Space

A verified concatenative systems programming language.

Space combines stack-based execution with linear types, isolated memory universes, and machine-checked proofs. Implemented in F*, extracted to C via Karamel.

Status: v0.8 alpha

Component	Status
Core types & stack	✓ Complete, verified
Discipline system	✓ Complete, verified
Universe lifecycle	✓ Complete, verified
Borrow system	✓ Complete, verified
Warp traversal	✓ Complete, verified
Arithmetic & bitwise	✓ Complete, verified
Control flow	✓ Complete
Text/Unicode	✓ Complete, verified (UAX #29 grapheme clusters)
Compiler: Lexer	✓ Complete (UTF-8, escapes, literals)
Compiler: Parser	✓ Complete (recursive descent)
Compiler: Bytecode	✓ Complete (full opcode set)
Compiler: Codegen	✓ Complete
Memory operations	✓ Complete (cell + byte level)
Borrow/Warp ops	✓ Complete (fetch/store through borrows and warps)
I/O primitives	✓ Complete (emit/read with channel abstraction)
VM interpreter	◐ Modules complete, exec_prim needs wiring
Unicode tables	◐ Placeholder tables, Full profile needs UCD data
REPL	✗ Not started
C extraction	✗ Not yet tested

Remaining Work

1. Wire exec_prim — Memory, I/O, borrow, warp operations are implemented in separate modules but return "not implemented" in Space.Execute.fst. Connect the calls.

2. Expand prim_op — Bytecode has opcodes for all operations, but Space.Instruction.fst only defines a subset. Add nip, tuck, pick, divs, neg, min, max, and all text/borrow/warp ops.

3. Unicode tables — Normalization and case mapping use placeholder lookups. Full profile needs actual UCD (Unicode Character Database) tables. This is data (~85KB), not code.

4. Complex text slicing — text_slice_simple only handles ASCII. Slicing text with emoji/combining characters needs grapheme index lookup.

What's Here

Implementation (49 F* files)

src/
├── Core Types & Verification
│   ├── Space.Types.fst              # Core types: cell, discipline, universe_id
│   ├── Space.Stack.fst              # Stack operations: push, pop, dup, swap, over, rot
│   ├── Space.Stack.Properties.fst   # Stack verification lemmas
│   ├── Space.Discipline.fst         # Linear/affine/unrestricted rules
│   ├── Space.Universe.fst           # Isolated memory regions, self-destruction
│   ├── Space.Universe.Properties.fst
│   ├── Space.Borrow.fst             # Cross-universe pointer borrowing
│   ├── Space.Borrow.Properties.fst  # 15 lemmas proving borrow safety
│   ├── Space.Warp.fst               # Structured traversal without escaping pointers
│   ├── Space.Warp.Properties.fst    # 28 lemmas proving warp correctness
│   ├── Space.Arithmetic.Properties.fst  # 26 arithmetic lemmas
│   └── ...
│
├── Compiler Pipeline
│   ├── Space.Compiler.Token.fst     # Token types, keywords, primitives
│   ├── Space.Compiler.Lexer.fst     # UTF-8 lexer with escape sequences
│   ├── Space.Compiler.AST.fst       # Abstract syntax tree
│   ├── Space.Compiler.Parser.fst    # Recursive descent parser
│   ├── Space.Compiler.Bytecode.fst  # Opcode definitions, module format
│   ├── Space.Compiler.Codegen.fst   # AST to bytecode compilation
│   ├── Space.Compiler.Decoder.fst   # Bytecode decoding
│   └── Space.Compiler.Test.fst      # Compiler tests
│
├── Text/Unicode (14 files, ~1,945 lines)
│   ├── Space.Text.Types.fst         # Text representation
│   ├── Space.Text.UTF8.fst          # UTF-8 encoding/decoding
│   ├── Space.Text.UTF16.fst         # UTF-16 for interop
│   ├── Space.Text.Grapheme.fst      # UAX #29 grapheme clusters
│   ├── Space.Text.Normalize.fst     # NFC/NFD/NFKC/NFKD
│   ├── Space.Text.Case.fst          # Case mapping
│   └── ...
│   # (F* has no built-in Unicode — implemented from scratch)
│
├── VM Runtime
│   ├── Space.Interpreter.fst        # Machine state
│   ├── Space.Execute.fst            # Primitive execution
│   ├── Space.Step.fst               # Single-step VM
│   ├── Space.World.fst              # Multi-universe runtime
│   └── ...
│
└── Makefile

93+ Machine-Checked Lemmas

Every core operation has verified properties:

(* Stack: push then pop returns original *)
let push_pop_identity (s: stack) (v: cell) :
  Lemma (pop (push s v) == Some (v, s)) = ()

(* Linear universe must be empty to end *)
let linear_self_destruct_condition (u: universe) :
  Lemma (should_self_destruct u <==>
         (u.discipline = Linear && stack_empty u && is_live u)) = ()

(* Borrowed pointer can't return to wrong universe *)
let return_requires_source_match (b: borrowed) (src: universe) :
  Lemma (requires b.source_id <> src.id)
        (ensures None? (return_borrowed b src)) = ()

Building

Requires F* and Z3 (version 4.15.4).

cd src
make verify    # Type-check and verify all proofs
make extract   # Generate Karamel output (requires krml)

Runtime Architecture

The F* implementation extracts to C via Karamel. Space programs compile to bytecode that runs on this verified runtime.

program.space  →  Compiler  →  bytecode  →  VM (extracted C)

Runtime sizes:

Profile	Includes	Binary
Embedded	Core only	~2KB
Standard	Core + Text	~35KB
Full	Core + Text + Unicode tables	~120KB

For comparison: Lua ~280KB, mruby ~400KB, QuickJS ~600KB. Embedded fits microcontrollers with 8KB flash.

The Design

Universes are isolated memory regions. Pointers cannot escape. Each universe has a discipline:

• Unrestricted: Values can be copied and dropped freely
• Affine: Values can be dropped but not copied
• Linear: Values must be consumed exactly once

Linear universes self-destruct when their obligations are fulfilled:

1024 linear create-universe as scratch
    42 push
    pop              \ obligation fulfilled
end-universe         \ universe already gone

Borrowing enables temporary cross-universe access. Borrowed pointers track their source and must be dropped before the source can be destroyed.

Warps provide structured traversal of data structures without exposing internal pointers. You can navigate without creating references that might escape.

Documentation

• spacelang.org — Language specification
• spacelang.org/formal-verification — Verification approach
• spacelang.org/philosophy — Design philosophy
• spacelang.org/heritage — Intellectual lineage

Heritage

Space synthesizes ideas from:

• Forth (1970) — Concatenative execution
• StrongForth (2003) — Static typing for stack languages
• Linear Logic (1987) — Discipline system
• Rust (2010) — Borrowing semantics
• F* (2011) — Verification infrastructure

Forth powered Open Firmware (IEEE 1275) and runs actual spacecraft today. Space inherits this heritage and adds what Forth lacked: static types, linear resources, and machine-checked proofs.

License

Apache 2.0. See LICENSE.

Author

Created by Danslav Slavenskoj. Design conceived summer 2025, first implemented in F* 2026-02-10.

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This is alpha software. Core semantics and compiler are complete; VM execution loop needs wiring. Expect breaking changes.