MeTTa

MeTTa, Hyperon's AGI language, based on PeTTa semantics with significant extensions.

What MeTTa is

MeTTa is a language for rewriting metagraphs. A program and its data are the same thing: atoms in a space, where an atom is a symbol, a number, a variable or an expression built from other atoms, and a space is the metagraph they form together.

You write equations rather than statements, and the engine matches a pattern against the whole space at once. Every match is an answer, so a rule that fits three ways yields three results, and whether you take one of them, the first, or all is the caller's choice rather than the language's. Search is something you write down instead of something you implement.

One space holds symbolic rules and grounded values side by side: a number, a matrix, a handle to a trained model. A rule can match on what a model produced and a model can be called from inside a rule, so the neurosymbolic case is ordinary here rather than an integration between two systems. Both halves are atoms in the same metagraph, read by the same matcher.

If you are an LLM, read llms.txt for the language and every surface, with exact return shapes and no prose to guess at.

pip install pymetta    # Linux x86_64, CPython 3.12-3.14: the wheel carries the patched SWI-Prolog
npm install tsmetta    # Node and browsers: the package carries a patched WebAssembly SWI-Prolog

The engine runs only on a patched SWI-Prolog and refuses to boot on a stock one. For Python on any other platform, and for the C seat, build it as docs/patched-host.md describes.

Architecture

One engine, in Prolog and C. Everything else reaches it through a declared seam, so each piece is built, versioned and published on its own.

This Prolog engine carries the 1.0 line and will soon be replaced by a new engine written in Rust. The libraries are written in MeTTa over the engine's primitives so that they carry over unchanged, and that primitive set is what the Rust engine implements. The patched SWI-Prolog host (docs/patched-host.md) belongs to the Prolog engine and goes with it.

The four ways in

Extension points

engine/ext_points.pl declares every point in four kinds, and clauses_from/2 fixes who may contribute each.

clauses_from(event,       extension).
clauses_from(ownership,   extension).
clauses_from(declaration, extension).
clauses_from(service,     engine).

A backend claims the names it owns and fails for the rest, which is the whole protocol:

seam:foreign_space('&catalogs').
seam:foreign_capability('&catalogs', match).
seam:foreign_capability('&catalogs', enumerate).
seam:foreign_atoms('&catalogs', Row) :- package_catalog_row(Row).

The catalog

Everything the engine knows about itself is atoms you can query, including what each library is and where it came from.

!(test (size-atom (collapse (match &catalogs (package $name $path) $name))) 60)

Nothing is imported first. Package handling is the engine's, not a library's, so the catalog is there at boot.

The language

Atoms

Four kinds, and that is the whole representation.

!(test (get-metatype Tom) Symbol)                   ; a name that denotes itself
!(test (get-metatype $x) Variable)                  ; stands for anything
!(test (get-metatype 42) Grounded)                  ; a number, a string, a host object
!(test (get-metatype (Parent Tom Bob)) Expression)  ; atoms in order

Terms read and print as themselves.

!(test (repr 42) "42")
!(test (repr "42") "\"42\"")
!(test (repr (A (B C))) "(A (B C))")
!(test (repr (A (, B , C ,))) "(A (, B , C ,))")
!(test (repr 2025_12_12) "2025_12_12")
!(test (repr ()) "()")

Spaces and matching

A space is where a program lives, and match reads it.

(= (matchtrickery)
   (let* (($t1 (add-atom &self (foo a)))
          ($t2 (add-atom &self (foo b))))
         (match &self (foo $1) (bar $1))))

!(test (collapse (matchtrickery))
       ((bar a) (bar b)))

A pattern's head can be a constant, so the head is just another position.

(= (h (justdata haha $B) $C)
   (+ $B $C))

!(test (h (justdata haha 30) 40) 70)

Equations

An equation is an atom, so partial application and composition fall out of the same rule.

(= (mp) (+))

!(test (mp 1 1) 2)

(= (.. $f1 $f2 $arg) ($f1 ($f2 $arg)))

(= (plus1times2) (.. (* 2) (+ 1)))

!(test (plus1times2 1) 4)

Many answers

Nondeterminism is the default, and empty is the answer with no answers.

(= (y) (empty))

!(test (collapse (y))
       ())

once commits to the first.

(foo 1)
(foo 2)

(= (match-single $space $pat $ret)
   (once (match $space $pat $ret)))

!(let $x (match-single &self (foo $1) $1) (add-atom &self (bar $x)))

!(test (collapse (match &self (bar $1) (bar $1)))
       ((bar 1)))

Control flow

if takes a boolean and two branches.

!(test (if True 42) 42)

case dispatches on shape.

(= (casetest $x)
   (case $x ((4 42)
             ($otherpattern 44)
             ($otherother $45))))

!(test (casetest 5) 44)

chain sequences.

!(test (chain (+ 2 4) $n (* 3 $n))
       18)

!(test (chain (+ 1 3) $n (chain (* 2 $n) $m (+ $n $m)))
       12)

A cut commits to what has been found.

(foo 1)
(foo 2)

(= (match-single $space $pat $ret)
   (let* (($x (match $space $pat $ret))
          ($temp (cut)))
         $x))

!(let $x (match-single &self (foo $1) $1) (add-atom &self (bar $x)))

!(test (collapse (match &self (bar $1) (bar $1)))
       ((bar 1)))

Recursion under an explicit branch budget.

(= (fib $N)
   (if (< $N 2)
       $N
       (+ (fib (- $N 1))
          (fib (- $N 2)))))

!(test (with-pragma! ((max-stack-depth 100000000)) (fib 30)) 832040)

Data

Multiset operations over atoms.

!(test (unique-atom (a b c d d)) (a b c d))
!(test (union-atom (a b b c) (b c c d)) (a b b c b c c d))
!(test (intersection-atom (a b c c) (b c c c d)) (b c c))
!(test (subtraction-atom (a b b c) (b c c d)) (a b))
!(test (intersection-atom (a b c c) (b c d)) (b c))
!(test (intersection-atom (a a a) (a)) (a))
!(test (subtraction-atom (a a a) (a)) (a a))
!(test (intersection-atom (a b) ()) ())

Sequence variables

A pattern child that stands for a run of atoms. Upstream PeTTa has no such pattern, so this is the one part of the language below that a stock kernel will not parse, and sixteen of the library pack's libraries are written with it.

!(test (collapse (let ((:seg $pre) SEP (:seg $post)) (a b SEP c SEP d)
                      (pair $pre $post)))
       ((pair (a b) (c SEP d)) (pair (a b SEP c) (d))))

!(test (let (row (:seg $r)) (row) $r) ())
!(test (let (row (:seg $r)) (row a b c) $r) (a b c))

!(test (get-metatype (let (row (:seg $r)) (row a b) $r)) Expression)
!(test (size-atom (let (row (:seg $r)) (row a b) $r)) 2)
!(test (car-atom (let (row (:seg $r)) (row a b) $r)) a)

!(test (let (f (:seg $x) g (:seg $x)) (f a b g a b) $x) (a b))
!(test (collapse (let (f (:seg $x) g (:seg $x)) (f a b g c) $x)) ())
!(test (let (f (:seg $x) g (:seg $x)) (f 1 g 1.0) took) took)

!(test (collapse (let (f ... g ...) (f a g b c) done)) (done))

!(test (let (f (g ...) b) (f (g 1 2) b) nested) nested)
!(test (collapse (let (A ... D) (A b c E) never)) ())

!(add-atom &self (edge a b))
!(add-atom &self (edge b c d))
!(add-atom &self (tag b hot))
!(test (collapse (match &self (edge a ... $last) $last)) (b))
!(test (collapse (match &self (, (edge ... $mid) (tag $mid $heat)) ($mid $heat)))
       ((b hot)))

Numbers

!(test (exp-math 0) 1.0)
!(test (exp-math 1.0) 2.718281828459045)
!(test (< (abs-math (- (exp-math 2.0) (* 2.718281828459045 2.718281828459045))) 1.0e-12) true)
!(test (< (abs-math (- (log-math 2.718281828459045 (exp-math 3.0)) 3.0)) 1.0e-12) true)

(= (in-range $lo $hi $x) (and (<= $lo $x) (<= $x $hi)))
!(test (in-range 1 6 (random-int 1 6)) true)
!(test (in-range 0.0 1.0 (random-float 0.0 1.0)) true)
!(test (in-range 5 5 (random-int 5 5)) true)

Python as a notation

!(test (repr (py-call (str true))) "True")
!(test (repr (py-call (str false))) "False")
!(test (py-call (sorted (true false))) (false true))
!(test (py-call (len (true false true))) 3)
!(test (py-call (isinstance true (py-call (type false)))) true)
!(test (py-call (bool 1)) true)
!(test (py-call (bool 0)) false)
!(test (py-call (.bit_length true)) 1)
!(test (repr (py-call (.upper abc))) "ABC")

Types

Optional, and parametric.

(: apply (-> (-> $tx $ty) $tx $ty))
(= (apply $f $x) ($f $x))
!(apply not False) ; True
!(get-type (apply not False))
!(test (let (get-type apply) (-> (-> Bool Bool) Bool $result) $result)
       Bool)

Errors and refusals

A refusal names what went wrong rather than failing silently.

!(test (throw (my-ball 1)) (Error (throw (my-ball 1)) (my-ball 1)))
!(test (throw "text") (Error (throw "text") "text"))

!(test (if-error (throw oops) caught fine) caught)
!(test (if-error 42 caught fine) fine)
!(test (return-on-error (throw oops) carried-on) (Error (throw oops) oops))
!(test (return-on-error 42 carried-on) carried-on)

!(test (throw (Error (inner 1) because)) (Error (inner 1) because))
!(test (throw (throw first)) (Error (throw first) first))

(= (half $n) (if (== (% $n 2) 0) (/ $n 2) (throw (odd $n))))
!(test (half 10) 5)
!(test (half 7) (Error (throw (odd 7)) (odd 7)))
!(test (if-error (half 7) refused (half 7)) refused)

!(test (trace! "the answer" 42) 42)
!(test (+ 1 (trace! "adding one to" 41)) 42)
!(test (trace! (half 10) (half 10)) 5)

!(test (trace! (checking (odd 7)) ok) ok)

Testing

Every example checks itself, using the same forms you would.

!(import! &self (library lib_he))

(= (add 1 2) 3)

!(test (id 5) 5)

!(test (=alpha (Father $X) (Father $Y)) True)

!(test (=alpha (Father $X) (Son $X)) False)

!(test (if-equal 1 1 "Equal" "Not Equal") "Equal")

Seeing your program

!(import! &self (library lib_string))

!(test (> (current-time) 1700000000.0) True)

!(test (<= (current-time) (current-time)) True)

!(test (format-time "abc") abc)
!(test (== (format-time "abc") "abc") False)
!(test (string-length (format-time "a literal")) 9)
!(test (string-length (format-time "")) 0)
!(test (string-length (format-time "%%")) 1)

!(test (string-length (format-time "%Y")) 4)
!(test (string-length (format-time "%Y-%m-%d")) 10)
!(test (string-length (format-time "%H:%M:%S")) 8)

!(test (collapse (argv 999)) ())
!(test (collapse (argv -1)) ())

!(test (== (argv 0) (argv 0)) True)

(= (argument-or $index $default)
   (let $found (collapse (argv $index))
        (if (== $found ()) $default (car-atom $found))))
!(test (argument-or 999 no-such-argument) no-such-argument)
!(test (== (argument-or 0 no-such-argument) no-such-argument) False)

Events and standing queries

!(test (match &metta (vocabulary delivery $a $b $c) ($a $b $c))
       (at-most-once at-least-once per-write-exactly))
!(test (match &metta (vocabulary event-order $a $b) ($a $b))
       (ordered unordered))
!(test (match &metta (kind events $ctx $delivery $order) $delivery)
       (one-of delivery))

!(test (if-error (catch (add-atom &metta (events &feed eventually)))
                 refused admitted)
       refused)

!(add-atom &native-events (reading 1))
!(test (collapse (match &metta (events &native-events $d $o) declared)) ())

!(test (match &metta (vocabulary agenda-policy $a $b $c $d $e) ($a $b $c $d $e))
       (declaration recency specificity priority user))
!(test (match &metta (policy reaction-order $knob $default) ($knob $default))
       (agenda declaration))
!(test (match &metta (kind agenda $ctx $policy $fn) $policy)
       (one-of agenda-policy))

!(test (match &metta (kind on $ctx $pattern $op $priority) $priority)
       (optional integer))

Concurrency

!(add-atom &Point (: Point (-> Number Number Point)))
!(add-atom &Point (= (Point-x (Point $x $y)) $x))
!(add-atom &Point (= (Point-y (Point $x $y)) $y))

!(add-atom &Point
  (= (Point-norm (Point $x $y)) (sqrt-math (+ (* $x $x) (* $y $y)))))

!(add-atom &Point
  (= (Point-add (Point $x1 $y1) (Point $x2 $y2)) (Point (+ $x1 $x2) (+ $y1 $y2))))

!(add-atom &Point
  (= (Point-quadrant $p)
     (case $p (((Point 0 0) origin) ((Point 0 $y) axis) ((Point $x $y) plane)))))

!(add-atom &self (from &Point))

!(test (Point-norm (Point 3 4)) 5.0)
!(test (Point-add (Point 1 2) (Point 3 4)) (Point 4 6))
!(test (Point-quadrant (Point 0 0)) origin)
!(test (Point-quadrant (Point 0 4)) axis)
!(test (Point-quadrant (Point 3 4)) plane)
!(test (== (Point-add (Point 1 2) (Point 3 4)) (Point 4 6)) True)

Worlds and state

!(bind! state (new-state rest))
!(test (get-state state) rest)

!(test (change-state! state active) true)
!(test (get-state state) active)

!(test (get-type (new-state 5)) (StateMonad Number))
!(test (get-type (new-state "hi")) (StateMonad String))

!(test (let $cell (new-state 1)
            (let $_ (change-state! $cell 2) (get-state $cell)))
       2)

Performance

Memoisation is a library, not a keyword.

!(import! &self (library lib_memo))

!(memoize sq)
(= (sq $x) (* $x $x))

!(test (sq 9) 81)
!(test (sq 9) 81)
!(test (sq 9) 81)

Spaces backed by anything

A space of your own, inheriting what it does not answer.

!(add-atom &family-parent (edge a b))
!(add-atom &family-parent (parent-only kept))
!(add-atom &family-parent (layer parent))
!(new-space &family-child (inherits &family-parent))
!(add-atom &family-child (edge b c))
!(add-atom &family-child (child-only local))
!(add-atom &family-child (layer child))

!(test (collapse (match &family-child
                         (, (edge $x $y) (edge $y $z))
                         ($x $z)))
       ((a c)))

!(test (collapse (match &family-child (layer $x) $x)) (child parent))
!(test (space-atom-count &family-child) 3)

!(test (collapse (match &family-parent (parent-only $x) $x)) (kept))
!(test (collapse (match &family-child (parent-only $x) $x)) (kept))
!(test (collapse (match &family-parent (child-only $x) $x)) ())

Rows in a CSV file, queried as atoms.

!(import! &self (library lib_csv))
!(import! &self (library lib_file))

!(bind! &csv-path (temp-path! "metta-csv-example"))
!(write-file! &csv-path "id,amount\n001,12.50\n002,9\n002,9\n")
!(bind! &sales (csv-space &csv-path))

!(test (collapse (match &sales (row $id $amount) ($id $amount)))
       (("id" "amount") ("001" "12.50") ("002" "9") ("002" "9")))
!(test (match &sales (row "001" $amount) (parse-number $amount)) 12.5)

!(write-file! &csv-path "003,42\n")
!(test (collapse (match &sales (row $id $amount) ($id $amount)))
       (("003" "42")))
!(delete-file! &csv-path)

A reasoner

(= (myf $M)
   (and (and (member a $M)
             (member b $M))
        (== (size-atom $M) 2)))

!(test (if (once (myf $M)) $M)
       (a b))

Weighted answers

!(import! &self (library lib_pln))

(= (STV A) (stv 0.5 0.9))
(= (STV B) (stv 0.25 0.9))
(= (STV C) (stv 0.25 0.9))
(= (STV D) (stv 0.5 0.9))

(= (kb)
   ((Sentence ((Inheritance A B) (stv 0.25 0.9)) (1))
    (Sentence ((Inheritance A C) (stv 0.25 0.9)) (2))
    (Sentence ((Inheritance B D) (stv 0.5 0.9)) (3))
    (Sentence ((Inheritance C D) (stv 0.5 0.9)) (4))
   ))

!(test (with-pragma! ((max-stack-depth 100000000))
                     (PLN.Query (kb) (Inheritance A D)))
       ((stv 0.5 0.9473684210526316) (1 2 3 4)))

Search

!(add-atom &self (= (fib $N)
                    (if (< $N 2)
                        $N
                        (+ (fib (- $N 1))
                           (fib (- $N 2))))))

!(test (with-pragma! ((max-stack-depth 100000000)) (fib 30)) 832040)

Extending the engine

A translator rule changes what a form compiles to.

(= (runtime42 $arg)
   (cons 42 $arg))

(= (compileeval42 $arg)
   (cons 42 $arg))

(= (compile42 $arg)
   (noeval (cons 42 $arg)))

!(add-translator-rule! compileeval42)
!(add-translator-rule! compile42)

!(test (runtime42 (43)) (42 43))
!(test (compileeval42 (43)) (42 43))
!(test (compile42 (43)) (42 43))

Prolog underneath, when you want it.

!(test (progn (translatePredicate (is $x 2))
              (translatePredicate (+ $x 40 $z)) $z)
       42)

MeTTa's own evaluator, written in MeTTa.

(: myinterpreter (-> Atom %Undefined%))
(= (myinterpreter $code)
   (let $temp (println! ("Runtime-interpreting code" $code))
        (eval $code)))

(= (w) 42)
(= (v) 43)

!(test (myinterpreter (if (== 1 1) (w) (v))) 42)
!(test (myinterpreter (if (== 1 2) (w) (v))) 43)

git-import! fetches and builds a library from source; see the example.

Documentation

Citing

@software{petta,
  author = {Hammer, Patrick},
  title  = {PeTTa},
  url    = {https://github.com/patham9/PeTTa},
  note   = {The MeTTa implementation whose semantics this engine follows}
}

@software{metta_kernel,
  author  = {MesTTo},
  title   = {MeTTa Kernel},
  url     = {https://github.com/MesTTo/MeTTa},
  version = {0.8.0}
}

Licence

Apache-2.0. See LICENSE.