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ELPI - Embeddable λProlog Interpreter








ELPI - Embeddable λProlog Interpreter

ELPI implements a variant of λProlog enriched with Constraint Handling Rules,
a programming language well suited to manipulate syntax trees with binders.

ELPI is designed to be embedded into larger applications written in OCaml as
an extension language. It comes with an API to drive the interpreter and
with an FFI for defining built-in predicates and data types, as well as
quotations and similar goodies that come in handy to adapt the language to the host

ELPI is free software released under LGPL vesion 2.1 or above.

How to install ELPI

ELPI runs on Linux, MacOS and Windows.

The simplest way is to use OPAM and type

opam install elpi

This command gives you the command line tool elpi as well as the findlib
-package elpi switch.

To install the development version of elpi directly from github
you can type

opam pin add elpi https://github.com/LPCIC/elpi.git

You can also clone this repository and type make build.

Finally, each CI run builds statically linked binaries for the
three supported operating systems, click on any
job from the Actions tab
to download them.

Syntax highlight in Visual studio code

The extension for vscode is available in the
market place, just look for Elpi.

Syntax highlight in vim

We recommend to add the following lines to ~/.vimrc

(click to expand)

autocmd BufRead,BufNewFile *.elpi set filetype=lprolog

autocmd FileType lprolog syn match   lprologIdentifier  "\<\l[-a-zA-Z\.+*/\\^<>=`'~?@#$&!_]*\>"
autocmd FileType lprolog syn region  lprologClause start="^\<\l[-a-zA-Z\.+*/\\^<>=`'~?@#$&!_]*\>" end=" \|:-\|\."
autocmd FileType lprolog syn match lprologClauseSymbols ":-"
autocmd FileType lprolog syn match lprologClauseSymbols "\."
autocmd FileType lprolog hi def link lprologClauseSymbols Type

autocmd FileType lprolog syn keyword elpiKeyword mode macro type pred namespace rule constraint uvar shorten
autocmd FileType lprolog syn match elpiKeyword ":before"
autocmd FileType lprolog syn match elpiKeyword ":after"
autocmd FileType lprolog syn match elpiKeyword ":name"
autocmd FileType lprolog syn match elpiMacro "@\(\w\|-\)\+"
autocmd FileType lprolog syn match elpiSpill "{"
autocmd FileType lprolog syn match elpiSpill "}"
autocmd FileType lprolog syn region elpiQuotation start="{{" end="}}" contains=@elpiAntiQuotation
autocmd FileType lprolog hi def link elpiKeyword Keyword
autocmd FileType lprolog hi def link elpiMacro Special
autocmd FileType lprolog hi def link elpiSpill Special


The language is quite compatible with standard
and ELPI is known to be able to run most of the λProlog programs out there
(see the list of known incompatibilities
with the Teyjus system).
Reading Programming with Higher-Order Logic
by Miller and Nadathur is highly recommended and covers standard λProlog.

The extensions to λProlog implemented in ELPI are described in the
ELPI file, built-in predicates are documented in

There is a short paper describing
the implementation of the interpreter, in particular how it deals with
binder mobility.

A longer paper describes, among other
things, the part of the language
for declaring and manipulating constraints.

For a lightweight introduction to Elpi one can look at the
slides of
the talk given at the ML Family workshop 2018 titled "Elpi: an extension
language with binders and unification variables". The companion
code of toyml
that implements W (ML type inference) in Elpi is also available.

How to embed ELPI in your software

The easiest way of embedding ELPI is by linking it using
as in ocamlfind opt -package elpi -linkpkg mycode.ml -o myprogram.
The API the host application can use to drive ELPI is documented in the
API.mli file (html rendering). The
Builtin.ml file contains example of
(basic) built-in predicates declaration via ELPI's FFI.

The command line interface to ELPI is a very simple
example of a client using ELPI as a library.
More complex examples of embeddings of ELPI are
coq-elpi and


ELPI is a research project aimed at providing a programming platform
for the so called elaborator component of an interactive theorem prover.

What's an elaborator and what's so special about it?

The elaborator of an interactive prover is the component in
charge of turning a term as input by the user into a well
typed one. In a prover like Coq it performs type inference
and is typically extended by the user.

The elaborator manipulates terms with binders and holes
(unification variables) representing missing piece of
information. Some of them have to be filled in order
to make the term well typed. Some others are filled in because
the user has programmed the eleborator to do so, e.g. ad-hoc polymorphism.

Such software component is characterized by an high complexity
coming from the interplay of binders, reduction and unification,
the heuristics to make it work in practice and the user extensions
to customize its behavior.

What problem does ELPI solve and how?

The programming language has the following features

  • Native support for variable binding and substitution, via an Higher Order
    Abstract Syntax (HOAS) embedding of the object language.
    The programmer does not need to care about technical devices to handle
    bound variables, like De Bruijn indices.

  • Native support for hypothetical context. When moving under a binder one can
    attach to the bound variable extra information that is collected when the
    variable gets out of scope. For example when writing a type-checker the
    programmer needs not to care about managing the typing context.

  • Native support for higher order unification variables, again via HOAS.
    Unification variables of the meta-language (λProlog) can be reused to
    represent the unification variables of the object language. The programmer
    does not need to care about the unification-variable assignment map and
    cannot assign to a unification variable a term containing variables out of
    scope, or build a circular assignment.

  • Native support for syntactic constraints and their meta-level handling rules.
    The generative semantics of Prolog can be disabled by turning a goal into a
    syntactic constraint (suspended goal). A syntactic constraint is resumed as
    soon as relevant variables gets assigned. Syntactic constraints can be
    manipulated by constraint handling rules (CHR).

  • Native support for backtracking. To ease implementation of search.

  • The constraint store is extensible. The host application can declare
    non-syntactic constraints and use custom constraint solvers to check their

  • Clauses are graftable. The user is free to extend an existing program by
    inserting/removing clauses, both at runtime (using implication) and at
    "compilation" time by accumulating files.

Most of these feature come with λProlog. Constraints and propagation rules are novel in ELPI.