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Graphical and incremental type inference. A graph transformation approach

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Higher-Order and Symbolic Computation

Abstract

We present a graph grammar based type inference system for a totally graphic development language. NiMo (Nets in Motion) can be seen as a graphic equivalent to Haskell that acts as an on-line tracer and debugger. Programs are process networks that evolve giving total visibility of the execution state, and can be interactively completed, changed or stored at any step. In such a context, type inference must be incremental. During the net construction or modification only type safe connections are allowed. The user visualizes the type information evolution and, in case of conflict, can easily identify the causes. Though based on the same ideas, the type inference system has significant differences with its analogues in functional languages. Process types are a non-trivial generalization of functional types to handle multiple outputs and deferred arguments even in higher order parameters, partial application in any order and curried-uncurried coercion. Here we present the elements to model graphical inference, the notion of structural and non-structural equivalence of type graphs, and a graph unification and composition calculus for typing nets in an incremental way.

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Notes

  1. The symbol ? is also used in gradually-typed \(\lambda \)-calculus standing for dynamic types [16].

  2. Being both out-ports they cannot be connected but their TDs would be unified e.g. if they were connected as values of two list-items in a same list.

  3. It can be seen as the equivalent to the Damas-Milner instantiation rule.

  4. The right side cannot be obtained by overlapping as in Fig. 14. The screen-shot was obtained by first connecting the F-out ports of f and g to a pair of connected list-items (then deleted).

  5. Because all them have at least one output connected.

  6. Ordering is significant for ports of higher order parameters, which are clockwise applied, but not for a non-parameterised net. If it finally becomes a net-process (see Sect. 2.4) the user selects the open ports to be the parameters and results, and sets both orderings.

  7. This rule applies also when connecting a vertical green-arrow; it is not a special case.

  8. Since none of the connections closes the other ports.

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Acknowledgments

The authors would like to thank the anonymous reviewers for the detailed and helpful comments to improve the final version. Partially supported by “Generalitat de Catalunya” Project 2009SGR 1137(ALBCOM).

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Authors and Affiliations

  1. Department Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona, Spain

    Silvia Clerici, Cristina Zoltan & Guillermo Prestigiacomo

Authors
  1. Silvia Clerici
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  2. Cristina Zoltan
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  3. Guillermo Prestigiacomo
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Correspondence to Silvia Clerici.

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Clerici, S., Zoltan, C. & Prestigiacomo, G. Graphical and incremental type inference. A graph transformation approach. Higher-Order Symb Comput 26, 29–62 (2013). https://doi.org/10.1007/s10990-014-9104-8

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  • DOI: https://doi.org/10.1007/s10990-014-9104-8

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