# Rewriting Micheline with `tezos-micheline-rewriting`

¶

`tezos-micheline-rewriting`

allows to construct rewriting rules
on Micheline, enumerate matches and perform rewritings. It is
fairly generic and deserves a documentation of its own.
This library manipulates the following basic elements:

Micheline terms

Paths

Patterns

Informally, the library allows to find patterns in terms: the result is a list of paths, corresponding to the location of these patterns. Rewriting is then performed by substituting a subterm at a given path by another one. The library also provides facilities for manipulating hash-consed terms and patterns, which is crucial in all non-trivial applications.

## Constructing Micheline terms¶

The type of Micheline terms has two parameters: the type of locations
and the type of primitives. We abstract away from the underlying
representation of terms via the `Micheline_sig.S`

module type:

```
module type S = sig
type label
type head
type node = (label, head) Micheline.node
val default_label : label
val int : Z.t -> node
val string : string -> node
val bytes : Bytes.t -> node
val prim : head -> node list -> string list -> node
val seq : node list -> node
val label : node -> label
end
```

We provide two functors for manipulating Micheline terms:

`Micheline_without_hash_consing.Make`

`Micheline_with_hash_consing.Make`

Both functors provide implementations of the `Micheline_sig.S`

signature
(with distinct type constraints however). They both take as input some additional
structure on the type of primitives, as specified in the `Signature.S`

module type:

```
module type S = sig
type t
val compare : t -> t -> int
val hash : t -> int
val pp : Format.formatter -> t -> unit
end
```

ie primitives must be totally ordered, hashable and pretty-printable.

`Micheline_without_hash_consing.Make`

has type

```
functor (X : Signature.S) (Label : sig type t val default : t end) -> Micheline_sig.S with type label = Label.t and type head = X.t
```

and provides a simple overlay over the Micheline constructors, setting the label to its default value.

`Micheline_with_hash_consing.Make`

has type

```
functor (X : Signature.S) (P : sig val initial_size : int option end) -> Micheline_sig.S with type label = hcons_info and type head = X.t
```

We use the label slot to store hash-consing information on terms: the type `hcons_info`

contains a unique id for the term and its hash. This implementation of `Micheline_sig.S`

performs maximal sharing: it is important that terms are only constructed through
the interface provided by the module for the required invariants to hold true. A weak
hash table is used to store terms, its initial size is fixed by `P.initial_size`

.
One can use the unique id contained in `hcons_info`

to construct a separate map
from the term to some other annotation.

## Manipulating paths in Micheline terms¶

A Micheline term is either a primitive application, a sequence, or one of three atoms (int, string or byte). The primitive application and sequence constructors have variable arity (the take lists of subterms as arguments). It follows that one can designate a subterm of a given term as a list of integers, each integer denoting an index in the list of subterms of either a primitive or sequence application.

We provide two implementations of path-manipulating modules: one without hash-consing and one with. Both implement the following signature:

```
module type S = sig
type desc = private Root | At_index of int * t
and t = private {tag : int; hash : int; rev_path_desc : desc}
val compare : t -> t -> int
val root : t
val at_index : int -> t -> t
val concat : above:t -> under:t -> t
val to_string : t -> string
end
```

We observe that paths, contrary to our intuition, are not directed from the root
to the subterm but rather from the subterm to the root. This allows
easy hash-consing and follows the usual way paths are constructed during the
pattern matching process. The two fundamental operations are `root`

,
corresponding to an empty path, and `at_index i p`

, corresponding
to the ith subterm of the term at path `p`

.

## Pattern-matching Micheline¶

The `Pattern`

module provides two functors implementing a
small pattern description language, as well as functions for enumerating
matches of a pattern in a given term. The signature is the following:

```
module type S = sig
type head
type path
type t
type plist
type node
val pattern_matches : t -> node -> bool
val all_matches : t -> node -> path list
val focus_matches : t -> path list -> path list
val int : (Z.t -> bool) option -> t
val string : (string -> bool) option -> t
val bytes : (Bytes.t -> bool) option -> t
val prim : head -> plist -> t
val prim_pred : (head -> bool) -> plist -> t
val seq : plist -> t
val any : t
val focus : t -> t
val list_any : plist
val list_empty : plist
val list_cons : t -> plist -> plist
val ( @. ) : t -> plist -> plist
val pp : Format.formatter -> t -> unit
val uid : t -> int
end
```

The comments describing all these constructs can be found in pattern.mli. It is worth describing a subset of these functions here:

`pattern_matches patt node`

returns true if and only if`patt`

matches`node`

.`all_matches patt node`

returns the list of all paths in of subterms of`node`

matching`patt`

.`focus patt`

constructs a focused subpattern. There can be several focused subpatterns but the cannot be nested.`focus_matches patt matches`

converts a list of matches for`patt`

into a list of matches for the focused subpatterns of`patt`

.

The focusing mechanism allows patterns to have a contextual part, corresponding to the subterm matched by the whole pattern, and a “point of interest” in the context, corresponding to a subterm of the subterm matched by the whole pattern. For instance, we can match on integers that are directly under a particular primitive, etc.

The signatures of the non-hash-consing functor is as follows:

```
Make : functor (X : Signature.S) (Micheline : Micheline_sig.S with type head = X.t) (Path : Path.S) -> S with type head = X.t and type path = Path.t and type node = Micheline.node
```

While the hash-consing implementation has the following slightly more complicated type:

```
module Make_with_hash_consing : functor
(X : Signature.S)
(Micheline : Micheline_sig.S
with type head = X.t
and type label = Micheline_with_hash_consing.hcons_info)
(Path : Path.S) -> sig
include
S
with type head = X.t
and type path = Path.t
and type node = Micheline.node
val all_matches_with_hash_consing : t -> node -> path list
end
```

I.e the default implementation of match enumeration does not use hash-consing; one has
to use `all_matches_with_hash_consing`

to do so.

## Performing substitutions¶

The `Rewrite`

module provides facilities for performing substitutions. There is
only one implementation here (as all hash-consing is taken care of in previously
described modules). The module provides a functor taking implementations for
terms, paths and patterns and provides the following functions:

```
module type S = sig
type label
type head
type path
type patt
type node = (label, head) Micheline.node
exception Rewrite_error of string * node option
val get_subterm : term:node -> path:path -> node
val subst : term:node -> path:path -> replacement:node -> node
val pattern_matches : patt -> node -> bool
val all_matches : patt -> node -> path list
end
```

The key function here is `subst`

which performs the substitution.
The implementation proceeds as one might expect, by recursive descent
on the term together with the specified path.

## An example?¶

An example can be found in the `test`

subdirectory. It consists in
a reimplementation of the migration of addresses towards pairs of
addresses and chain ids in multisignature contracts.