the problem of typing lambda-terms in second-order DLAL. For that we give a procedure which, starting with a term typed in system F, finds all possible ways to decorate it into a DLAL typed term. We show that our procedure can be run in time polynomial in the size of the original Church typed system F term.

[1]  Stephen A. Cook,et al.  A new recursion-theoretic characterization of the polytime functions , 1992, STOC '92.

[2]  Paolo Coppola,et al.  Typing Lambda Terms in Elementary Logic with Linear Constraints , 2001, TLCA.

[3]  Ugo Dal Lago,et al.  Elementary Affine Logic and the Call-by-Value Lambda Calculus , 2005, TLCA.

[4]  Daniel Leivant,et al.  Lambda Calculus Characterizations of Poly-Time , 1993, Fundam. Informaticae.

[5]  Vincent Danos,et al.  Linear logic and elementary time , 2003, Inf. Comput..

[6]  Martin Hofmann,et al.  Linear types and non-size-increasing polynomial time computation , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[7]  Kazushige Terui,et al.  Light affine lambda calculus and polytime strong normalization , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[8]  Joe B. Wells,et al.  Typability and Type Checking in System F are Equivalent and Undecidable , 1999, Ann. Pure Appl. Log..

[9]  Andrea Asperti,et al.  Intuitionistic Light Affine Logic , 2002, TOCL.

[10]  Patrick Baillot.  Type inference for light affine logic via constraints on words , 2004, Theor. Comput. Sci..

[11]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .

[12]  Jean-Yves Girard,et al.  Light Linear Logic , 1998, Inf. Comput..

[13]  Kazushige Terui,et al.  Light types for polynomial time computation in lambda-calculus , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[14]  Kazushige Terui.  Light Affine Set Theory: A Naive Set Theory of Polynomial Time , 2004, Stud Logica.

[15]  Jean-Yves Marion,et al.  Efficient First Order Functional Program Interpreter with Time Bound Certifications , 2000, LPAR.

[16]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[17]  Patrick Baillot.  Checking Polynomial Time Complexity with Types , 2002, IFIP TCS.

[18]  Michael Mendler,et al.  The NASA STI Program Office provides , 2000 .

[19]  Martin Hofmann,et al.  Static prediction of heap space usage for first-order functional programs , 2003, POPL '03.

[20]  Roberto M. Amadio.  Synthesis of max-plus quasi-interpretations , 2005, Fundam. Informaticae.

[21]  Paolo Coppola,et al.  Principal Typing in Elementary Affine Logic , 2003, TLCA.

[22]  Kazushige Terui,et al.  A Feasible Algorithm for Typing in Elementary Affine Logic , 2005, TLCA.