Parsing

Coq's parser is based on Camlp5 using an extensible grammar. Somewhat helpful Camlp5 documentation is available here. However, the Camlp5 code has been copied into the Coq source tree and may differ from the Camlp5 release.

Notable attributes of the parser include:

The grammar is extensible at run time. This is essential for supporting notations and optionally-loaded plugins that extend the grammar.
The grammar is split into multiple source files. Nonterminals can be local to a file or global.
While 95% of the nonterminals and almost all the productions are defined in the grammar, a few are defined directly in OCaml code. Since many developers have worked on the parser over the years, this code can be idiosyncratic, reflecting various coding styles.
The parser is a recursive descent parser that, by default, only looks at the next token to make a parsing decision. It's possible to hand-code additional lookahead where necessary by writing OCaml code.
There's no code that checks whether a grammar is ambiguous or whether every production can be recognized. Developers who modify the grammar may, in some cases, need to structure their added productions in specific ways to ensure that their additions are parsable and that they don't break existing productions.

Grammars: `*.mlg` File Structure

Grammars are defined in *.mlg files, which coqpp compiles into *.ml files at build time. coqpp code is in the coqpp directory. coqpp uses yacc and lex to parse the grammar files. You can examine its yacc and lex input files in coqpp_lex.mll and coqpp_parse.mly for details not fully covered here.

In addition, there is a doc_grammar build utility that uses the coqpp parser to extract the grammar, then edits and inserts it into the documentation. This is described in doc/tools/docgram/README.md. doc_grammar generates doc/tools/docgram/fullGrammar, which has the full grammar for Coq (not including some optionally-loaded plugins). This may be easier to read since everything is in one file and the parser action routines and other OCaml code are omitted.

*.mlg files contain the following types of nodes (See node in the yacc grammar). This part is very specific to Coq (not so similar to Camlp5):

OCaml code - OCaml code enclosed in curly braces, which is copied verbatim to the generated *.ml file
Comments - comments in the *.mlg file in the form (* … *), which are not copied to the generated *.ml file. Comments in OCaml code are preserved.
DECLARE_PLUGIN "*_plugin" - associates the file with a specific plugin, for example "ltac_plugin"
GRAMMAR EXTEND - adds additional nonterminals and productions to the grammar and declares global nonterminals referenced in the GRAMMAR EXTEND:

GRAMMAR EXTEND Gram GLOBAL: bignat bigint …; <nonterminal definitions> END

Global nonterminals are declared in pcoq.ml, e.g. let bignat = Entry.create "bignat". All the *.mlg files include open Pcoq and often its modules, e.g. open Pcoq.Prim.

GRAMMAR EXTEND should be used only for large syntax additions. To add new commands and tactics, use these instead:

VERNAC COMMAND EXTEND to add new commands
TACTIC EXTEND to add new tactics
ARGUMENT EXTEND to add new nonterminals

These constructs provide essential semantic information that's provided in a more complex, less readable way with GRAMMAR EXTEND.

VERNAC COMMAND EXTEND - adds new command syntax by adding productions to the command nonterminal. For example:

VERNAC COMMAND EXTEND ExtractionLibrary CLASSIFIED AS QUERY | [ "Extraction" "Library" ident(m) ] -> { extraction_library false m } END

Productions here are represented with alternate syntax, described later.

New commands should be added using this construct rather than GRAMMAR EXTEND so they are correctly registered, such as having the correct command classifier.

TODO: explain "ExtractionLibrary", CLASSIFIED AS, CLASSIFIED BY, "{ tactic_mode }", STATE

VERNAC { … } EXTEND - TODO. A variant. The { … } is a block of OCaml code.
TACTIC EXTEND - adds new tactic syntax by adding productions to simple_tactic. For example:

TACTIC EXTEND btauto | [ "btauto" ] -> { Refl_btauto.Btauto.tac } END

adds a new nonterminal btauto.

New tactics should be added using this construct rather than GRAMMAR EXTEND.

TODO: explain DEPRECATED, LEVEL (not shown)

ARGUMENT EXTEND - defines a new nonterminal

ARGUMENT EXTEND ast_closure_term PRINTED BY { pp_ast_closure_term } INTERPRETED BY { interp_ast_closure_term } GLOBALIZED BY { glob_ast_closure_term } SUBSTITUTED BY { subst_ast_closure_term } RAW_PRINTED BY { pp_ast_closure_term } GLOB_PRINTED BY { pp_ast_closure_term } | [ term_annotation(a) constr(c) ] -> { mk_ast_closure_term a c } END

See comments in tacentries.mli for partial information on the various arguments.

VERNAC ARGUMENT EXTEND - (part of argument_extend in the yacc grammar) defines productions for a single nonterminal. For example:

VERNAC ARGUMENT EXTEND language PRINTED BY { pr_language } | [ "Ocaml" ] -> { let _ = warn_deprecated_ocaml_spelling () in Ocaml } | [ "OCaml" ] -> { Ocaml } | [ "Haskell" ] -> { Haskell } | [ "Scheme" ] -> { Scheme } | [ "JSON" ] -> { JSON } END

TODO: explain PRINTED BY, CODE

DOC_GRAMMAR - Used in doc_grammar-generated files to permit simplified syntax

Note that you can reverse engineer many details by comparing the .mlg input file with the .ml generated by coqpp.

Grammars: Nonterminals and Productions

Here's a simple nonterminal definition in the Camlp5 format:

universe: [ [ IDENT "max"; "("; ids = LIST1 universe_expr SEP ","; ")" -> { ids } | u = universe_expr -> { [u] } ] ] ;

In which: * universe is the nonterminal being defined * productions are separated by | and, as a group, are enclosed in [ [ … ] ]; * u = universe_expr refers to the universe_expr nonterminal. u is bound to the value returned by that nonterminal's action routine, which can be referred to in the action routine. For ids = LIST1 universe_expr SEP ",", ids is bound to the list of values returned by universe_expr. * -> { … } contains the OCaml action routine, which is executed when the production is recognized and returns a value * Semicolons separate adjacent grammatical elements (nonterminals, strings or other constructs)

Grammatical elements that appear in productions are:

nonterminal names - identifiers in the form [a-zA-Z0-9_]*. These correspond to variables in the generated .ml code. In some cases a qualified name, such as Prim.name, is used.
"…" - a literal string that becomes a keyword and cannot be used as an ident. The string doesn't have to be a valid identifier; frequently the string will contain only punctuation characters. Generally we try to avoid adding new keywords that are also valid identifiers--though there is an unresolved debate among the developers about whether having more such keywords in general is good (e.g. it makes it easier to highlight keywords in GUIs) or bad (more keywords for the user to avoid and new keywords may require changes to existing proof files).
IDENT "…" - a literal string that has the form of an ident that doesn't become a keyword
OPT element - optionally include element (e.g. a nonterminal, IDENT "…" or "…"). The value is of type 'a option.
LIST1 element - a list of one or more elements. The value is of type 'a list.
LIST0 element - an optional list of elements
LIST1 element SEP sep - a list of elements separated by sep
LIST0 element SEP sep - an optional list of elements separated by sep
( elements ) - grouping to represent a series of elements as a unit, useful within OPT and LIST*.
[ elements1 | elements2 | … ] - alternatives (either elements1 or elements2 or …), actually nested productions, each of which can have its own action routines

Nonterminals can also be defined with multiple levels to specify precedence and associativity of its productions. This is described in the Coq documentation under the Print Grammar command. The first square bracket around a nonterminal definition is for grouping level definitions, which are separated with |, for example:

ltac_expr: [ "5" RIGHTA [ te = binder_tactic -> { te } ] | "4" LEFTA :

Grammar extensions can specify what level they are modifying, for example:

ltac_expr: LEVEL "1" [ RIGHTA [ tac = ltac_expr; intros = ssrintros_ne -> { tclintros_expr ~loc tac intros } ] ];

Alternate production syntax

Except for GRAMMAR EXTEND, the EXTEND nodes in the *.mlgs use simplified syntax in productions that's similar to what's used in the Tactic Notation and Ltac2 Notation commands. For example:

TACTIC EXTEND cc | [ "congruence" ] -> { congruence_tac 1000 [] } | [ "congruence" integer(n) ] -> { congruence_tac n [] } | [ "congruence" "with" ne_constr_list(l) ] -> { congruence_tac 1000 l } | [ "congruence" integer(n) "with" ne_constr_list(l) ] -> { congruence_tac n l } END

Nonterminals appearing in the alternate production syntax are accessed through wit_* symbols defined in the OCaml code. Some commonly used symbols are defined in stdarg.ml. Others are defined in the code generated by ARGUMENT EXTEND and VERNAC ARGUMENT EXTEND constructs. References to nonterminals that don't have wit_* symbols cause compilation errors.

The differences are: * The outer : [ … ]; is omitted. Each production is enclosed in | [ … ]. * The action routine is outside the square brackets * Literal strings that are valid identifiers don't become reserved keywords * No semicolons separating elements of the production * integer(n) is used to bind a nonterminal value to a variable instead of n = integer * Alternate forms of constructs are used: * ne_entry_list for LIST1 entry * entry_list for LIST0 entry * ne_entry_list_sep(var, sep) for LIST1 entry SEP sep where the list is bound to var * entry_list_sep(var, sep) for LIST0 entry SEP sep where the list is bound to var * entry_opt for OPT entry * There's no way to define LEVELs * There's no equivalent to ( elements ) or [ elements1 | elements2 | … ], which may require repeating similar syntax several times. For example, this single production is equivalent to 8 productions in TACTIC EXTEND representing all possible expansions of three OPTs:

| IDENT "Add"; IDENT "Parametric"; IDENT "Relation"; LIST0 binder; ":"; constr; constr; OPT [ IDENT "reflexivity"; IDENT "proved"; IDENT "by"; constr -> { … } ]; OPT [ IDENT "symmetry"; IDENT "proved"; IDENT "by"; constr -> { … } ]; OPT [ IDENT "transitivity"; IDENT "proved"; IDENT "by"; constr -> { … } ]; IDENT "as"; ident -> { … }

Usage notes

Other components

Coq's lexer is in clexer.ml. Its 10 token types are defined in tok.ml.

The parser is in grammar.ml. The extensive use of GADT (generalized algebraic datatypes) makes it harder for the uninitiated to understand it.

When the parser is invoked, the call tells the parser which nonterminal to parse. vernac_control is the start symbol for commands. tactic_mode is the start symbol for tactics. Tactics give syntax errors if Coq is not in proof mode. There are additional details not mentioned here.

Parsing productions

Some thoughts, not to be taken as identifying all the issues:

Since the parser examines only the next token to make a parsing decision (and perhaps because of other potentially fixable limitations), some productions have to be ordered or structured in a particular way to parse correctly in all cases.

For example, consider these productions:

``` command: [ [ | IDENT "Print"; p = printable -> { VernacPrint p } | IDENT "Print"; qid = smart_global; l = OPT univ_name_list -> { VernacPrint (PrintName (qid,l)) } | IDENT "Print"; IDENT "Module"; "Type"; qid = global -> { VernacPrint (PrintModuleType qid) } | IDENT "Print"; IDENT "Module"; qid = global -> { VernacPrint (PrintModule qid) } | IDENT "Print"; IDENT "Namespace" ; ns = dirpath -> { VernacPrint (PrintNamespace ns) } :

printable: [ [ IDENT "Term"; qid = smart_global; l = OPT univ_name_list -> { PrintName (qid,l) } | IDENT "All" -> { PrintFullContext } | IDENT "Section"; s = global -> { PrintSectionContext s } : ```

Reversing the order of the first two productions in command causes the All in Print All to be parsed incorrectly as a smart_global, making that command unavailable. Print Namespace nat. still works correctly, though.

Similarly, the production for Print Module Type has to appear before Print Module <global> in order to be reachable.

Internally, the parser generates a tree that represents the possible prefixes for the productions of a nonterminal as described in the Camlp5 documentation.

Here's another example in which the way the productions are written matters. OPT at the beginning of a production doesn't always work well:

command: [ [ | IDENT "Foo"; n = natural -> { VernacBack 1 } | OPT (IDENT "ZZ"); IDENT "Foo" -> { VernacBack 1 } :

Foo. looks like it should be accepted, but it gives a parse error:

``` Unnamed_thm < Foo. Toplevel input, characters 3-4:

Foo. ^ Error: Syntax error: [prim:natural] expected after 'Foo' (in [vernac:command]). ```

Reversing the order of the productions doesn't help, but splitting the 'OPT' production into 2 productions works:

``` | IDENT "Foo" -> { VernacBack 1 } | IDENT "ZZ"; IDENT "Foo" -> { VernacBack 1 } | IDENT "Foo"; n = natural -> { VernacBack 1 }

```

On the other hand, OPT works just fine when the parser has already found the right production. For example Back and Back <natural> can be combined using an OPT:

| IDENT "Back"; n = OPT natural -> { VernacBack (Option.default 1 n) }

Lookahead

It's possible to look ahead more than one symbol using OCaml code. Generally we avoid doing this unless there's a strong reason to do so. For example, this code defines a new nonterminal local_test_lpar_id_colon that checks that the next 3 tokens are "(" ident and ":" without consuming any input:

let local_test_lpar_id_colon = let open Pcoq.Lookahead in to_entry "lpar_id_colon" begin lk_kw "(" >> lk_ident >> lk_kw ":" end

This one checks that the next 2 tokens are "[" and "|" with no space between. This is a special case: intropatterns can have sequences like "[|]" that are 3 different tokens with empty nonterminals between them. Making "[|" a keyword would break existing code with "[|]":

let test_array_opening = let open Pcoq.Lookahead in to_entry "test_array_opening" begin lk_kw "[" >> lk_kw "|" >> check_no_space end

TODO: how to add a tactic or command