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lamtez: a typed lambda-calculus compiling to Tezos Michelson VM

Lamtez is Domain-Specific Language for smart contracts, and its compiler to Michelson, Tezos' virtual machine for smart contracts execution.

It is released under the MIT license, with no guaranty of any kind (among other, there's no proof that it compiles to sound nor correct Michelson code). I'm interested in feedbacks anyway, if you experiment with it.


The compiler is written in OCaml; the build process relies on ocamlbuild, and it depends on the parser generator menhir. If opam is installed on your system, opam install ocamlbuild menhir should be enough to get a building environment. If you compiled Tezos from sources, Lamtez requirements are a subset of Tezos'.


If you would rather look at source code examples first, before reading the fine manual, you can go and check It reimplements contract exmaples from [] and the Michelson specification.

Cheat sheet

For a quick summary of the language syntax and main features, a PDF two-pages summary is available as

General considerations on the language

The language is strongly influenced by ML dialects OCaml and Haskell: mostly functional, relying heavily on sum-types and product-types, statically typed with type inference. It also composes with some limitations in Michelson. Most of the limitations in Michelson language follow from the following assumptions:

  • Most useful smart contracts will be rather simple, commpared to typical programs written be profesionnal developers in general-purpose languages;

  • A very high level of confidence in contracts correctness will be required. Given how finding and exploiting bugs in smart contracts can be turned into tokens and actual money, every contract handling significant amounts of money will be thoroughly reviewed and attacked by black-het hackers, several of them smarter than the contract's author and white-hat reviewers.

  • Tezos being self-amending, it's better to start with a very limited language and progressively add empirically needed features, rather than start with many bells and whistles: some of them might prove less secure than anticipated, or not as useful as it first seemed, but each of them making formal proofs more tedious or complicated to produce.

Michelson closely ressembles a simply-typed lambda calculus, without native recursivity nor proper closures; drastic limitations also exist on the ability for a contract to call other contracts.

Compared to hand-written Michelson, Lamtez contracts offer higher-level features:

  • Sum and product types of arbitrary size and with arbitrary field/case names. In Michelson, sums with more than two alternatives and products with more than two fields have to be encoded with nested alternatives and pairs, thus quickly becoming hard to read for humans.

  • lexically scoped variables: keeping track of what is at which level of the stack is cumbersome when writing a program, and it makes reading someone else's contracts dreadful. Being able to name things rather than shuffling them on a stack greatly improves contract readability.

  • Limited support for closures: a function can use variables declared outside of it. It is done by either compiling functions as a pair of a LAMBDA with a tuple capturing its environment from the stack, by beta-reducing the closures when possible, or by reimplementing MAP and REDUCE operations with LOOP when the function needs its environment. Some cases remain, though, where Lamtez is not able to compile a closure.

  • type inference: as most ML dialects, lamtez uses a variant of the W algorithm to guess types with very little user annotations. However, contrary to ML, it expects the final contract not to be polymorphic, as Michelson doesn't support it. So you might get some "Add more type annotations" errors. Annotating function parameters is sufficient, although often not necessary, to ensure a monomorphic contract type. (inner polymorphic functions are technically possible, but NOT YET IMPLEMENTED)

  • storage management: instead of manually managing the storage, variables prefixed with @ are declared and stored in it, and can be updated in the contract through a simple and readable syntax (under some conditions). An option is provided to declare and extract an initial storage value from the contract source file.

  • TRANSFER_TOKEN, the act of calling another contract, can only be done under very strict conditions in Michelson (the stack must be empty). This restriction is partially lifted in Lamtez: it will dedicate a field in the storage to save the stack before calling, and restore it after it returns.

(note: currently, the stack is saved rather naively: a big sum type is reserved in the storage, one per invocation of TRANSFER_TOKEN, and the whole stack is saved in it. First the stack could be pruned before saving, as some slots won't be used after the contract call anymore, and two invocations with the same stack types above them should share their slot)

Lamtez is mostly functional. It has two kinds of side effects: storage updates and calls to other contracts. Normally, functional programming languages will only let you touch side effects with a ten foot pole. They typically call that pole a "monad"; wielding a monad towards unfamiliar developers scares them about as much as doing so with an actual ten foot pole.

Lamtez doesn't explicitly supports monads, but it enforces some (coarser) constraints about where side effects are accepted. Namely, these operations can't happen in an inner function (we couldn't keep track of them without monads then), nor in places where evaluation order isn't intuitively obvious: not in tuples/products, not in function arguments.

Whitespaces are not significant except to separate tokens, indentation is not significant, comments start with a # sign and run until the end of the current line.

Lamtez is not proved correct in any way; the proper way to ensure any correctness property is by working directly on the generated Michelson code. It is annotated and commented, among other with the stack's state after each instruction, in order to help analysis.

Anatomy of a contract

A contract is composed of:

  • a series of type declarations: it creates type structures, with arbitrary sizes, arbitrary labelled fields and alternative cases.

  • a series of stored variables: those variables, starting with a @ symbol, are kept between contract calls in the blockchain's storage. They can optionally be given an initial value; if all stored variables in the contract have an initial value, then one can extract a data initialization value from the contract, which can be directly passed to the tezos client. (In the future it will be possible to compile storage values from separate files; but the contract's type declarations are needed to properly encode sum and product values).

  • a function, taking a parameter and returning a result. This function can also, under controlled conditions, perform two kinds of effects: calling other contracts, and updating the content of stored variables.

Expression Syntax

Functions and function applications

In languages inspired by lambda calculus, functions are introduced by a $\lambda$ sign; In Lamtez as in ML we represent it with the fun keyword; we tolerate also the backslash \\, visually more similar, used by Haskell, more concise, but which might make the code look more cryptic at first sight.

The complete syntax for a function is fun x: body. Parameters can be annotated with types, through the :: infix operator: fun x :: nat: body. The result type can also be specified, although it can normally be inferred by the compiler: fun x :: nat :: unit: body.

Lamtez supports multi argument functions, but contrary to ML-inspired languages, they are encoded through tuples rather than through currying (nested functions returning functions, a standard idiom in λ-calcullus inspired languages). Currying is mainly useful for partial applications, and their usefulness is not demonstrated for Tezos smart contracts. They can always be encoded through eta-expansion if needed. Finally, currying leads to cumbersome code at best, in a target language that doesn't support closures.

Functions are syntactically applied the ML/λ-calculus way, by putting the arguments after the function, without parentheses nor separating commas, i.e. what's written f(x, y) in C-inspired syntaxes is written f x y, and equivalent to f(x, y), the application of function f to the pair (x, y). Parentheses are still needed for nested function applications, e.g. what would be written f(g(x), g(y)) in C would give f (g x) (g y) in Lamtez, as in most ML dialects.

Lamtez performs type inference, i.e. if there are enough hints in the code, it will correctly guess the types which the user omitted to write. However, unlike most other ML-family languages, polymorphism is not allowed, because the underlying Michelson VM doesn't support it (TODO: inner lambdas could be polymorphic, as long as it doesn't show on the outside type. Not sure hwo useful that would be in practice). So if the type inference algorithm determines that a function's best type is, say, ∀a: list a -> nat, the compiler will emit an error and demand more type annotations rather than accepting


fun x: x
fun x y: x + y
fun x :: nat, y ::nat: x - y
fun x :: nat, y: x * y
fun parameter: ((), map-update parameter (Some self-amount) @store)

For instance, the simplest contract, identity, which does nothing, just takes a unit parameter and returns a unit result, is written below:

fun p :: unit: p

The barely more interesting one, which adds one to its parameter, is:

fun p :: nat: p + 1


Lamtez supports the same literals as Michelson:

  • to distinguish naturals from positive integers, the later have to be prefixed with a + sign, so 42 is a natural number and +42 is typed as an integer. Beware therefore that f+1 is the application of function f to signed integer +1, and not an addition to number f.

  • dates are represented with the ISO format, without surrounding quotes: 2017-08-22T22:00:00Z, 2017-08-22T22:00:00+01:00

  • Tez amounts are represented with a tz prefix and optional cents: tz1, tz1.00, tz.05 (TODO: support _ characters). If there are cents, they must be two digits long: tz0., tz0.1 or tz.100 are illegal.

  • Signatures are represented with a sig: prefixing the base58 hash.

  • Key hashes are written directly, without surrounding quotes; they are by their tz1 followed by a base58 hash.


Variable names must start with a lowercase letter or an underscore; they are allowed to contain a -: this is currently used to sort primitive functions into pseudo-namespaces. As a result, it's important to leave spaces around - when used as a substraction infix operator.

Examples: foo, bar0, contract-call, _foo, foo_bar, fooBar

(In the future I might get rid of dashes in names, if there's a decent namespace system instead)

Let: local variables

ML-style local variables, let x=a; b evaluates b with x set to a. Equivalent, execution-wise, to (\x:b) a.


let x = 32;
let y = 10;
x + y

Lamtez being mostly functional, you can't update the value stored in a variable; however, and as often done in ML dialect, you can shadow a variable with a new variable of the same name:

let x = 10;
let x = 20;  # From here you can't refer to the first `x` variable anymore
do_stuff_with x

Tuples (unlabelled cartesian products)

Whereas Michelson supports pairs, Lamtez supports tuples of length bigger than 2 (and encodes them as nested pairs). Contrary to many ML dialects, tuples are mandatorily surrounded with parentheses to avoid misleading precedence issues; elements are separated with commas.

Elements are extracted from a tuple with the suffix .n, where n is a litteral positive integer, 0-indexed. The extractor suffix binds tighter than function application (same as most ML-family languages).

Tuples are encoded as balanced trees, i.e. so that the length of paths in n-products grows as log2(n). This can easily be changed if desired (left-folded or right-folded accessors have o(n) access and update times, but might lead to simpler proofs).


let triplet = (32, 5, 5);
triplet.0 + triplet.1 + triplet.2

(labelled) Cartesian products

For larger composite structures, it's easier to refer to individual elements by user-given names, rather than by number. This requires to declare a product type before using it. Labels are like identifiers except that they start with a capital letter.

Type declarations happen at the beginning of the contract (cf. infra); labelled product types are sequences of labels and types separated by * symbols.

Litteral product types are sequences of labels and types, separated by commas and surrounded by braces.

Access to product fields are made with a .Label suffix, which binds as tightly as unlabelled product accessors.

Finally, one can generate a product from another: a product which is equal to p except that field F has value 42 can be created through the syntax p <- F: 42.


type coordinates = Latitude: int * Longitude: int

let p = {Latitude: 43500, Longitude: 1500 };
let i_miss_trigonometry = p.Latitude * p.Latitude + p.Longitude * p.Longitude;

let p_2_degrees_north = p.Latitude <- p.Latitude+2;
let p_south_west =
  p <- Latitude: p.Latitude - 1
    <- Longitude: p.Longitude + 1;

(p, p_2_degrees_north, p_south_west)

Sum types

Equivalent of labelled unions, they are a generalization of the Left|Right Michelson operators with an arbitrary number of labels, freely named.

Types have to be declared; they are declared the same way as products, except that cases are separated with + instead of *.

A label can only belong to one sum type; for instance, it's illegal to have both type a = A: int + B: string and type b = A: int + C: bool.

Each case has one and only one associated value type. Make it a unit if you don't use it, make it a tuple or a product if you need several values. Syntactically, unit arguments can be omitted, though.

Sum expressions are built with a label followed by an expression. It binds as tightly as a function application.

Sum accessors, equivalent to ML's match/with or Michelson IF_LEFT, are of the form case expression | Label_0 v_0: e_0 |... | Label_n v_n: e_n end. the variables v_n can be omitted when they're not used in the corresponding e_n. In sum cases, unit values can be omitted too.

Booleans are encoded as type bool = False unit | True unit, so if/then/else operations can be encoded as sum accessors, as shown in the example below.

Option types Some x + None, binary alternatives Left/Right and list constructors Nil/Cons are also predeclared as sum types.


type operation = Withdrawal tez + GetBalance unit + Deposit tez
fun amount operation storage:
  case operation
  | Withdrawal a: (None, storage - a)
  | GetBalance:   (Some storage, storage)
  | Deposit:      (None, storage + a)

self-now > date ? True: "OK" | False: "Not yet"

Some syntax sugar is proposed for boolean cases, which allows to chain several if / then / else if * / else statements:

  • if <cond>: <body0> end is equivalent to case <cond> | True: <body0> | False: () end.

  • if <cond>: <body0> | else: <body1> end is equivalent to case <cond> | True: <body0> | False: <body1> end.

  • if <cond_0>: <body_0> | ... | <cond_n>: <body_n> else: <body_e> end is equivalent to nested if/then/elseif statements:

      case <cond_0>
      | True: <body_0>
      | False: case <cond_1>
           | True: <body_1>
           | False: case <cond_2>
                    | ...
                    | False: <body_e> end ... end

Binary and unary operators


Composite values

There are native syntaxes to enter lists, sets and maps:

l = (list 1 2 3 4)
s = (set "a" "b" "c" "d")
m = (map 1 "one" 2 "two" 3 "three")

Lists can also be built out of Cons and Nil sum types.

Type annotations

Expressions can be annotated with their types, with the :: infix operator. It serves several purposes: compiler-checked hint for contract readers, helping the compiler resolve a polymorphic type, or helping it produce a more precise error message when facing an unsound program.


Michelson contracts have a storage value; it is stored on the blockchain, passed as a parameter to contracts when they execute, and contracts return an updated storage object which is stored back on the blockchain.

As non-trivial programs often store multiple values, the store is generally a product type. Since Lamtez might need to store additional fields in the store, contract developpers are expected to declare and use the field they need through a dedicated @ syntax:

  • a sequence of @name :: type declarations after type declarations declare every storage field type and name;

  • optionally, a value can be associated, e.g. @n :: nat = 42. If all stored values have such an initial value, a data initializer can be extracted from the contract, and passed to the tezos client.

  • in the code, @name returns the current content of field name.

  • fields can be updated with the syntax @name <- expr.

Storage fields cannot be updated anywhere: you can't update them inside functions, in tuple or product elements, in function arguments.

If you want to update them inside a function, make the function return the updated value and perform the update from outside:

@n :: int

let f = fun x :: int: @n <- x + 1; () # Illegal
f 3

let f = fun x :: int: x + 1;
@n <- f 3 # Legal

Instead of performing storage updates in function arguments or products, perform them before in a let expression.



Loops are not very functional; however, in a languge that doesn't fully support closures and doesn't support contract calls from inside lambdas, access to the LOOP Michelson primitive is necessary. Although this isn't implemented, my intention is to introduce a syntax of the form loop (<var*>) = (<expr*>) while <condition> else (<expr*>):

  • the <expr*> and <var*> lists have the same sizes;
  • at step 0, the variables are assigned the values after the else;
  • as long as <condition> is true, an iteration of the loop is performed:
    • the expressions before the while are evaluated, with the current assignments for <var*>;
    • the result is assigned to <var*>, before a new condition checking, and maybe iteration, is performed.

As an example, here's what factorial would look like with the loop operator:

let fact = fun n:
  let loop (acc, i) = (1, n) then (acc*i, i-1) while i > 0

Some syntactic permissiveness might be granted for the order in which loop, while and else elements are ordered:

fun n: let (fact, _) = loop (acc, i) = (acc*i, i-1) while i > 0 else (1, n)
fun n: let (fact, _) = while i > 0 loop (acc, i) = (acc*i, i-1) else (1, n)
fun n: let (fact, _) = else (1, n) while i > 0 loop (acc, i) = (acc*i, i-1)

The first and second versions seem more naturally readable, the last one follows "natural evaluation order" more closely.

It might also be sensible to accept let loop (vars) = XXX while C else X0 as a shortcut for let (vars) = loop (vars) = XXX while C else X0

Type syntax

Types can be created at the beginning of the contract file. We've already seen the syntax to create labelled product types type name = Label_0 field_type_0 * ... * Label_n field_type_n, and sum types type name = Label_0: case_type_0 * ... * Label_n: case_type_n. Type aliases can also be created, with the notation type name = type.

Type can be polymorphic, i.e. take type parameters. Beware, however, that since Michelson is not polymorphic, some valid Lamtez programs will be rejected by the compiler. Type parameters are passed between the name and the = sign. Lists are encoded that way in Lamtez.


type option a = None unit + Some a  # Actually predeclared
type pair a b = (a * b)  # Actually predeclared
type assoc_list k v = list (pair k v)

Type annotations can be the following:

  • an identifier, i.e. the name of an alias, a sum type, a product type or a primitive.

  • if an identifier is polymorphic, as the option example above, it must receive the corresponding number of parameters after it. For instance, nat is a valid type, so is list int or list (pair string int), but list or pair int are not valid.

  • Tuples are represented as types, separated with * and surrounded by parentheses, e.g. (int * int) or (int*list a*tez).

  • functions types are denoted parameter_type -> result_type. The arrow is right associative, and multi-parameter functions are encoded as curried (nested) lambda terms. For instance, a function from two ints to a string has type int -> int -> string.


A contract with parameter type p, and result type r is represented in a file as a sequence of type declarations, then a sequence of store field declarations, then an expression of type p -> r. The


type operation = Withdrawal tez + GetBalance unit + Deposit tez

@store :: tez

fun amount operation:
  case operation
  | Withdrawal a: @store <- @store - a; None
  | GetBalance:   Some storage
  | Deposit:      @store <- @store + self-amount




The primitives are listed here, with their corresponding Michelson opcode as a title.


contract-call is the equivalent of TRANSFER_TOKEN, and as this opcode, it can only be called within very specific constraints, enforced by Michelson to make some classes of error harder to write: It cannot be in a function, and no variable existing before the call canbe used after.

contract-call: ∀ param result: contract param result → param → tez  → result

Other primitives TODO

type zero     = (+)
type unit     = (*)
type option a = None+Somea
type bool     = False + True
type list a   = Nil + Cons (a * (list a))
type account  = (contract unit unit)

val contract-call           :: ∀ param result:
    contract param result -> param -> tez -> result
val contract-create         :: ∀ param storage result:
    key -> option key -> bool -> bool -> tez ->
    (param * storage) -> (result * storage) -> storage -> contract param result
val contract-create-account :: key -> option key -> bool -> tez -> account
val contract-get            :: key -> account
val contract-manager        :: ∀ param storage: contract param storage -> key

val crypto-check :: key -> sig -> string -> bool
val crypto-hash  :: ∀ a: a -> string

val fail :: fail

val list-map    :: ∀ a b: list a -> (a -> b) -> list b
val list-reduce :: ∀ a acc: list a -> acc -> (a -> acc -> acc) -> acc

val map-get    :: ∀ k v: k -> map k v -> option v
val map-map    :: ∀ k v0 v1: map k v0 -> (k -> v0 -> v1) -> map k v1
val map-mem    :: ∀ k v: k -> map k v -> bool
val map-reduce :: ∀ k v acc: map k v -> acc -> (k -> v -> acc -> acc) -> acc
val map-update :: ∀ k v: k -> option v -> map k v -> map k v

val self-amount         :: tez
val self-balance        :: tez
val self-contract       :: ∀ param result: contract param result
val self-now            :: time
val self-source         :: ∀ param result: contract param result
val self-steps-to-quota :: nat

val set-map    :: ∀ a b: set a -> (a -> b) -> set b
val set-mem    :: ∀ elt: set elt -> elt -> bool
val set-reduce :: ∀ elt acc: set elt -> acc -> (elt -> acc -> acc) -> acc
val set-update :: ∀ elt: elt -> bool -> set elt


An ML-inspired smart contract language, compiling to Tezos' Michelson VM





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