package acgtk

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Abstract Categorial Grammar development toolkit


Dune Dependency






This toolkit provides a compiler and an interpreter for Abstract Categorial Grammars (ACGs). Grammars can be compiled and then used by the interpreter to parse (if the grammar is at most second-order) or to generate terms. See for more details and bibliographic references.

Published: 07 Sep 2021


ACGtk: an ACG development toolkit

ACGtk is a software package (2008-2021 INRIA©) for the development of abstract categorial grammars. This distribution provides two executables file: acgc and acg.

It is distributed with the CeCILL license (see the LICENSE file or Contributors are listed in the file.

A list of related publications is available at the ACG web page.


acgc is a "compiler" of ACG source code, i.e. files containing definitions of signatures and lexicons. It basically checks whether they are correctly written (syntactically and wrt types and constant typing) and outputs a .acgo object file. An interactive mode is available to parse terms according to signatures.


./acgc --help

to get help.


acg is an interpreter of command meant to be useful when using ACGs. To get a list of command, run


then, on the prompt, type


Example files are given in the examples directory. Read the file.

Basic usage

Let's assume you defined a file my_acg.acg in directory my_dir. A basic usage of the acgc and acg commands could be:

$ acgc -o my_acg.acgo my_acg.acg

This will produce a my_acg.acgo file (note that this is the default name and location if the -o option is not provided).

Then, running :

$ acg

will open a prompt in which you can type:

# load o my_acg.acgo;

to load the data contained in the my_acg.acg file. Assuming you have defined the signature Sig and the lexicon Lex, you can then run the following commands:

# Sig check lambda x.some_cst x: NP ->S;

to check whether lambda x.some_cst x is a term of type NP ->S according to Sig.

You can type:

# Lex realize lambda x.cst x: NP ->S;

to compute the image of lambda x.cst x by Lex (assuming this term and this type are correct according to the abstract signature of Lex).

You can type:

# Lex parse John+loves+Mary: S;

to check whether the term John+loves+Mary has an antecend of type S by Lex, assuming that John+loves+Mary is a term of type Lex (S) in the object signature of Lex.

Type CTRL-D to exit from the program, or type:

# exit;

SVG output

If the --nsvg option is not set when running acg, a file realize.svg (default name) is generated in the current directory whenever a realize command is invoked. In order to set another file name, use the option --svg other_filename.

This files contains a representation as a tree of the operations described by the term to realize (applications, abstractions). Each node contains the abstract term and its realizations by each of the lexicons specified on the command line. The graphic file can for instance been observed through a web browser.

Four rendering engines are available so far to render the terms in each node:

  • the default engine: just generates a lambda-term following the signature/lexicon syntax

  • the "logic" engine: formulas are rendered as logical formulas: non logical constants are in bold font, logical connectives are rendered using utf-8 if their names are as follows:

    • "Ex" -> "∃"

    • "ExUni" -> "∃!"

    • "Ex_l" -> "∃ₗ"

    • "Ex_t" -> "∃ₜ"

    • "All" -> "∀"

    • "All_t" -> "∀ₜ"

    • "TOP" -> "⊤"

    • "The" -> "ι"

    • "&" -> "∧"

    • ">" -> "⇒"

    • "~" -> "¬"

  • the "trees" engine: terms are rendered as trees (e.g., derivation trees)

  • the "unranked trees": terms are rendered as trees, but if a non-terminal is defined as [a-zA-Z]+[0-9]*, it is rendered only using the [a-zA-Z] part.

The association between the name of a signature and a rendering engine is declared in a configuration file that can be loaded through the --realize option and that looks like:

$ cat config.json
    "signatures": [
	{ "name": "TAG", "engine": "trees" },
	{ "name": "DSTAG", "engine": "trees" },
	{ "name": "CoTAG", "engine": "trees" },
	{ "name": "derivations", "engine": "trees" },
	{ "name": "strings", "engine" : "strings"},
	{ "name": "Strings", "engine" : "strings"},
	{ "name": "logic", "engine" : "logic"},
	{ "name": "low_logic", "engine" : "logic"},
	{ "name": "derived_trees", "engine" : "unranked trees"},
	{ "name": "Derived_trees", "engine" : "unranked trees"},
	{ "name": "trees", "engine" : "unranked trees"}
  "colors": {
      "node-background": (239, 239, 239),
      "background": (255,255,255)

An example file is given in examples/config.json

ACG emacs mode

There is an ACG emacs mode acg.el in the emacs directory.

Look at the file to see how to install it and where you can find the acg.el file if automatically installed (in particular using opam).

It's main feature is to be loaded when editing an acg data file (with signatures and lexicons). It is automatically loaded for files with a .acg extension

It basically contains compilation directives and next-error searching.

  1. First load an acg file

  2. then run M-x compile (or C-c C-c) to call the compiler (acgc)

  3. then run M-x next-error (or ``C-x ) to search for the next error (if any) and highlights it

Syntax of signature and lexicons

(See the examples/tag.acg file for an example).

Signatures are defined by:

signature my_sig_name=

sig_entries is a list of sig_entry, separated with a ;. A sig_entry can be:

  • a type declaration as in

    NP,S : type;
  • a type definition as in

    o :type;
    string = o -> o;

    Note that type constructors are -> and => for the linear and intuitionistic arrows respectively.

  • a constant declarations as in

    bar,dummy:NP -> S;
    infix + : string -> string -> string;
    prefix - : bool -> bool;
    binder All : (e =>t) -> t;
    infix > : bool -> bool -> bool; (*This means implication*)

    Note that infix and prefix are keywords to introduce symbols (of length 1. This probably will change). Also notes that comments are surrounded by (* and *).

  • constant definitions as in

    n = lambda n. bar n : NP -> S;
    infix + = lambda x y z.x(y z): string -> string -> string;
    prefix - = lambda p.not p:bool -> bool;
    everyone = lambda P. All x. (human x) > (P x) ;

    Note the syntax for binders (All in the last example). Available construction for terms are:

    • lambda x y z.t for linear abstraction

    • mbda x y z.t` for non-linear abstraction

    • u vfor application (equivalent to to(t u) v`)

    • t SYM u if SYM is a infix symbol (lowest priority). It is equal to ((SYM) t) u where SYM is used as usual constant, with the priority of application

    • SYM t if SYM is a prefix symbol (highest priority)

    • NDER x y z.tifBINDER` is a binder

  • About associativity and precedence of operators

    Prefix operators have precedence over application, and application has precedence over infix operators. Relative precedence among infix operators can be defined.

    When no associativity specification is set, the default is left associative.

    When no precedece definition is given, the default is higher precedence over any infix operator defined so far.

    When declaring or defining an infix operator with the keyword 'infix', the optional specification for the associativity and the relative precedence can be set.

    A specification is given between square brackets. The syntax is as follows:

    infix [specification] SYM …

    (the remaining part of the declaration is the same as without the specification)

    A specification is non-empty comma-separated list of:

    • an (optional) associativity specification, given by one of the keywords Left, Right, or NonAssoc. If not present, left associativity is set by default to infix operators

    • an (optional) precedence declaration (if not present, the highest precedence over all the infix operators defined so far is given). It is defined as < SYM (where SYM is a symbol). It assigns to the operator being declared or defined the greates precedence below the precedence of SYM.

    It is possible to use an infix symbol as a normal constant by surrounding it with left and right parenthesis, so that t SYM u = (SYM) t u

    See examples/infix-examples and examples/infix-examples-script for examples.


There are two ways to define a lexicon:

  1. By using the keyword lexicon or nl_lexicon as in : ``` lexicon my_lex_name(abstract_sig_name) : object_sig_name = lex_entries end


    nl_lexicon my_lex_name(abstract_sig_name) : object_sig_name = lex_entries end

    With the `lexicon` keyword, `lambda` (resp. `->`) is interpreted as `lambda` (resp. `->`), whereas with `nl_lexicon`, `lambda` (resp. `->`) is interpreted as `Lambda` (resp. `=>`). I.e., everything is interpreted non linearly. It is useful when not interested in linear constraints in the object signature (as, for instance, in the context-free lambda grammars).
    `Lex_entries` is a list of `lex_entry`, separated with a `;`. A `lex_entry` can be of the following forms:
    * `abstract_atomic_type1, abstract_atomic_type2 := object_type;`
    * `abstract_const1, abstract_const2 := object_term;`
  2. By lexicon composition as in:

    lexicon my_new_lex = lex_2 << lex_1


The keywords are signature, lexicon, nl_lexicon, end, type, prefix, infix, binder, lambda, and Lambda.

The reserved symbols are =, <<, ;, :, ,, (, ), ., ->, =>, and :=.

Inside a signature or a lexicon, signature, lexicon and nl_lexicon are not considered as keywords and can be used as identifier.

Other keywords can be used as identifier when escaped with \ (e.g., \end).

Dependencies (14)

  1. easy-format
  2. yojson >= "1.6.0"
  3. cairo2
  4. conf-cairo
  5. conf-pkg-config
  6. conf-freetype
  7. cmdliner >= "1.0.0" & < "1.1.0"
  8. mtime >= "1.0.0" & < "2.0.0"
  9. logs
  10. fmt
  11. ANSITerminal
  12. menhir >= "20181113"
  13. dune >= "1.4"
  14. ocaml >= "4.05.0"

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