# Michelson: the language of Smart Contracts in Tezos¶

The language is stack-based, with high level data types and primitives and strict static type checking. Its design cherry picks traits from several language families. Vigilant readers will notice direct references to Forth, Scheme, ML and Cat.

A Michelson program is a series of instructions that are run in sequence: each instruction receives as input the stack resulting of the previous instruction, and rewrites it for the next one. The stack contains both immediate values and heap allocated structures. All values are immutable and garbage collected.

A Michelson program receives as input a stack containing a single pair whose first element is an input value and second element the content of a storage space. It must return a stack containing a single pair whose first element is a list of internal operations, and second element the new contents of the storage space. Alternatively, a Michelson program can fail, explicitly using a specific opcode, or because something went wrong that could not be caught by the type system (e.g. division by zero, gas exhaustion).

The types of the input, output and storage are fixed and monomorphic, and the program is typechecked before being introduced into the system. No smart contract execution can fail because an instruction has been executed on a stack of unexpected length or contents.

This specification gives the complete instruction set, type system and semantics of the language. It is meant as a precise reference manual, not an easy introduction. Even though, some examples are provided at the end of the document and can be read first or at the same time as the specification.

## Semantics¶

This specification gives a detailed formal semantics of the Michelson language. It explains in a symbolic way the computation performed by the Michelson interpreter on a given program and initial stack to produce the corresponding resulting stack. The Michelson interpreter is a pure function: it only builds a result stack from the elements of an initial one, without affecting its environment. This semantics is then naturally given in what is called a big step form: a symbolic definition of a recursive reference interpreter. This definition takes the form of a list of rules that cover all the possible inputs of the interpreter (program and stack), and describe the computation of the corresponding resulting stacks.

### Rules form and selection¶

The rules have the main following form.

```
> (syntax pattern) / (initial stack pattern) => (result stack pattern)
iff (conditions)
where (recursions)
and (more recursions)
```

The left hand side of the `=>`

sign is used for selecting the rule.
Given a program and an initial stack, one (and only one) rule can be
selected using the following process. First, the toplevel structure of
the program must match the syntax pattern. This is quite simple since
there is only a few non trivial patterns to deal with instruction
sequences, and the rest is made of trivial pattern that match one
specific instruction. Then, the initial stack must match the initial
stack pattern. Finally, some rules add extra conditions over the values
in the stack that follow the `iff`

keyword. Sometimes, several rules
may apply in a given context. In this case, the one that appears first
in this specification is to be selected. If no rule applies, the result
is equivalent to the one for the explicit `FAILWITH`

instruction. This
case does not happen on well-typed programs, as explained in the next
section.

The right hand side describes the result of the interpreter if the rule
applies. It consists in a stack pattern, whose parts are either
constants, or elements of the context (program and initial stack) that
have been named on the left hand side of the `=>`

sign.

### Recursive rules (big step form)¶

Sometimes, the result of interpreting a program is derived from the result of interpreting another one (as in conditionals or function calls). In these cases, the rule contains a clause of the following form.

```
where (intermediate program) / (intermediate stack) => (partial result)
```

This means that this rules applies in case interpreting the intermediate state on the left gives the pattern on the right.

The left hand sign of the `=>`

sign is constructed from elements of
the initial state or other partial results, and the right hand side
identify parts that can be used to build the result stack of the rule.

If the partial result pattern does not actually match the result of the
interpretation, then the result of the whole rule is equivalent to the
one for the explicit `FAILWITH`

instruction. Again, this case does not
happen on well-typed programs, as explained in the next section.

### Format of patterns¶

Code patterns are of one of the following syntactical forms.

`INSTR`

(an uppercase identifier) is a simple instruction (e.g.`DROP`

).`INSTR (arg) ...`

is a compound instruction, whose arguments can be code, data or type patterns (e.g.`PUSH nat 3`

).`{ (instr) ; ... }`

is a possibly empty sequence of instructions, (e.g.`IF { SWAP ; DROP } { DROP }`

), nested sequences can drop the braces.`name`

is a pattern that matches any program and names a part of the matched program that can be used to build the result.`_`

is a pattern that matches any instruction.

Stack patterns are of one of the following syntactical forms.

`[FAILED]`

is the special failed state.`[]`

is the empty stack.`(top) : (rest)`

is a stack whose top element is matched by the data pattern`(top)`

on the left, and whose remaining elements are matched by the stack pattern`(rest)`

on the right (e.g.`x : y : rest`

).`name`

is a pattern that matches any stack and names it in order to use it to build the result.`_`

is a pattern that matches any stack.

Data patterns are of one of the following syntactical forms.

- integer/natural number literals, (e.g.
`3`

). - string literals, (e.g.
`"contents"`

). - raw byte sequence literals (e.g.
`0xABCDEF42`

). `Tag`

(capitalized) is a symbolic constant, (e.g.`Unit`

,`True`

,`False`

).`(Tag (arg) ...)`

tagged constructed data, (e.g.`(Pair 3 4)`

).- a code pattern for first class code values.
`name`

to name a value in order to use it to build the result.`_`

to match any value.

The domain of instruction names, symbolic constants and data constructors is fixed by this specification. Michelson does not let the programmer introduce its own types.

Be aware that the syntax used in the specification may differ a bit from the concrete syntax. In particular some instructions are annotated with types that are not present in the concrete language because they are synthesized by the typechecker.

### Shortcuts¶

Sometimes, it is easier to think (and shorter to write) in terms of program rewriting than in terms of big step semantics. When it is the case, and when both are equivalents, we write rules of the form:

```
p / S => S''
where p' / S' => S''
```

using the following shortcut:

```
p / S => p' / S'
```

The concrete language also has some syntax sugar to group some common sequences of operations as one. This is described in this specification using a simple regular expression style recursive instruction rewriting.

## Introduction to the type system and notations¶

This specification describes a type system for Michelson. To make things clear, in particular to readers that are not accustomed to reading formal programming language specifications, it does not give a typechecking or inference algorithm. It only gives an intentional definition of what we consider to be well-typed programs. For each syntactical form, it describes the stacks that are considered well-typed inputs, and the resulting outputs.

The type system is sound, meaning that if a program can be given a type, then if run on a well-typed input stack, the interpreter will never apply an interpretation rule on a stack of unexpected length or contents. Also, it will never reach a state where it cannot select an appropriate rule to continue the execution. Well-typed programs do not block, and do not go wrong.

### Type notations¶

The specification introduces notations for the types of values, terms and stacks. Apart from a subset of value types that appear in the form of type annotations in some places throughout the language, it is important to understand that this type language only exists in the specification.

A stack type can be written:

`[]`

for the empty stack.`(top) : (rest)`

for the stack whose first value has type`(top)`

and queue has stack type`(rest)`

.

Instructions, programs and primitives of the language are also typed, their types are written:

```
(type of stack before) -> (type of stack after)
```

The types of values in the stack are written:

`identifier`

for a primitive data-type (e.g.`bool`

).`identifier (arg)`

for a parametric data-type with one parameter type`(arg)`

(e.g.`list nat`

).`identifier (arg) ...`

for a parametric data-type with several parameters (e.g.`map string int`

).`[ (type of stack before) -> (type of stack after) ]`

for a code quotation, (e.g.`[ int : int : [] -> int : [] ]`

).`lambda (arg) (ret)`

is a shortcut for`[ (arg) : [] -> (ret) : [] ]`

.

### Meta type variables¶

The typing rules introduce meta type variables. To be clear, this has
nothing to do with polymorphism, which Michelson does not have. These
variables only live at the specification level, and are used to express
the consistency between the parts of the program. For instance, the
typing rule for the `IF`

construct introduces meta variables to
express that both branches must have the same type.

Here are the notations for meta type variables:

`'a`

for a type variable.`'A`

for a stack type variable.`_`

for an anonymous type or stack type variable.

### Typing rules¶

The system is syntax directed, which means here that it defines a single typing rule for each syntax construct. A typing rule restricts the type of input stacks that are authorized for this syntax construct, links the output type to the input type, and links both of them to the subexpressions when needed, using meta type variables.

Typing rules are of the form:

```
(syntax pattern)
:: (type of stack before) -> (type of stack after) [rule-name]
iff (premises)
```

Where premises are typing requirements over subprograms or values in the
stack, both of the form `(x) :: (type)`

, meaning that value `(x)`

must have type `(type)`

.

A program is shown well-typed if one can find an instance of a rule that applies to the toplevel program expression, with all meta type variables replaced by non variable type expressions, and of which all type requirements in the premises can be proven well-typed in the same manner. For the reader unfamiliar with formal type systems, this is called building a typing derivation.

Here is an example typing derivation on a small program that computes
`(x+5)*10`

for a given input `x`

, obtained by instantiating the
typing rules for instructions `PUSH`

, `ADD`

and for the sequence, as
found in the next sections. When instantiating, we replace the `iff`

with `by`

.

```
{ PUSH nat 5 ; ADD ; PUSH nat 10 ; SWAP ; MUL }
:: [ nat : [] -> nat : [] ]
by { PUSH nat 5 ; ADD }
:: [ nat : [] -> nat : [] ]
by PUSH nat 5
:: [ nat : [] -> nat : nat : [] ]
by 5 :: nat
and ADD
:: [ nat : nat : [] -> nat : [] ]
and { PUSH nat 10 ; SWAP ; MUL }
:: [ nat : [] -> nat : [] ]
by PUSH nat 10
:: [ nat : [] -> nat : nat : [] ]
by 10 :: nat
and { SWAP ; MUL }
:: [ nat : nat : [] -> nat : [] ]
by SWAP
:: [ nat : nat : [] -> nat : nat : [] ]
and MUL
:: [ nat : nat : [] -> nat : [] ]
```

Producing such a typing derivation can be done in a number of manners, such as unification or abstract interpretation. In the implementation of Michelson, this is done by performing a recursive symbolic evaluation of the program on an abstract stack representing the input type provided by the programmer, and checking that the resulting symbolic stack is consistent with the expected result, also provided by the programmer.

### Side note¶

As with most type systems, it is incomplete. There are programs that cannot be given a type in this type system, yet that would not go wrong if executed. This is a necessary compromise to make the type system usable. Also, it is important to remember that the implementation of Michelson does not accept as many programs as the type system describes as well-typed. This is because the implementation uses a simple single pass typechecking algorithm, and does not handle any form of polymorphism.

## Core data types and notations¶

`string`

,`nat`

,`int`

and`bytes`

: The core primitive constant types.`bool`

: The type for booleans whose values are`True`

and`False`

.`unit`

: The type whose only value is`Unit`

, to use as a placeholder when some result or parameter is non necessary. For instance, when the only goal of a contract is to update its storage.`list (t)`

: A single, immutable, homogeneous linked list, whose elements are of type`(t)`

, and that we note`{}`

for the empty list or`{ first ; ... }`

. In the semantics, we use chevrons to denote a subsequence of elements. For instance`{ head ; <tail> }`

.`pair (l) (r)`

: A pair of values`a`

and`b`

of types`(l)`

and`(r)`

, that we write`(Pair a b)`

.`option (t)`

: Optional value of type`(t)`

that we note`None`

or`(Some v)`

.`or (l) (r)`

: A union of two types: a value holding either a value`a`

of type`(l)`

or a value`b`

of type`(r)`

, that we write`(Left a)`

or`(Right b)`

.`set (t)`

: Immutable sets of values of type`(t)`

that we note as lists`{ item ; ... }`

, of course with their elements unique, and sorted.`map (k) (t)`

: Immutable maps from keys of type`(k)`

of values of type`(t)`

that we note`{ Elt key value ; ... }`

, with keys sorted.`big_map (k) (t)`

: Lazily deserialized maps from keys of type`(k)`

of values of type`(t)`

that we note`{ Elt key value ; ... }`

, with keys sorted. These maps should be used if you intend to store large amounts of data in a map. They have higher gas costs than standard maps as data is lazily deserialized. You are limited to a single`big_map`

per program, which must appear on the left hand side of a pair in the contract’s storage.

## Core instructions¶

### Control structures¶

`FAILWITH`

: Explicitly abort the current program.‘a :: _ -> _

This special instruction aborts the current program exposing the top of the stack in its error message (first rule below). It makes the output useless since all subsequent instructions will simply ignore their usual semantics to propagate the failure up to the main result (second rule below). Its type is thus completely generic.

```
> FAILWITH / a : _ => [FAILED]
> _ / [FAILED] => [FAILED]
```

`{}`

: Empty sequence.

```
:: 'A -> 'A
> {} / SA => SA
```

`{ I ; C }`

: Sequence.

```
:: 'A -> 'C
iff I :: [ 'A -> 'B ]
C :: [ 'B -> 'C ]
> I ; C / SA => SC
where I / SA => SB
and C / SB => SC
```

`IF bt bf`

: Conditional branching.

```
:: bool : 'A -> 'B
iff bt :: [ 'A -> 'B ]
bf :: [ 'A -> 'B ]
> IF bt bf / True : S => bt / S
> IF bt bf / False : S => bf / S
```

`LOOP body`

: A generic loop.

```
:: bool : 'A -> 'A
iff body :: [ 'A -> bool : 'A ]
> LOOP body / True : S => body ; LOOP body / S
> LOOP body / False : S => S
```

`LOOP_LEFT body`

: A loop with an accumulator.

```
:: (or 'a 'b) : 'A -> 'b : 'A
iff body :: [ 'a : 'A -> (or 'a 'b) : 'A ]
> LOOP_LEFT body / (Left a) : S => body ; LOOP_LEFT body / a : S
> LOOP_LEFT body / (Right b) : S => b : S
```

`DIP code`

: Runs code protecting the top of the stack.

```
:: 'b : 'A -> 'b : 'C
iff code :: [ 'A -> 'C ]
> DIP code / x : S => x : S'
where code / S => S'
```

`EXEC`

: Execute a function from the stack.

```
:: 'a : lambda 'a 'b : 'C -> 'b : 'C
> EXEC / a : f : S => r : S
where f / a : [] => r : []
```

### Stack operations¶

`DROP`

: Drop the top element of the stack.

```
:: _ : 'A -> 'A
> DROP / _ : S => S
```

`DUP`

: Duplicate the top of the stack.

```
:: 'a : 'A -> 'a : 'a : 'A
> DUP / x : S => x : x : S
```

`SWAP`

: Exchange the top two elements of the stack.

```
:: 'a : 'b : 'A -> 'b : 'a : 'A
> SWAP / x : y : S => y : x : S
```

`PUSH 'a x`

: Push a constant value of a given type onto the stack.

```
:: 'A -> 'a : 'A
iff x :: 'a
> PUSH 'a x / S => x : S
```

`UNIT`

: Push a unit value onto the stack.

```
:: 'A -> unit : 'A
> UNIT / S => Unit : S
```

`LAMBDA 'a 'b code`

: Push a lambda with given parameter and return types onto the stack.

```
:: 'A -> (lambda 'a 'b) : 'A
> LAMBDA _ _ code / S => code : S
```

### Generic comparison¶

Comparison only works on a class of types that we call comparable. A
`COMPARE`

operation is defined in an ad hoc way for each comparable
type, but the result of compare is always an `int`

, which can in turn
be checked in a generic manner using the following combinators. The
result of `COMPARE`

is `0`

if the top two elements of the stack are
equal, negative if the first element in the stack is less than the
second, and positive otherwise.

`EQ`

: Checks that the top of the stack EQuals zero.

```
:: int : 'S -> bool : 'S
> EQ / 0 : S => True : S
> EQ / v : S => False : S
iff v <> 0
```

`NEQ`

: Checks that the top of the stack does Not EQual zero.

```
:: int : 'S -> bool : 'S
> NEQ / 0 : S => False : S
> NEQ / v : S => True : S
iff v <> 0
```

`LT`

: Checks that the top of the stack is Less Than zero.

```
:: int : 'S -> bool : 'S
> LT / v : S => True : S
iff v < 0
> LT / v : S => False : S
iff v >= 0
```

`GT`

: Checks that the top of the stack is Greater Than zero.

```
:: int : 'S -> bool : 'S
> GT / v : S => C / True : S
iff v > 0
> GT / v : S => C / False : S
iff v <= 0
```

`LE`

: Checks that the top of the stack is Less Than of Equal to zero.

```
:: int : 'S -> bool : 'S
> LE / v : S => True : S
iff v <= 0
> LE / v : S => False : S
iff v > 0
```

`GE`

: Checks that the top of the stack is Greater Than of Equal to zero.

```
:: int : 'S -> bool : 'S
> GE / v : S => True : S
iff v >= 0
> GE / v : S => False : S
iff v < 0
```

## Operations¶

### Operations on booleans¶

`OR`

```
:: bool : bool : 'S -> bool : 'S
> OR / x : y : S => (x | y) : S
```

`AND`

```
:: bool : bool : 'S -> bool : 'S
> AND / x : y : S => (x & y) : S
```

`XOR`

```
:: bool : bool : 'S -> bool : 'S
> XOR / x : y : S => (x ^ y) : S
```

`NOT`

```
:: bool : 'S -> bool : 'S
> NOT / x : S => ~x : S
```

### Operations on integers and natural numbers¶

Integers and naturals are arbitrary-precision, meaning the only size limit is fuel.

`NEG`

```
:: int : 'S -> int : 'S
:: nat : 'S -> int : 'S
> NEG / x : S => -x : S
```

`ABS`

```
:: int : 'S -> nat : 'S
> ABS / x : S => abs (x) : S
```

`ADD`

```
:: int : int : 'S -> int : 'S
:: int : nat : 'S -> int : 'S
:: nat : int : 'S -> int : 'S
:: nat : nat : 'S -> nat : 'S
> ADD / x : y : S => (x + y) : S
```

`SUB`

```
:: int : int : 'S -> int : 'S
:: int : nat : 'S -> int : 'S
:: nat : int : 'S -> int : 'S
:: nat : nat : 'S -> int : 'S
> SUB / x : y : S => (x - y) : S
```

`MUL`

```
:: int : int : 'S -> int : 'S
:: int : nat : 'S -> int : 'S
:: nat : int : 'S -> int : 'S
:: nat : nat : 'S -> nat : 'S
> MUL / x : y : S => (x * y) : S
```

`EDIV`

Perform Euclidian division

```
:: int : int : 'S -> option (pair int nat) : 'S
:: int : nat : 'S -> option (pair int nat) : 'S
:: nat : int : 'S -> option (pair int nat) : 'S
:: nat : nat : 'S -> option (pair nat nat) : 'S
> EDIV / x : 0 : S => None : S
> EDIV / x : y : S => Some (Pair (x / y) (x % y)) : S
iff y <> 0
```

Bitwise logical operators are also available on unsigned integers.

`OR`

```
:: nat : nat : 'S -> nat : 'S
> OR / x : y : S => (x | y) : S
```

`AND`

(also available when the top operand is signed)

```
:: nat : nat : 'S -> nat : 'S
:: int : nat : 'S -> nat : 'S
> AND / x : y : S => (x & y) : S
```

`XOR`

```
:: nat : nat : 'S -> nat : 'S
> XOR / x : y : S => (x ^ y) : S
```

`NOT`

The return type of`NOT`

is an`int`

and not a`nat`

. This is because the sign is also negated. The resulting integer is computed using two’s complement. For instance, the boolean negation of`0`

is`-1`

. To get a natural back, a possibility is to use`AND`

with an unsigned mask afterwards.

```
:: nat : 'S -> int : 'S
:: int : 'S -> int : 'S
> NOT / x : S => ~x : S
```

`LSL`

```
:: nat : nat : 'S -> nat : 'S
> LSL / x : s : S => (x << s) : S
iff s <= 256
> LSL / x : s : S => [FAILED]
iff s > 256
```

`LSR`

```
:: nat : nat : 'S -> nat : 'S
> LSR / x : s : S => (x >> s) : S
iff s <= 256
> LSR / x : s : S => [FAILED]
iff s > 256
```

`COMPARE`

: Integer/natural comparison

```
:: int : int : 'S -> int : 'S
:: nat : nat : 'S -> int : 'S
> COMPARE / x : y : S => -1 : S
iff x < y
> COMPARE / x : y : S => 0 : S
iff x = y
> COMPARE / x : y : S => 1 : S
iff x > y
```

### Operations on strings¶

Strings are mostly used for naming things without having to rely on external ID databases. They are restricted to the printable subset of 7-bit ASCII, plus some escaped characters (see section on constants). So what can be done is basically use string constants as is, concatenate or splice them, and use them as keys.

`CONCAT`

: String concatenation.

```
:: string : string : 'S -> string : 'S
> CONCAT / s : t : S => (s ^ t) : S
:: string list : 'S -> string : 'S
> CONCAT / {} : S => "" : S
> CONCAT / { s ; <ss> } : S => (s ^ r) : S
where CONCAT / { <ss> } : S => r : S
```

`SIZE`

: number of characters in a string.

```
:: string : 'S -> nat : 'S
```

`SLICE`

: String access.

```
:: nat : nat : string : 'S -> option string : 'S
> SLICE / offset : length : s : S => Some ss : S
where ss is the substring of s at the given offset and of the given length
iff offset and (offset + length) are in bounds
> SLICE / offset : length : s : S => None : S
iff offset or (offset + length) are out of bounds
```

`COMPARE`

: Lexicographic comparison.

```
:: string : string : 'S -> int : 'S
> COMPARE / s : t : S => -1 : S
iff s < t
> COMPARE / s : t : S => 0 : S
iff s = t
> COMPARE / s : t : S => 1 : S
iff s > t
```

### Operations on pairs¶

`PAIR`

: Build a pair from the stack’s top two elements.

```
:: 'a : 'b : 'S -> pair 'a 'b : 'S
> PAIR / a : b : S => (Pair a b) : S
```

`CAR`

: Access the left part of a pair.

```
:: pair 'a _ : 'S -> 'a : 'S
> CAR / (Pair a _) : S => a : S
```

`CDR`

: Access the right part of a pair.

```
:: pair _ 'b : 'S -> 'b : 'S
> CDR / (Pair _ b) : S => b : S
```

### Operations on sets¶

`EMPTY_SET 'elt`

: Build a new, empty set for elements of a given type.The

`'elt`

type must be comparable (the`COMPARE`

primitive must be defined over it).

```
:: 'S -> set 'elt : 'S
> EMPTY_SET _ / S => {} : S
```

`MEM`

: Check for the presence of an element in a set.

```
:: 'elt : set 'elt : 'S -> bool : 'S
> MEM / x : {} : S => false : S
> MEM / x : { hd ; <tl> } : S => r : S
iff COMPARE / x : hd : [] => 1 : []
where MEM / x : { <tl> } : S => r : S
> MEM / x : { hd ; <tl> } : S => true : S
iff COMPARE / x : hd : [] => 0 : []
> MEM / x : { hd ; <tl> } : S => false : S
iff COMPARE / x : hd : [] => -1 : []
```

`UPDATE`

: Inserts or removes an element in a set, replacing a previous value.

```
:: 'elt : bool : set 'elt : 'S -> set 'elt : 'S
> UPDATE / x : false : {} : S => {} : S
> UPDATE / x : true : {} : S => { x } : S
> UPDATE / x : v : { hd ; <tl> } : S => { hd ; <tl'> } : S
iff COMPARE / x : hd : [] => 1 : []
where UPDATE / x : v : { <tl> } : S => { <tl'> } : S
> UPDATE / x : false : { hd ; <tl> } : S => { <tl> } : S
iff COMPARE / x : hd : [] => 0 : []
> UPDATE / x : true : { hd ; <tl> } : S => { hd ; <tl> } : S
iff COMPARE / x : hd : [] => 0 : []
> UPDATE / x : false : { hd ; <tl> } : S => { hd ; <tl> } : S
iff COMPARE / x : hd : [] => -1 : []
> UPDATE / x : true : { hd ; <tl> } : S => { x ; hd ; <tl> } : S
iff COMPARE / x : hd : [] => -1 : []
```

`ITER body`

: Apply the body expression to each element of a set. The body sequence has access to the stack.

```
:: (set 'elt) : 'A -> 'A
iff body :: [ 'elt : 'A -> 'A ]
> ITER body / {} : S => S
> ITER body / { hd ; <tl> } : S => body; ITER body / hd : { <tl> } : S
```

`SIZE`

: Get the cardinality of the set.

```
:: set 'elt : 'S -> nat : 'S
> SIZE / {} : S => 0 : S
> SIZE / { _ ; <tl> } : S => 1 + s : S
where SIZE / { <tl> } : S => s : S
```

### Operations on maps¶

`EMPTY_MAP 'key 'val`

: Build a new, empty map from keys of a given type to values of another given type.The

`'key`

type must be comparable (the`COMPARE`

primitive must be defined over it).

```
:: 'S -> map 'key 'val : 'S
> EMPTY_MAP _ _ / S => {} : S
```

`GET`

: Access an element in a map, returns an optional value to be checked with`IF_SOME`

.

```
:: 'key : map 'key 'val : 'S -> option 'val : 'S
> GET / x : {} : S => None : S
> GET / x : { Elt k v ; <tl> } : S => opt_y : S
iff COMPARE / x : k : [] => 1 : []
where GET / x : { <tl> } : S => opt_y : S
> GET / x : { Elt k v ; <tl> } : S => Some v : S
iff COMPARE / x : k : [] => 0 : []
> GET / x : { Elt k v ; <tl> } : S => None : S
iff COMPARE / x : k : [] => -1 : []
```

`MEM`

: Check for the presence of a binding for a key in a map.

```
:: 'key : map 'key 'val : 'S -> bool : 'S
> MEM / x : {} : S => false : S
> MEM / x : { Elt k v ; <tl> } : S => r : S
iff COMPARE / x : k : [] => 1 : []
where MEM / x : { <tl> } : S => r : S
> MEM / x : { Elt k v ; <tl> } : S => true : S
iff COMPARE / x : k : [] => 0 : []
> MEM / x : { Elt k v ; <tl> } : S => false : S
iff COMPARE / x : k : [] => -1 : []
```

`UPDATE`

: Assign or remove an element in a map.

```
:: 'key : option 'val : map 'key 'val : 'S -> map 'key 'val : 'S
> UPDATE / x : None : {} : S => {} : S
> UPDATE / x : Some y : {} : S => { Elt x y } : S
> UPDATE / x : opt_y : { Elt k v ; <tl> } : S => { Elt k v ; <tl'> } : S
iff COMPARE / x : k : [] => 1 : []
where UPDATE / x : opt_y : { <tl> } : S => { <tl'> } : S
> UPDATE / x : None : { Elt k v ; <tl> } : S => { <tl> } : S
iff COMPARE / x : k : [] => 0 : []
> UPDATE / x : Some y : { Elt k v ; <tl> } : S => { Elt k y ; <tl> } : S
iff COMPARE / x : k : [] => 0 : []
> UPDATE / x : None : { Elt k v ; <tl> } : S => { Elt k v ; <tl> } : S
iff COMPARE / x : k : [] => -1 : []
> UPDATE / x : Some y : { Elt k v ; <tl> } : S => { Elt x y ; Elt k v ; <tl> } : S
iff COMPARE / x : k : [] => -1 : []
```

`MAP body`

: Apply the body expression to each element of a map. The body sequence has access to the stack.

```
:: (map 'key 'val) : 'A -> (map 'key 'b) : 'A
iff body :: [ (pair 'key 'val) : 'A -> 'b : 'A ]
> MAP body / {} : S => {} : S
> MAP body / { Elt k v ; <tl> } : S => { Elt k (body (Pair k v)) ; <tl'> } : S
where MAP body / { <tl> } : S => { <tl'> } : S
```

`ITER body`

: Apply the body expression to each element of a map. The body sequence has access to the stack.

```
:: (map 'elt 'val) : 'A -> 'A
iff body :: [ (pair 'elt 'val : 'A) -> 'A ]
> ITER body / {} : S => S
> ITER body / { Elt k v ; <tl> } : S => body ; ITER body / (Pair k v) : { <tl> } : S
```

`SIZE`

: Get the cardinality of the map.

```
:: map 'key 'val : 'S -> nat : 'S
> SIZE / {} : S => 0 : S
> SIZE / { _ ; <tl> } : S => 1 + s : S
where SIZE / { <tl> } : S => s : S
```

### Operations on `big_maps`

¶

The behavior of these operations is the same as if they were normal maps, except that under the hood, the elements are loaded and deserialized on demand.

`GET`

: Access an element in a`big_map`

, returns an optional value to be checked with`IF_SOME`

.

```
:: 'key : big_map 'key 'val : 'S -> option 'val : 'S
```

`MEM`

: Check for the presence of an element in a`big_map`

.

```
:: 'key : big_map 'key 'val : 'S -> bool : 'S
```

`UPDATE`

: Assign or remove an element in a`big_map`

.

```
:: 'key : option 'val : big_map 'key 'val : 'S -> big_map 'key 'val : 'S
```

### Operations on optional values¶

`SOME`

: Pack a present optional value.

```
:: 'a : 'S -> option 'a : 'S
> SOME / v : S => (Some v) : S
```

`NONE 'a`

: The absent optional value.

```
:: 'S -> option 'a : 'S
> NONE / v : S => None : S
```

`IF_NONE bt bf`

: Inspect an optional value.

```
:: option 'a : 'A -> 'B
iff bt :: [ 'A -> 'B]
bf :: [ 'a : 'A -> 'B]
> IF_NONE bt bf / (None) : S => bt / S
> IF_NONE bt bf / (Some a) : S => bf / a : S
```

### Operations on unions¶

`LEFT 'b`

: Pack a value in a union (left case).

```
:: 'a : 'S -> or 'a 'b : 'S
> LEFT / v : S => (Left v) : S
```

`RIGHT 'a`

: Pack a value in a union (right case).

```
:: 'b : 'S -> or 'a 'b : 'S
> RIGHT / v : S => (Right v) : S
```

`IF_LEFT bt bf`

: Inspect a value of a union.

```
:: or 'a 'b : 'A -> 'B
iff bt :: [ 'a : 'A -> 'B]
bf :: [ 'b : 'A -> 'B]
> IF_LEFT bt bf / (Left a) : S => bt / a : S
> IF_LEFT bt bf / (Right b) : S => bf / b : S
```

`IF_RIGHT bt bf`

: Inspect a value of a union.

```
:: or 'a 'b : 'A -> 'B
iff bt :: [ 'b : 'A -> 'B]
bf :: [ 'a : 'A -> 'B]
> IF_RIGHT bt bf / (Right b) : S => bt / b : S
> IF_RIGHT bt bf / (Left a) : S => bf / a : S
```

### Operations on lists¶

`CONS`

: Prepend an element to a list.

```
:: 'a : list 'a : 'S -> list 'a : 'S
> CONS / a : { <l> } : S => { a ; <l> } : S
```

`NIL 'a`

: The empty list.

```
:: 'S -> list 'a : 'S
> NIL / S => {} : S
```

`IF_CONS bt bf`

: Inspect a list.

```
:: list 'a : 'A -> 'B
iff bt :: [ 'a : list 'a : 'A -> 'B]
bf :: [ 'A -> 'B]
> IF_CONS bt bf / { a ; <rest> } : S => bt / a : { <rest> } : S
> IF_CONS bt bf / {} : S => bf / S
```

`MAP body`

: Apply the body expression to each element of the list. The body sequence has access to the stack.

```
:: (list 'elt) : 'A -> (list 'b) : 'A
iff body :: [ 'elt : 'A -> 'b : 'A ]
> MAP body / { a ; <rest> } : S => { body a ; <rest'> } : S
where MAP body / { <rest> } : S => { <rest'> } : S
> MAP body / {} : S => {} : S
```

`SIZE`

: Get the number of elements in the list.

```
:: list 'elt : 'S -> nat : 'S
> SIZE / { _ ; <rest> } : S => 1 + s : S
where SIZE / { <rest> } : S => s : S
> SIZE / {} : S => 0 : S
```

`ITER body`

: Apply the body expression to each element of a list. The body sequence has access to the stack.

```
:: (list 'elt) : 'A -> 'A
iff body :: [ 'elt : 'A -> 'A ]
> ITER body / { a ; <rest> } : S => body ; ITER body / a : { <rest> } : S
> ITER body / {} : S => S
```

## Domain specific data types¶

`timestamp`

: Dates in the real world.`mutez`

: A specific type for manipulating tokens.`contract 'param`

: A contract, with the type of its code.`address`

: An untyped contract address.`operation`

: An internal operation emitted by a contract.`key`

: A public cryptography key.`key_hash`

: The hash of a public cryptography key.`signature`

: A cryptographic signature.

## Domain specific operations¶

### Operations on timestamps¶

Current Timestamps can be obtained by the `NOW`

operation, or
retrieved from script parameters or globals.

`ADD`

Increment / decrement a timestamp of the given number of seconds.

```
:: timestamp : int : 'S -> timestamp : 'S
:: int : timestamp : 'S -> timestamp : 'S
> ADD / seconds : nat (t) : S => (seconds + t) : S
> ADD / nat (t) : seconds : S => (t + seconds) : S
```

`SUB`

Subtract a number of seconds from a timestamp.

```
:: timestamp : int : 'S -> timestamp : 'S
> SUB / seconds : nat (t) : S => (seconds - t) : S
```

`SUB`

Subtract two timestamps.

```
:: timestamp : timestamp : 'S -> int : 'S
> SUB / seconds(t1) : seconds(t2) : S => (t1 - t2) : S
```

`COMPARE`

: Timestamp comparison.

```
:: timestamp : timestamp : 'S -> int : 'S
> COMPARE / seconds(t1) : seconds(t2) : S => -1 : S
iff t1 < t2
> COMPARE / seconds(t1) : seconds(t2) : S => 0 : S
iff t1 = t2
> COMPARE / seconds(t1) : seconds(t2) : S => 1 : S
iff t1 > t2
```

### Operations on Mutez¶

Mutez (micro-Tez) are internally represented by a 64 bit signed integers. There are restrictions to prevent creating a negative amount of mutez. Operations are limited to prevent overflow and mixing them with other numerical types by mistake. They are also mandatory checked for under/overflows.

`ADD`

```
:: mutez : mutez : 'S -> mutez : 'S
> ADD / x : y : S => [FAILED] on overflow
> ADD / x : y : S => (x + y) : S
```

`SUB`

```
:: mutez : mutez : 'S -> mutez : 'S
> SUB / x : y : S => [FAILED]
iff x < y
> SUB / x : y : S => (x - y) : S
```

`MUL`

```
:: mutez : nat : 'S -> mutez : 'S
:: nat : mutez : 'S -> mutez : 'S
> MUL / x : y : S => [FAILED] on overflow
> MUL / x : y : S => (x * y) : S
```

`EDIV`

```
:: mutez : nat : 'S -> option (pair mutez mutez) : 'S
:: mutez : mutez : 'S -> option (pair nat mutez) : 'S
> EDIV / x : 0 : S => None
> EDIV / x : y : S => Some (Pair (x / y) (x % y)) : S
iff y <> 0
```

`COMPARE`

```
:: mutez : mutez : 'S -> int : 'S
> COMPARE / x : y : S => -1 : S
iff x < y
> COMPARE / x : y : S => 0 : S
iff x = y
> COMPARE / x : y : S => 1 : S
iff x > y
```

### Operations on contracts¶

`CREATE_CONTRACT { storage 'g ; parameter 'p ; code ... }`

: Forge a new contract from a literal.

```
:: key_hash : option key_hash : bool : bool : mutez : 'g : 'S
-> operation : address : 'S
```

Originate a contract based on a literal. This is currently the only way
to include transfers inside of an originated contract. The first
parameters are the manager, optional delegate, then spendable and
delegatable flags and finally the initial amount taken from the
currently executed contract. The contract is returned as a first class
value (to be dropped, passed as parameter or stored).
The `CONTRACT 'p`

instruction will fail until it is actually originated.

`CREATE_ACCOUNT`

: Forge an account (a contract without code) creation operation.

```
:: key_hash : option key_hash : bool : mutez : 'S
-> operation : address : 'S
```

Take as argument the manager, optional delegate, the delegatable flag and finally the initial amount taken from the currently executed contract.

`TRANSFER_TOKENS`

: Forge a transaction.

```
:: 'p : mutez : contract 'p : 'S -> operation : 'S
```

The parameter must be consistent with the one expected by the contract, unit for an account.

`SET_DELEGATE`

: Forge a delegation.

```
:: option key_hash : 'S -> operation : 'S
```

`BALANCE`

: Push the current amount of mutez of the current contract.

```
:: 'S -> mutez : 'S
```

`ADDRESS`

: Push the address of a contract.

```
:: contract _ : 'S -> address : 'S
```

`CONTRACT 'p`

: Push the untyped version of a contract.

```
:: address : 'S -> option (contract 'p) : 'S
> CONTRACT / addr : S => Some addr : S
iff addr exists and is a contract of parameter type 'p
> CONTRACT / addr : S => Some addr : S
iff 'p = unit and addr is an implicit contract
> CONTRACT / addr : S => None : S
otherwise
```

`SOURCE`

: Push the contract that initiated the current transaction, i.e. the contract that paid the fees and storage cost, and whose manager signed the operation that was sent on the blockchain. Note that since`TRANSFER_TOKENS`

instructions can be chained,`SOURCE`

and`SENDER`

are not necessarily the same.

```
:: 'S -> address : 'S
```

`SENDER`

: Push the contract that initiated the current internal transaction. It may be the`SOURCE`

, but may also not if the source sent an order to an intermediate smart contract, which then called the current contract.

```
:: 'S -> address : 'S
```

`SELF`

: Push the current contract.

```
:: 'S -> contract 'p : 'S
where contract 'p is the type of the current contract
```

`AMOUNT`

: Push the amount of the current transaction.

```
:: 'S -> mutez : 'S
```

`IMPLICIT_ACCOUNT`

: Return a default contract with the given public/private key pair. Any funds deposited in this contract can immediately be spent by the holder of the private key. This contract cannot execute Michelson code and will always exist on the blockchain.

```
:: key_hash : 'S -> contract unit : 'S
```

### Special operations¶

`STEPS_TO_QUOTA`

: Push the remaining steps before the contract execution must terminate.

```
:: 'S -> nat : 'S
```

`NOW`

: Push the timestamp of the block whose validation triggered this execution (does not change during the execution of the contract).

```
:: 'S -> timestamp : 'S
```

### Operations on bytes¶

Bytes are used for serializing data, in order to check signatures and compute hashes on them. They can also be used to incorporate data from the wild and untyped outside world.

`PACK`

: Serializes a piece of data to its optimized binary representation.

```
:: 'a : 'S -> bytes : 'S
```

`UNPACK 'a`

: Deserializes a piece of data, if valid.

```
:: bytes : 'S -> option 'a : 'S
```

`CONCAT`

: Byte sequence concatenation.

```
:: bytes : bytes : 'S -> bytes : 'S
> CONCAT / s : t : S => (s ^ t) : S
:: bytes list : 'S -> bytes : 'S
> CONCAT / {} : S => 0x : S
> CONCAT / { s ; <ss> } : S => (s ^ r) : S
where CONCAT / { <ss> } : S => r : S
```

`SIZE`

: size of a sequence of bytes.

```
:: bytes : 'S -> nat : 'S
```

`SLICE`

: Bytes access.

```
:: nat : nat : bytes : 'S -> option bytes : 'S
> SLICE / offset : length : s : S => Some ss : S
where ss is the substring of s at the given offset and of the given length
iff offset and (offset + length) are in bounds
> SLICE / offset : length : s : S => None : S
iff offset or (offset + length) are out of bounds
```

`COMPARE`

: Lexicographic comparison.

```
:: bytes : bytes : 'S -> int : 'S
> COMPARE / s : t : S => -1 : S
iff s < t
> COMPARE / s : t : S => 0 : S
iff s = t
> COMPARE / s : t : S => 1 : S
iff s > t
```

### Cryptographic primitives¶

`HASH_KEY`

: Compute the b58check of a public key.

```
:: key : 'S -> key_hash : 'S
```

`BLAKE2B`

: Compute a cryptographic hash of the value contents using the Blake2B cryptographic hash function.

```
:: bytes : 'S -> bytes : 'S
```

`SHA256`

: Compute a cryptographic hash of the value contents using the Sha256 cryptographic hash function.

```
:: bytes : 'S -> bytes : 'S
```

`SHA512`

: Compute a cryptographic hash of the value contents using the Sha512 cryptographic hash function.

```
:: bytes : 'S -> bytes : 'S
```

`CHECK_SIGNATURE`

: Check that a sequence of bytes has been signed with a given key.

```
:: key : signature : bytes : 'S -> bool : 'S
```

`COMPARE`

:

```
:: key_hash : key_hash : 'S -> int : 'S
> COMPARE / x : y : S => -1 : S
iff x < y
> COMPARE / x : y : S => 0 : S
iff x = y
> COMPARE / x : y : S => 1 : S
iff x > y
```

## Macros¶

In addition to the operations above, several extensions have been added to the language’s concrete syntax. If you are interacting with the node via RPC, bypassing the client, which expands away these macros, you will need to desugar them yourself.

These macros are designed to be unambiguous and reversible, meaning that errors are reported in terms of desugared syntax. Below you’ll see these macros defined in terms of other syntactic forms. That is how these macros are seen by the node.

### Compare¶

Syntactic sugar exists for merging `COMPARE`

and comparison
combinators, and also for branching.

`CMP{EQ|NEQ|LT|GT|LE|GE}`

```
> CMP(\op) / S => COMPARE ; (\op) / S
```

`IF{EQ|NEQ|LT|GT|LE|GE} bt bf`

```
> IF(\op) bt bf / S => (\op) ; IF bt bf / S
```

`IFCMP{EQ|NEQ|LT|GT|LE|GE} bt bf`

```
> IFCMP(\op) / S => COMPARE ; (\op) ; IF bt bf / S
```

### Fail¶

The `FAIL`

macros is equivalent to `UNIT; FAILWITH`

and is callable
in any context since it does not use its input stack.

`FAIL`

```
> FAIL / S => UNIT; FAILWITH / S
```

### Assertion macros¶

All assertion operations are syntactic sugar for conditionals with a
`FAIL`

instruction in the appropriate branch. When possible, use them
to increase clarity about illegal states.

`ASSERT`

```
> ASSERT => IF {} {FAIL}
```

`ASSERT_{EQ|NEQ|LT|LE|GT|GE}`

```
> ASSERT_(\op) => IF(\op) {} {FAIL}
```

`ASSERT_CMP{EQ|NEQ|LT|LE|GT|GE}`

```
> ASSERT_CMP(\op) => IFCMP(\op) {} {FAIL}
```

`ASSERT_NONE`

```
> ASSERT_NONE => IF_NONE {} {FAIL}
```

`ASSERT_SOME`

```
> ASSERT_SOME @x => IF_NONE {FAIL} {RENAME @x}
```

`ASSERT_LEFT`

```
> ASSERT_LEFT @x => IF_LEFT {RENAME @x} {FAIL}
```

`ASSERT_RIGHT`

```
> ASSERT_RIGHT @x => IF_LEFT {FAIL} {RENAME @x}
```

### Syntactic Conveniences¶

These are macros are simply more convenient syntax for various common operations.

`DII+P code`

: A syntactic sugar for working deeper in the stack.

```
> DII(\rest=I*)P code / S => DIP (DI(\rest)P code) / S
```

`DUU+P`

: A syntactic sugar for duplicating the`n`

th element of the stack.

```
> DUU(\rest=U*)P / S => DIP (DU(\rest)P) ; SWAP / S
```

`P(\left=A|P(\left)(\right))(\right=I|P(\left)(\right))R`

: A syntactic sugar for building nested pairs.

```
> PA(\right)R / S => DIP ((\right)R) ; PAIR / S
> P(\left)IR / S => PAIR ; (\left)R / S
> P(\left)(\right)R => (\right)R ; (\left)R ; PAIR / S
```

A good way to quickly figure which macro to use is to mentally parse the
macro as `P`

for pair constructor, `A`

for left leaf and `I`

for
right leaf. The macro takes as many elements on the stack as there are
leaves and constructs a nested pair with the shape given by its name.

Take the macro `PAPPAIIR`

for instance:

```
P A P P A I I R
( l, ( ( l, r ), r ))
```

A typing rule can be inferred:

```
PAPPAIIR
:: 'a : 'b : 'c : 'd : 'S -> (pair 'a (pair (pair 'b 'c) 'd))
```

`UNP(\left=A|P(\left)(\right))(\right=I|P(\left)(\right))R`

: A syntactic sugar for destructing nested pairs. These macros follow the same convention as the previous one.

```
> UNPAIR / S => DUP ; CAR ; DIP { CDR } / S
> UNPA(\right)R / S => UNPAIR ; DIP (UN(\right)R) / S
> UNP(\left)IR / S => UNPAIR ; UN(\left)R / S
> UNP(\left)(\right)R => UNPAIR ; UN(\left)R ; UN(\right)R / S
```

`C[AD]+R`

: A syntactic sugar for accessing fields in nested pairs.

```
> CA(\rest=[AD]+)R / S => CAR ; C(\rest)R / S
> CD(\rest=[AD]+)R / S => CDR ; C(\rest)R / S
```

`IF_SOME bt bf`

: Inspect an optional value.

```
:: option 'a : 'A -> 'B
iff bt :: [ 'a : 'A -> 'B]
bf :: [ 'A -> 'B]
> IF_SOME / (Some a) : S => bt / a : S
> IF_SOME / (None) : S => bf / S
```

`SET_CAR`

: Set the left field of a pair.

```
> SET_CAR => CDR ; SWAP ; PAIR
```

`SET_CDR`

: Set the right field of a pair.

```
> SET_CDR => CAR ; PAIR
```

`SET_C[AD]+R`

: A syntactic sugar for setting fields in nested pairs.

```
> SET_CA(\rest=[AD]+)R / S =>
{ DUP ; DIP { CAR ; SET_C(\rest)R } ; CDR ; SWAP ; PAIR } / S
> SET_CD(\rest=[AD]+)R / S =>
{ DUP ; DIP { CDR ; SET_C(\rest)R } ; CAR ; PAIR } / S
```

`MAP_CAR`

code: Transform the left field of a pair.

```
> MAP_CAR code => DUP ; CDR ; DIP { CAR ; code } ; SWAP ; PAIR
```

`MAP_CDR`

code: Transform the right field of a pair.

```
> MAP_CDR code => DUP ; CDR ; code ; SWAP ; CAR ; PAIR
```

`MAP_C[AD]+R`

code: A syntactic sugar for transforming fields in nested pairs.

```
> MAP_CA(\rest=[AD]+)R code / S =>
{ DUP ; DIP { CAR ; MAP_C(\rest)R code } ; CDR ; SWAP ; PAIR } / S
> MAP_CD(\rest=[AD]+)R code / S =>
{ DUP ; DIP { CDR ; MAP_C(\rest)R code } ; CAR ; PAIR } / S
```

## Concrete syntax¶

The concrete language is very close to the formal notation of the specification. Its structure is extremely simple: an expression in the language can only be one of the four following constructs.

- An integer.
- A character string.
- The application of a primitive to a sequence of expressions.
- A sequence of expressions.

This simple four cases notation is called Micheline.

The encoding of a Micheline source file must be UTF-8, and non-ASCII characters can only appear in comments and strings.

### Constants¶

There are three kinds of constants:

- Integers or naturals in decimal notation.
- Strings, with some usual escape sequences:
`\n`

,`\\`

,`\"`

. Unescaped line-breaks (both`\n`

and`\r`

) cannot appear in a string. - Byte sequences in hexadecimal notation, prefixed with
`0x`

.

The current version of Michelson restricts strings to be the printable subset of 7-bit ASCII, namely charactes with codes from within [32, 126] range, plus the escaped characters mentioned above.

### Primitive applications¶

A primitive application is a name followed by arguments

```
prim arg1 arg2
```

When a primitive application is the argument to another primitive application, it must be wrapped with parentheses.

```
prim (prim1 arg11 arg12) (prim2 arg21 arg22)
```

### Sequences¶

Successive expression can be grouped as a single sequence expression using curly braces as delimiters and semicolon as separators.

```
{ expr1 ; expr2 ; expr3 ; expr4 }
```

A sequence can be passed as argument to a primitive.

```
prim arg1 arg2 { arg3_expr1 ; arg3_expr2 }
```

Primitive applications right inside a sequence cannot be wrapped.

```
{ (prim arg1 arg2) } # is not ok
```

### Indentation¶

To remove ambiguities for human readers, the parser enforces some indentation rules.

- For sequences:
- All expressions in a sequence must be aligned on the same column.
- An exception is made when consecutive expressions fit on the same line, as long as the first of them is correctly aligned.
- All expressions in a sequence must be indented to the right of the opening curly brace by at least one column.
- The closing curly brace cannot be on the left of the opening one.

- For primitive applications:
- All arguments in an application must be aligned on the same column.
- An exception is made when consecutive arguments fit on the same line, as long as the first of them is correctly aligned.
- All arguments in a sequence must be indented to the right of the primitive name by at least one column.

### Differences with the formal notation¶

The concrete syntax follows the same lexical conventions as the specification: instructions are represented by uppercase identifiers, type constructors by lowercase identifiers, and constant constructors are Capitalized.

All domain specific constants are Micheline constants with specific formats. Some have two variants accepted by the data type checker: a readable one in a string and an optimized.

`mutez`

amounts are written as naturals.`timestamp`

s are written either using`RFC3339`

notation in a string (readable), or as the number of seconds since Epoch in a natural (optimized).`contract`

s,`address`

es,`key`

s and`signature`

s are written as strings, in their usual Base58 encoded versions (readable), or as their raw bytes (optimized).

The optimized versions should not reach the RPCs, the protocol code will convert to optimized by itself when forging operations, storing to the database, and before hashing to get a canonical representation of a datum for a given type.

To prevent errors, control flow primitives that take instructions as parameters require sequences in the concrete syntax.

```
IF { instr1_true ; instr2_true ; ... }
{ instr1_false ; instr2_false ; ... }
```

### Main program structure¶

The toplevel of a smart contract file must be an un-delimited sequence
of three primitive applications (in no particular order) that provide its
`code`

, `parameter`

and `storage`

fields.

See the next section for a concrete example.

### Comments¶

A hash sign (`#`

) anywhere outside of a string literal will make the
rest of the line (and itself) completely ignored, as in the following
example.

```
{ PUSH nat 1 ; # pushes 1
PUSH nat 2 ; # pushes 2
ADD } # computes 2 + 1
```

Comments that span on multiple lines or that stop before the end of the
line can also be written, using C-like delimiters (`/* ... */`

).

## Annotations¶

The annotation mechanism of Michelson provides ways to better track data
on the stack and to give additional type constraints. Annotations are
only here to add constraints, *i.e.* they cannot turn an otherwise
rejected program into an accepted one.

Stack visualization tools like the Michelson’s Emacs mode print annotations associated with each type in the program, as propagated by the typechecker as well as variable annotations on the types of elements in the stack. This is useful as a debugging aid.

We distinguish three kinds of annotations:

- type annotations, written
`:type_annot`

, - variable annotations, written
`@var_annot`

, - and field or constructors annotations, written
`%field_annot`

.

### Type annotations¶

Each type can be annotated with at most one type annotation. They are used to give names to types. For types to be equal, their unnamed version must be equal and their names must be the same or at least one type must be unnamed.

For instance, the following Michelson program which put its integer parameter in the storage is not well typed:

```
parameter (int :p) ;
storage (int :s) ;
code { UNPAIR ; SWAP ; DROP ; NIL operation ; PAIR }
```

Whereas this one is:

```
parameter (int :p) ;
storage int ;
code { UNPAIR ; SWAP ; DROP ; NIL operation ; PAIR }
```

Inner components of composed typed can also be named.

```
(pair :point (int :x_pos) (int :y_pos))
```

Push-like instructions, that act as constructors, can also be given a type annotation. The stack type will then have a correspondingly named type on top.

```
UNIT :t
:: 'A -> (unit :t) : 'A
PAIR :t
:: 'a : 'b : 'S -> (pair :t 'a 'b) : 'S
SOME :t
:: 'a : 'S -> (option :t 'a) : 'S
NONE :t 'a
:: 'S -> (option :t 'a) : 'S
LEFT :t 'b
:: 'a : 'S -> (or :t 'a 'b) : 'S
RIGHT :t 'a
:: 'b : 'S -> (or :t 'a 'b) : 'S
NIL :t 'a
:: 'S -> (list :t 'a) : 'S
EMPTY_SET :t 'elt
:: 'S -> (set :t 'elt) : 'S
EMPTY_MAP :t 'key 'val
:: 'S -> (map :t 'key 'val) : 'S
```

A no-op instruction `CAST`

ensures the top of the stack has the
specified type, and change its type if it is compatible. In particular,
this allows to change or remove type names explicitly.

```
CAST 'b
:: 'a : 'S -> 'b : 'S
iff 'a = 'b
> CAST t / a : S => a : S
```

### Variable annotations¶

Variable annotations can only be used on instructions that produce
elements on the stack. An instruction that produces `n`

elements on
the stack can be given at most `n`

variable annotations.

The stack type contains both the types of each element in the stack, as well as an optional variable annotation for each element. In this sub-section we note:

`[]`

for the empty stack,`@annot (top) : (rest)`

for the stack whose first value has type`(top)`

and is annotated with variable annotation`@annot`

and whose queue has stack type`(rest)`

.

The instructions which do not accept any variable annotations are:

```
DROP
SWAP
IF_NONE
IF_LEFT
IF_CONS
ITER
IF
LOOP
LOOP_LEFT
DIP
FAILWITH
```

The instructions which accept at most one variable annotation are:

```
DUP
PUSH
UNIT
SOME
NONE
PAIR
CAR
CDR
LEFT
RIGHT
NIL
CONS
SIZE
MAP
MEM
EMPTY_SET
EMPTY_MAP
UPDATE
GET
LAMBDA
EXEC
ADD
SUB
CONCAT
MUL
OR
AND
XOR
NOT
ABS
IS_NAT
INT
NEG
EDIV
LSL
LSR
COMPARE
EQ
NEQ
LT
GT
LE
GE
ADDRESS
CONTRACT
SET_DELEGATE
IMPLICIT_ACCOUNT
NOW
AMOUNT
BALANCE
HASH_KEY
CHECK_SIGNATURE
BLAKE2B
STEPS_TO_QUOTA
SOURCE
SENDER
SELF
CAST
RENAME
```

The instructions which accept at most two variable annotations are:

```
CREATE_ACCOUNT
CREATE_CONTRACT
```

Annotations on instructions that produce multiple elements on the stack
will be used in order, where the first variable annotation is given to
the top-most element on the resulting stack. Instructions that produce
`n`

elements on the stack but are given less than `n`

variable
annotations will see only their top-most stack type elements annotated.

```
CREATE_ACCOUNT @op @addr
:: key_hash : option key_hash : bool : mutez : 'S
-> @op operation : @addr address : 'S
CREATE_ACCOUNT @op
:: key_hash : option key_hash : bool : mutez : 'S
-> @op operation : address : 'S
```

A no-op instruction `RENAME`

allows to rename variables in the stack
or to erase variable annotations in the stack.

```
RENAME @new
:: @old 'a ; 'S -> @new 'a : 'S
RENAME
:: @old 'a ; 'S -> 'a : 'S
```

### Field and constructor annotations¶

Components of pair types, option types and or types can be annotated with a field or constructor annotation. This feature is useful to encode records fields and constructors of sum types.

```
(pair :point
(int %x)
(int %y))
```

The previous Michelson type can be used as visual aid to represent the record type (given in OCaml-like syntax):

```
type point = { x : int ; y : int }
```

Similarly,

```
(or :t
(int %A)
(or
(bool %B)
(pair %C
(nat %n1)
(nat %n2))))
```

can be used to represent the algebraic data type (in OCaml-like syntax):

```
type t =
| A of int
| B of bool
| C of { n1 : nat ; n2 : nat }
```

Field annotations are part of the type (at the same level as type name annotations), and so types with differing field names (if present) are not considered equal.

Instructions that construct elements of composed types can also be annotated with one or multiple field annotations (in addition to type and variable annotations).

```
PAIR %fst %snd
:: 'a : 'b : 'S -> (pair ('a %fst) ('b %snd)) : 'S
LEFT %left %right 'b
:: 'a : 'S -> (or ('a %left) ('b %right)) : 'S
RIGHT %left %right 'a
:: 'b : 'S -> (or ('a %left) ('b %right)) : 'S
NONE %some 'a
:: 'S -> (option ('a %some))
SOME %some
:: 'a : 'S -> (option ('a %some))
```

To improve readability and robustness, instructions `CAR`

and `CDR`

accept one field annotation. For the contract to type check, the name of
the accessed field in the destructed pair must match the one given here.

```
CAR %fst
:: (pair ('a %fst) 'b) : S -> 'a : 'S
CDR %snd
:: (pair 'a ('b %snd)) : S -> 'b : 'S
```

### Syntax¶

Primitive applications can receive one or many annotations.

An annotation is a sequence of characters that matches the regular
expression `[@:%](|@|%|%%|[_a-zA-Z][_0-9a-zA-Z\.]*)`

. They come after
the primitive name and before its potential arguments.

```
(prim @v :t %x arg1 arg2 ...)
```

Ordering between different kinds of annotations is not significant, but ordering among annotations of the same kind is. Annotations of a same kind must be grouped together.

For instance these two annotated instructions are equivalent:

```
PAIR :t @my_pair %x %y
PAIR %x %y :t @my_pair
```

An annotation can be empty, in this case is will mean *no annotation*
and can be used as a wildcard. For instance, it is useful to annotate
only the right field of a pair instruction `PAIR % %right`

or to
ignore field access constraints, *e.g.* in the macro ```
UNPPAIPAIR %x1 %
%x3 %x4
```

.

### Annotations and macros¶

Macros also support annotations, which are propagated on their expanded
forms. As with instructions, macros that produce `n`

values on the
stack accept `n`

variable annotations.

```
DUU+P @annot
> DUU(\rest=U*)P @annot / S => DIP (DU(\rest)P @annot) ; SWAP / S
C[AD]+R @annot %field_name
> CA(\rest=[AD]+)R @annot %field_name / S => CAR ; C(\rest)R @annot %field_name / S
> CD(\rest=[AD]+)R @annot %field_name / S => CDR ; C(\rest)R @annot %field_name / S
``CMP{EQ|NEQ|LT|GT|LE|GE}`` @annot
> CMP(\op) @annot / S => COMPARE ; (\op) @annot / S
```

The variable annotation on `SET_C[AD]+R`

and `MAP_C[AD]+R`

annotates
the resulting toplevel pair while its field annotation is used to check
that the modified field is the expected one.

```
SET_C[AD]+R @var %field
> SET_CAR @var %field => CDR %field ; SWAP ; PAIR @var
> SET_CDR @var %field => CAR %field ; PAIR @var
> SET_CA(\rest=[AD]+)R @var %field / S =>
{ DUP ; DIP { CAR ; SET_C(\rest)R %field } ; CDR ; SWAP ; PAIR @var } / S
> SET_CD(\rest=[AD]+)R @var %field/ S =>
{ DUP ; DIP { CDR ; SET_C(\rest)R %field } ; CAR ; PAIR @var } / S
MAP_C[AD]+R @var %field code
> MAP_CAR code => DUP ; CDR ; DIP { CAR %field ; code } ; SWAP ; PAIR @var
> MAP_CDR code => DUP ; CDR %field ; code ; SWAP ; CAR ; PAIR @var
> MAP_CA(\rest=[AD]+)R @var %field code / S =>
{ DUP ; DIP { CAR ; MAP_C(\rest)R %field code } ; CDR ; SWAP ; PAIR @var} / S
> MAP_CD(\rest=[AD]+)R @var %field code / S =>
{ DUP ; DIP { CDR ; MAP_C(\rest)R %field code } ; CAR ; PAIR @var} / S
```

Macros for nested `PAIR`

and `UNPAIR`

accept multiple
annotations. Field annotations for `PAIR`

give names to leaves of the
constructed nested pair, in order. Variable annotations for `UNPAIR`

give names to deconstructed components on the stack. This next snippet
gives examples instead of generic rewrite rules for readability
purposes.

```
PAPPAIIR @p %x1 %x2 %x3 %x4
:: 'a : 'b : 'c : 'd : 'S
-> @p (pair ('a %x1) (pair (pair ('b %x) ('c %x3)) ('d %x4))) : 'S
PAPAIR @p %x1 %x2 %x3
:: 'a : 'b : 'c : 'S -> @p (pair ('a %x1) (pair ('b %x) ('c %x3))) : 'S
UNPAIR @x @y
:: (pair 'a 'b) : 'S -> @x 'a : @y 'b : 'S
UNPAPPAIIR @x1 @x2 @x3 @x4
:: (pair 'a (pair (pair 'b 'c) 'd )) : 'S
-> @x1 'a : @x2 'b : @x3 'c : @x4 'd : 'S
```

### Automatic variable and field annotations inferring¶

When no annotation is provided by the Michelson programmer, the typechecker infers some annotations in specific cases. This greatly helps users track information in the stack for bare contracts.

For unannotated accesses with `CAR`

and `CDR`

to fields that are
named will be appended (with an additional `.`

character) to the pair
variable annotation.

```
CDAR
:: @p (pair ('a %foo) (pair %bar ('b %x) ('c %y))) : 'S -> @p.bar.x 'b : 'S
```

If fields are not named but the pair is still named in the stack then
`.car`

or `.cdr`

will be appended.

```
CDAR
:: @p (pair 'a (pair 'b 'c)) : 'S -> @p.cdr.car 'b : 'S
```

If the original pair is not named in the stack, but a field annotation is present in the pair type the accessed value will be annotated with a variable annotation corresponding to the field annotation alone.

```
CDAR
:: (pair ('a %foo) (pair %bar ('b %x) ('c %y))) : 'S -> @bar.x 'b : 'S
```

A similar mechanism is used for context dependent instructions:

```
ADDRESS :: @c contract _ : 'S -> @c.address address : 'S
CONTRACT 'p :: @a address : 'S -> @a.contract contract 'p : 'S
BALANCE :: 'S -> @balance mutez : 'S
SOURCE :: 'S -> @source address : 'S
SENDER :: 'S -> @sender address : 'S
SELF :: 'S -> @self contract 'p : 'S
AMOUNT :: 'S -> @amount mutez : 'S
STEPS_TO_QUOTA :: 'S -> @steps nat : 'S
NOW :: 'S -> @now timestamp : 'S
```

Inside nested code blocks, bound items on the stack will be given a
default variable name annotation depending on the instruction and stack
type (which can be changed). For instance the annotated typing rule for
`ITER`

on lists is:

```
ITER body
:: @l (list 'e) : 'A -> 'A
iff body :: [ @l.elt e' : 'A -> 'A ]
```

### Special annotations¶

The special variable annotations `@%`

and `@%%`

can be used on instructions
`CAR`

and `CDR`

. It means to use the accessed field name (if any) as
a name for the value on the stack. The following typing rule
demonstrates their use for instruction `CAR`

.

```
CAR @%
:: @p (pair ('a %fst) ('b %snd)) : 'S -> @fst 'a : 'S
CAR @%%
:: @p (pair ('a %fst) ('b %snd)) : 'S -> @p.fst 'a : 'S
```

The special variable annotation `%@`

can be used on instructions
`PAIR`

, `SOME`

, `LEFT`

, `RIGHT`

. It means to use the variable
name annotation in the stack as a field name for the constructed
element. Two examples with `PAIR`

follows, notice the special
treatment of annotations with `.`

.

```
PAIR %@ %@
:: @x 'a : @y 'b : 'S -> (pair ('a %x) ('b %y)) : 'S
PAIR %@ %@
:: @p.x 'a : @p.y 'b : 'S -> @p (pair ('a %x) ('b %y)) : 'S
:: @p.x 'a : @q.y 'b : 'S -> (pair ('a %x) ('b %y)) : 'S
```

## JSON syntax¶

Micheline expressions are encoded in JSON like this:

An integer

`N`

is an object with a single field`"int"`

whose value is the decimal representation as a string.`{ "int": "N" }`

A string

`"contents"`

is an object with a single field`"string"`

whose value is the decimal representation as a string.`{ "string": "contents" }`

A sequence is a JSON array.

`[ expr, ... ]`

A primitive application is an object with two fields

`"prim"`

for the primitive name and`"args"`

for the arguments (that must contain an array). A third optional field`"annots"`

contains a list of annotations, including their leading`@`

,`%`

or`:`

sign.`{ "prim": "pair", "args": [ { "prim": "nat", "args": [] }, { "prim": "nat", "args": [] } ], "annots": [":t"] }`

As in the concrete syntax, all domain specific constants are encoded as strings.

## Examples¶

Contracts in the system are stored as a piece of code and a global data
storage. The type of the global data of the storage is fixed for each
contract at origination time. This is ensured statically by checking on
origination that the code preserves the type of the global data. For
this, the code of the contract is checked to be of type
`lambda (pair 'arg 'global) -> (pair (list operation) 'global)`

where
`'global`

is the type of the original global store given on origination.
The contract also takes a parameter and returns a list of internal operations,
hence the complete calling convention above. The internal operations are
queued for execution when the contract returns.

### Empty contract¶

The simplest contract is the contract for which the `parameter`

and
`storage`

are all of type `unit`

. This contract is as follows:

```
code { CDR ; # keep the storage
NIL operation ; # return no internal operation
PAIR }; # respect the calling convention
storage unit;
parameter unit;
```

### Multisig contract¶

The multisig is a typical access control contract. The ownership of
the multisig contract is shared between `N`

participants represented
by their public keys in the contract’s storage. Any action on the
multisig contract needs to be signed by `K`

participants where the
threshold `K`

is also stored in the storage.

To avoid replay of the signatures sent to the contract, the signed data include not only a description of the action to perform but also the address of the multisig contract and a counter that gets incremented at each successful call to the contract.

The multisig commands of Tezos command line client use this smart contract. Moreover, functional correctness of this contract has been verified using the Coq proof assistant.

```
parameter (pair
(pair :payload
(nat %counter) # counter, used to prevent replay attacks
(or :action # payload to sign, represents the requested action
(pair :transfer # transfer tokens
(mutez %amount) # amount to transfer
(contract %dest unit)) # destination to transfer to
(or
(option %delegate key_hash) # change the delegate to this address
(pair %change_keys # change the keys controlling the multisig
(nat %threshold) # new threshold
(list %keys key))))) # new list of keys
(list %sigs (option signature))); # signatures
storage (pair (nat %stored_counter) (pair (nat %threshold) (list %keys key))) ;
code
{
UNPAIR ; SWAP ; DUP ; DIP { SWAP } ;
DIP
{
UNPAIR ;
# pair the payload with the current contract address, to ensure signatures
# can't be replayed accross different contracts if a key is reused.
DUP ; SELF ; ADDRESS ; PAIR ;
PACK ; # form the binary payload that we expect to be signed
DIP { UNPAIR @counter ; DIP { SWAP } } ; SWAP
} ;
# Check that the counters match
UNPAIR @stored_counter; DIP { SWAP };
ASSERT_CMPEQ ;
# Compute the number of valid signatures
DIP { SWAP } ; UNPAIR @threshold @keys;
DIP
{
# Running count of valid signatures
PUSH @valid nat 0; SWAP ;
ITER
{
DIP { SWAP } ; SWAP ;
IF_CONS
{
IF_SOME
{ SWAP ;
DIP
{
SWAP ; DIIP { DIP { DUP } ; SWAP } ;
# Checks signatures, fails if invalid
CHECK_SIGNATURE ; ASSERT ;
PUSH nat 1 ; ADD @valid } }
{ SWAP ; DROP }
}
{
# There were fewer signatures in the list
# than keys. Not all signatures must be present, but
# they should be marked as absent using the option type.
FAIL
} ;
SWAP
}
} ;
# Assert that the threshold is less than or equal to the
# number of valid signatures.
ASSERT_CMPLE ;
DROP ; DROP ;
# Increment counter and place in storage
DIP { UNPAIR ; PUSH nat 1 ; ADD @new_counter ; PAIR} ;
# We have now handled the signature verification part,
# produce the operation requested by the signers.
NIL operation ; SWAP ;
IF_LEFT
{ # Transfer tokens
UNPAIR ; UNIT ; TRANSFER_TOKENS ; CONS }
{ IF_LEFT {
# Change delegate
SET_DELEGATE ; CONS }
{
# Change set of signatures
DIP { SWAP ; CAR } ; SWAP ; PAIR ; SWAP }} ;
PAIR }
```

## Full grammar¶

```
<data> ::=
| <int constant>
| <natural number constant>
| <string constant>
| <timestamp string constant>
| <signature string constant>
| <key string constant>
| <key_hash string constant>
| <mutez string constant>
| <contract string constant>
| Unit
| True
| False
| Pair <data> <data>
| Left <data>
| Right <data>
| Some <data>
| None
| { <data> ; ... }
| { Elt <data> <data> ; ... }
| instruction
<instruction> ::=
| { <instruction> ... }
| DROP
| DUP
| SWAP
| PUSH <type> <data>
| SOME
| NONE <type>
| UNIT
| IF_NONE { <instruction> ... } { <instruction> ... }
| PAIR
| CAR
| CDR
| LEFT <type>
| RIGHT <type>
| IF_LEFT { <instruction> ... } { <instruction> ... }
| IF_RIGHT { <instruction> ... } { <instruction> ... }
| NIL <type>
| CONS
| IF_CONS { <instruction> ... } { <instruction> ... }
| SIZE
| EMPTY_SET <comparable type>
| EMPTY_MAP <comparable type> <type>
| MAP { <instruction> ... }
| ITER { <instruction> ... }
| MEM
| GET
| UPDATE
| IF { <instruction> ... } { <instruction> ... }
| LOOP { <instruction> ... }
| LOOP_LEFT { <instruction> ... }
| LAMBDA <type> <type> { <instruction> ... }
| EXEC
| DIP { <instruction> ... }
| FAILWITH <data>
| CAST
| RENAME
| CONCAT
| SLICE
| PACK
| UNPACK
| ADD
| SUB
| MUL
| EDIV
| ABS
| NEG
| LSL
| LSR
| OR
| AND
| XOR
| NOT
| COMPARE
| EQ
| NEQ
| LT
| GT
| LE
| GE
| SELF
| CONTRACT <type>
| TRANSFER_TOKENS
| SET_DELEGATE
| CREATE_ACCOUNT
| CREATE_CONTRACT { <instruction> ... }
| IMPLICIT_ACCOUNT
| NOW
| AMOUNT
| BALANCE
| CHECK_SIGNATURE
| BLAKE2B
| SHA256
| SHA512
| HASH_KEY
| STEPS_TO_QUOTA
| SOURCE
| SENDER
| ADDRESS
<type> ::=
| <comparable type>
| key
| unit
| signature
| option <type>
| list <type>
| set <comparable type>
| operation
| contract <type>
| pair <type> <type>
| or <type> <type>
| lambda <type> <type>
| map <comparable type> <type>
| big_map <comparable type> <type>
<comparable type> ::=
| int
| nat
| string
| bytes
| mutez
| bool
| key_hash
| timestamp
| address
```

## Reference implementation¶

The language is implemented in OCaml as follows:

The lower internal representation is written as a GADT whose type parameters encode exactly the typing rules given in this specification. In other words, if a program written in this representation is accepted by OCaml’s typechecker, it is guaranteed type-safe. This of course also valid for programs not handwritten but generated by OCaml code, so we are sure that any manipulated code is type-safe.

In the end, what remains to be checked is the encoding of the typing rules as OCaml types, which boils down to half a line of code for each instruction. Everything else is left to the venerable and well trusted OCaml.

The interpreter is basically the direct transcription of the rewriting rules presented above. It takes an instruction, a stack and transforms it. OCaml’s typechecker ensures that the transformation respects the pre and post stack types declared by the GADT case for each instruction.

The only things that remain to be reviewed are value dependent choices, such as that we did not swap true and false when interpreting the If instruction.

The input, untyped internal representation is an OCaml ADT with the only 5 grammar constructions:

`String`

,`Int`

,`Seq`

and`Prim`

. It is the target language for the parser, since not all parsable programs are well typed, and thus could simply not be constructed using the GADT.The typechecker is a simple function that recognizes the abstract grammar described in section X by pattern matching, producing the well-typed, corresponding GADT expressions. It is mostly a checker, not a full inferrer, and thus takes some annotations (basically the input and output of the program, of lambdas and of uninitialized maps and sets). It works by performing a symbolic evaluation of the program, transforming a symbolic stack. It only needs one pass over the whole program.

Here again, OCaml does most of the checking, the structure of the function is very simple, what we have to check is that we transform a

`Prim ("If", ...)`

into an`If`

, a`Prim ("Dup", ...)`

into a`Dup`

, etc.