Abstract
We present a formal study of semantics for the relational programming language miniKanren. First, we formulate a denotational semantics which corresponds to the minimal Herbrand model for definite logic programs. Second, we present operational semantics which models interleaving, the distinctive feature of miniKanren implementation, and prove its soundness and completeness w.r.t. the denotational semantics. Our development is supported by a Coq specification, from which a reference interpreter can be extracted. We also derive from our main result a certified semantics (and a reference interpreter) for SLD resolution with cut and prove its soundness.
The reported study was funded by RFBR, project number 18-01-00380.
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Notes
- 1.
A detailed Prolog-to-miniKanren comparison can be found here: http://minikanren.org/minikanren-and-prolog.html.
- 2.
We respect here a conventional tradition for miniKanren programming to superscript all relational names with “\(^o\)”.
- 3.
The extended version of this paper is available at https://arxiv.org/abs/2005.01018.
- 4.
There still can be differences in observable behavior of concrete goals under different sound and complete search strategies. For example, a goal can be refutationally complete [6] under one strategy and non-complete under another.
- 5.
The specification is available at https://github.com/dboulytchev/miniKanren-coq.
- 6.
Possible slowdown and loss of termination after reorderings in conjunction is a famous example of this phenomenon in miniKanren, known as conjunction non-commutativity [6].
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Rozplokhas, D., Vyatkin, A., Boulytchev, D. (2020). Certified Semantics for Relational Programming. In: Oliveira, B.C.d.S. (eds) Programming Languages and Systems. APLAS 2020. Lecture Notes in Computer Science(), vol 12470. Springer, Cham. https://doi.org/10.1007/978-3-030-64437-6_9
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