POPL 2017
Sun 15 - Sat 21 January 2017
Thu 19 Jan 2017 10:55 - 11:20 at Auditorium - Type Systems 2 Chair(s): Andrew D. Gordon

Lambda calculi with algebraic data types lie at the core of functional programming languages and proof assistants, but conceal at least two fundamental theoretical problems already in the presence of the simplest non-trivial data type, the sum type. First, we do not know of an explicit and implemented algorithm for deciding the beta-eta-equality of terms—and this in spite of the first decidability results proven two decades ago. Second, it is not clear how to decide when two types are essentially the same, i.e. isomorphic, in spite of the meta-theoretic results on decidability of the isomorphism.

In this paper, we present the exp-log normal form of types—derived from the representation of exponential polynomials via the unary exponential and logarithmic functions—that any type built from arrows, products, and sums, can be isomorphically mapped to. The type normal form can be used as a simple heuristic for deciding type isomorphism, thanks to the fact that it is a systematic application of the high-school identities.

We then show that the type normal form allows to reduce the standard beta-eta equational theory of the lambda calculus to a specialized version of itself, while preserving completeness of the equality on terms.

We end by describing an alternative representation of normal terms of the lambda calculus with sums, together with a Coq-implemented converter into/from our new term calculus. The difference with the only other previously implemented heuristic for deciding interesting instances of eta-equality by Balat, Di Cosmo, and Fiore, is that we exploits the type information of terms substantially and this often allows us to obtain a canonical representation of terms without performing a sophisticated term analyses.

Thu 19 Jan

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10:30 - 12:10
Type Systems 2POPL at Auditorium
Chair(s): Andrew D. Gordon Microsoft Research and University of Edinburgh
10:30
25m
Talk
Deciding equivalence with sums and the empty type
POPL
Gabriel Scherer Northeastern University
10:55
25m
Talk
The exp-log normal form of types: Decomposing extensional equality and representing terms compactly
POPL
Danko Ilik Trusted Labs
11:20
25m
Talk
Contextual isomorphisms
POPL
11:45
25m
Talk
Typed Self-Evaluation via Intensional Type Functions
POPL
Matt Brown UCLA, Jens Palsberg University of California, Los Angeles