miniKanren, live and untagged

Abstract

We present relational interpreters for several subsets of Scheme, written in the pure logic programming language miniKanren. We demonstrate these interpreters running "backwards"-that is, generating programs that evaluate to a specified value-and show how the interpreters can trivially generate quines (programs that evaluate to themselves). We demonstrate how to transform environmentpassing interpreters written in Scheme into relational interpreters written in miniKanren. We show how constraint extensions to core miniKanren can be used to allow shadowing of the interpreter's primitive forms (using the absent o tree constraint), and to avoid having to tag expressions in the languages being interpreted (using disequality constraints and symbol/number type-constraints), simplifying the interpreters and eliminating the need for parsers/unparsers.We provide four appendices to make the code in the paper completely self-contained. Three of these appendices contain new code: the complete implementation of core miniKanren extended with the new constraints; an extended relational interpreter capable of running factorial and doing list processing; and a simple pattern matcher that uses Dijkstra guards. The other appendix presents our preferred version of code that has been presented elsewhere: the miniKanren relational arithmetic system used in the extended interpreter.

Typed Embedding of a Relational Language in OCaml

“…• quines, twines, trines -self/co-evaluating program synthesis problems from [7]. The concrete tests took the first 100, 15 and 2 answers for these problems respectively.…”

“…Apart from being interesting from a purely theoretical standpoint, this approach may have a practical value: some problems look much simpler when considered as queries to some relational specification [5]. There are a number of appealing examples confirming this observation: a type checker for simply typed lambda calculus (and, at the same time, a type inferencer and solver for the inhabitation problem), an interpreter (capable of generating "quines" -programs producing themselves as a result) [7], list sorting (capable of producing all permutations), etc.…”

“…Next, a number of miniKanren applications require additional constraints to be implemented. In the untyped setting, when everything can be anything, some symbols or data structures tend to percolate into undesirable contexts [7]. In order to prevent this from happening, some auxiliary constraints ("absent o ", "symbol o ", etc.)…”

A Framework for Extending microKanren with Constraints

“…Interested readers should consult the references, tutorials, and myriad implementations at miniKanren.org for further details. Although Kumar [25] has formally specified miniKanren's syntax and given several semantics, implementers have been encumbered by neither, and none of the more widely used implementations obey these specifications [29,4]. Instead, miniKanren is better described as a family of related logic programming languages, traditionally shallowly embedded in a declarative host language, most of whose semantics are informally specified by direct appeal to their host languages' features.…”

“…Instead, this all-moded logic programming technique inspires non-traditional sorts of symbolic computation. Such Kanren programming examples include a typechecker that also behaves as a type inhabiter [28], an automated theorem prover that doubles as a proof assistant [3], and a programminglanguage interpreter that also serves as a quine generator [4]. Many of these miniKanren examples are available in the browser at tca.github.io/veneer/examples/editor.…”