Module Mlang.Mast

Abstract Syntax Tree


type application = string

Applications are rule annotations. The 3 main DGFiP applications seem to be:

  • batch: deprecated, used to compute the income tax but not anymore;
  • bareme: seems to compute the income tax;
  • iliad: usage unkown, much bigger than bareme.
module DomainId = StrSet
module DomainIdSet = StrSetSet
module DomainIdMap = StrSetMap
type chaining = string

"enchaineur" in the M source code, utility unknown

module ChainingSet = StrSet
module ChainingMap = StrMap
type variable_name = string

Variables are just strings

type func_name = string

Func names are just string for the moment

type variable_generic_name = {
base : string;
parameters : char list;

For generic variables, we record the list of their lowercase parameters

type error_name = string

Ununsed for now


type variable =
| Normal of variable_name
| Generic of variable_generic_name

A variable is either generic (with loop parameters) or normal

type literal =
| Variable of variable
| Float of float
type table_index =
| LiteralIndex of int
| SymbolIndex of variable

A table index is used in expressions like TABLE[X], and can be variables, integer or the special X variable that stands for a "generic" index (to define table values as a function of the index). X is contained here in SymbolIndex because there can also be a variable named "X"...

type set_value =
| FloatValue of float Pos.marked
| VarValue of variable Pos.marked
| Interval of int Pos.marked * int Pos.marked


type set_value_loop =
| Single of literal Pos.marked
| Range of literal Pos.marked * literal Pos.marked
| Interval of literal Pos.marked * literal Pos.marked

Values that can be substituted for loop parameters

type loop_variable = char Pos.marked * set_value_loop list

A loop variable is the character that should be substituted in variable names inside the loop plus the set of value to substitute.

type loop_variables =
| ValueSets of loop_variable list
| Ranges of loop_variable list

There are two kind of loop variables declaration, but they are semantically the same though they have different concrete syntax.


type comp_op =
| Gt
| Gte
| Lt
| Lte
| Eq
| Neq

Comparison operators

type binop =
| And
| Or
| Add
| Sub
| Mul
| Div

Binary operators

val precedence : binop -> int
val has_priority : binop -> binop -> bool
val is_right_associative : 'a -> bool
val is_left_associative : binop -> bool
type unop =
| Not
| Minus

Unary operators

type expression =
| TestInSet of bool * expression Pos.marked * set_value list

Test if an expression is in a set of value (or not in the set if the flag is set to false)

| Comparison of comp_op Pos.marked * expression Pos.marked * expression Pos.marked

Compares two expressions and produce a boolean

| Binop of binop Pos.marked * expression Pos.marked * expression Pos.marked
| Unop of unop * expression Pos.marked
| Index of variable Pos.marked * table_index Pos.marked

Access a cell in a table

| Conditional of expression Pos.marked * expression Pos.marked * expression Pos.marked option

Classic conditional with an optional else clause (None only for verification conditions)

| FunctionCall of func_name Pos.marked * func_args
| Literal of literal
| Loop of loop_variables Pos.marked * expression Pos.marked

The loop is prefixed with the loop variables declarations

The main type of the M language

and func_args =
| ArgList of expression Pos.marked list
| LoopList of loop_variables Pos.marked * expression Pos.marked

Functions can take a explicit list of argument or a loop expression that expands into a list

Toplevel clauses


type lvalue = {
var : variable Pos.marked;
index : table_index Pos.marked option;

An lvalue (left value) is a variable being assigned. It can be a table or a non-table variable

type formula_decl = {
lvalue : lvalue Pos.marked;
formula : expression Pos.marked;
type formula =
| SingleFormula of formula_decl
| MultipleFormulaes of loop_variables Pos.marked * formula_decl

In the M language, you can define multiple variables at once. This is the way they do looping since the definition can depend on the loop variable value (e.g Xi can depend on i).

type rule = {
rule_number : int Pos.marked;
rule_tag_names : string Pos.marked list Pos.marked;
rule_applications : application Pos.marked list;
rule_chaining : chaining Pos.marked option;
rule_formulaes : formula Pos.marked list;

A rule can contain many variable definitions

type 'a domain_decl = {
dom_names : string Pos.marked list Pos.marked list;
dom_parents : string Pos.marked list Pos.marked list;
dom_by_default : bool;
dom_data : 'a;
type rule_domain_data = {
rdom_computable : bool;
type rule_domain_decl = rule_domain_data domain_decl

Variable declaration

Input variables

type variable_attribute = string Pos.marked * literal Pos.marked
type value_typ =
| Boolean
| DateYear
| DateDayMonthYear
| DateMonth
| Integer
| Real

Here are all the types a value can have. Date types don't seem to be used at all though.

type input_variable = {
input_name : variable_name Pos.marked;
input_category : string Pos.marked list;
input_attributes : variable_attribute list;
input_alias : variable_name Pos.marked;

Unused for now

input_is_givenback : bool;
input_description : string Pos.marked;
input_typ : value_typ Pos.marked option;
type computed_variable = {
comp_name : variable_name Pos.marked;
comp_table : int Pos.marked option;

size of the table, None for non-table variables

comp_attributes : variable_attribute list;
comp_category : string Pos.marked list;
comp_typ : value_typ Pos.marked option;
comp_is_givenback : bool;
comp_description : string Pos.marked;
type variable_decl =
| ComputedVar of computed_variable Pos.marked
| ConstVar of variable_name Pos.marked * literal Pos.marked

The literal is the constant value

| InputVar of input_variable Pos.marked
type var_type =
| Input
| Computed
type var_category_decl = {
var_type : var_type;
var_category : string Pos.marked list;
var_attributes : string Pos.marked list;
val input_category : string
val computed_category : string
val base_category : string
val givenback_category : string

Verification clauses

type verification_condition = {
verif_cond_expr : expression Pos.marked;
verif_cond_error : error_name Pos.marked * variable_name Pos.marked option;

A verification condition error can ba associated to a variable

type verification = {
verif_number : int Pos.marked;
verif_tag_names : string Pos.marked list Pos.marked;
verif_applications : application Pos.marked list;

Verification conditions are application-specific

verif_conditions : verification_condition Pos.marked list;
type verif_auth_decl = string Pos.marked list Pos.marked
type verif_domain_data = {
vdom_auth : verif_auth_decl list;
type verif_domain_decl = verif_domain_data domain_decl
type error_typ =
| Anomaly
| Discordance
| Information
val compare_error_type : error_typ -> error_typ -> int
type error_ = {
error_name : error_name Pos.marked;
error_typ : error_typ Pos.marked;
error_descr : string Pos.marked list;

M programs

type source_file_item =
| Application of application Pos.marked

Declares an application

| Chaining of chaining * application Pos.marked list

Unused, declares an "enchaineur"

| VariableDecl of variable_decl
| Rule of rule
| Verification of verification
| Error of error_

Declares an error

| Output of variable_name Pos.marked

Declares an output variable

| Function

Declares a function, unused

| VarCatDecl of var_category_decl Pos.marked
| RuleDomDecl of rule_domain_decl
| VerifDomDecl of verif_domain_decl
type source_file = source_file_item Pos.marked list
type program = source_file list

Function specification AST

type function_spec = {
spec_inputs : variable_name Pos.marked list;
spec_consts : (variable_name Pos.marked * expression Pos.marked) list;
spec_outputs : variable_name Pos.marked list;
spec_conditions : expression Pos.marked list;

Helper functions

val get_variable_name : variable -> string