xqcp 0.3.1

High-level constraint programming DSL compiling to XQVM assembly.

XQCP — X-Quadratic Constraint Programmer

A constraint programming DSL that compiles high-level problem descriptions into three XQVM assembly programs: encoder, verifier, and decoder.

Overview

Instead of writing .xqasm by hand, define your problem in Python using symbolic expressions, loops, and model operations. XQCP records these operations and compiles them into assembly that the XQVM executor can run directly.

from xqcp import Problem, Types
from xqvm_py import XQMXDomain

problem = Problem("MyProblem")

n = problem.input("n", type=Types.Int)
problem.define_model(size=n, domain=XQMXDomain.BINARY)

# ... define objective, constraints, decoder ...

programs = problem.compile()
# programs.encoder   -> str (.xqasm source)
# programs.verifier  -> str
# programs.decoder   -> str

Architecture

XQCP uses a record-then-compile pattern:

1. Record — DSL calls (input, define_model, range, stow, model.linear[i].add(w), etc.) append Action objects to an ordered list.
2. Compile — The compiler walks the action list and emits assembly for each of the three programs, with automatic register allocation and loop nesting.

Module Structure

Module	Purpose
problem.py	Problem container, action recording, register allocator
expression.py	Symbolic expression tree nodes that emit assembly
symbols.py	Symbolic references: InputRef, LoopVar, ModelRef, SampleRef, OutputRef, CoefficientRef, LinearProxy, QuadraticProxy
compiler.py	Three compiler functions: compile_encoder, compile_verifier, compile_decoder
__init__.py	Public API re-exports and xq_* helper functions

DSL Reference

Inputs

Declare runtime inputs with a name and type:

n = problem.input("n", type=Types.Int)           # integer scalar
edges = problem.input("edges", type=Types.Vec)    # integer vector

InputRef supports arithmetic (+, -, *, //, %, unary -) and vector operations:

edges.get(i)        # VECGET: access element at index i
edges.veclen()      # VECLEN: get vector length

Model

Define the XQMX model the encoder will build:

# 1D model (flat variables)
problem.define_model(size=n, domain=XQMXDomain.BINARY)

# 2D model (grid with rows and columns)
problem.define_model(
    size=n * n, domain=XQMXDomain.BINARY,
    rows=n, cols=n,
)

Note: Discrete domain (XQMXDomain.DISCRETE) is not yet supported in the CP layer.

Model Coefficients

Access linear and quadratic coefficients via subscript proxies:

# Linear coefficients
model.linear[i]              # get (returns Expr → GETLINE)
model.linear[i] = weight     # set (→ SETLINE)
model.linear[i].add(weight)  # add (→ ADDLINE)

# Quadratic coefficients
model.quadratic[i, j]              # get (returns Expr → GETQUAD)
model.quadratic[i, j] = weight     # set (→ SETQUAD)
model.quadratic[i, j].add(weight)  # add (→ ADDQUAD)

# 2D models accept tuple coordinates (auto-flattened via IDXGRID)
model.quadratic[(row_a, col_a), (row_b, col_b)].add(weight)

Constraints

# One-hot constraints (2D models)
model.apply_onehot_row(row, penalty=100)    # → ONEHOTR
model.apply_onehot_col(col, penalty=100)    # → ONEHOTC

# Mutual exclusion (variables i and j cannot both be 1)
model.apply_exclude(i, j, penalty=100)      # → EXCLUDE

# Implication (if variable i is 1, variable j must be 1)
model.apply_implies(i, j, penalty=100)      # → IMPLIES

# 2D models accept tuple coordinates for exclude/implies
model.apply_exclude((r1, c1), (r2, c2), penalty=100)

Loops

problem.range(start, end) emits a RANGE loop:

with problem.range(0, n) as i:
    with problem.range(i + 1, n) as j:
        # body executes for all (i, j) pairs where i < j

problem.iter(vec, start, end) emits an ITER loop over vec elements:

# Always yields (idx, val) — unpack as needed
with problem.iter(distances, 0, n) as (idx, val):
    model.linear[idx].add(val)

with problem.iter(distances, 0, n) as (_, val):
    # discard index, use value only

The yielded LoopVars support full arithmetic and can be used as indices, coordinates, or operands.

Stow

Evaluate an expression and store it in a register for reuse:

dist = problem.stow("dist", edges.get(xq_triu(i, j)))
w = problem.stow("w", edges.get(offset + 2))

Returns a RegLoad that can be used in subsequent expressions. Pass an existing RegLoad to overwrite:

weight = problem.stow("weight", 0)       # allocate new register
problem.stow(weight, dist * 10)           # overwrite same register

Branch

Conditional multi-arm branching with first-match semantics:

problem.branch(
    dist > threshold, lambda: model.linear[i].add(dist * 10),  # if
    dist > 0,         lambda: model.linear[i].add(dist),       # elif
    None,                                                       # else (do nothing)
)

• Variadic (condition, callable) pairs followed by a mandatory default (callable or None)
• Minimum 3 arguments: (cond, callable, default)
• Conditions use comparison operators (>, <, ==, >=, <=)

Outputs

Declare decoder outputs:

tour = problem.output("tour", type=Types.Vec)

with problem.range(0, n) as pos:
    tour.append(problem.sample.colfind(col=pos, value=1))   # VECPUSH
    # or
    tour.append(problem.sample.getline(pos))                 # VECPUSH

# Random-access write/read
tour[i] = value    # VECSET
val = tour[i]      # VECGET

Sample

problem.sample provides read access to the solution sample in the decoder:

problem.sample.colfind(col=pos, value=1)   # find row where column has value (2D)
problem.sample.rowfind(row=pos, value=1)   # find col where row has value (2D)
problem.sample.getline(index)               # read variable by index (1D)
problem.sample.rowsum(row)                  # sum all values in row
problem.sample.colsum(col)                  # sum all values in column

Operators

All symbolic types (InputRef, LoopVar, RegLoad, Literal) support:

Arithmetic

Operator	Assembly	Notes
a + b	ADD	Optimizes to INC when adding 1
a - b	SUB	Optimizes to DEC when subtracting 1
a * b	MUL
a // b	DIV	Integer division
a % b	MOD
-a	NEG	Unary negation

Comparison

Operator	Assembly
a == b	EQ
a < b	LT
a > b	GT
a <= b	LTE
a >= b	GTE

Bitwise

Operator	Assembly
a & b	BAND
a | b	BOR
a ^ b	BXOR
~a	BNOT
a << b	SHL
a >> b	SHR

Free Functions

from xqcp import (
    xq_triu, xq_grid, xq_sqr, xq_abs, xq_min, xq_max,
    xq_not, xq_and, xq_or, xq_xor, xq_bnot,
)

Index Math

Function	Assembly	Description
xq_triu(i, j)	IDXTRIU	Upper triangular index
xq_grid(row, col, cols)	IDXGRID	Grid flat index (row * cols + col)

Arithmetic

Function	Assembly	Description
xq_sqr(x)	SQR	Square
xq_abs(x)	ABS	Absolute value
xq_min(a, b)	MIN	Minimum
xq_max(a, b)	MAX	Maximum

Logical (Python keywords and/or/not can't be overloaded)

Function	Assembly	Description
xq_not(x)	NOT	Logical NOT
xq_and(a, b)	AND	Logical AND
xq_or(a, b)	OR	Logical OR
xq_xor(a, b)	XOR	Logical XOR
xq_bnot(x)	BNOT	Bitwise NOT

Compiled Output

problem.compile() returns a CompiledPrograms dataclass with three .xqasm source strings:

• Encoder — reads inputs, allocates the XQMX model, emits objective terms and constraints
• Verifier — reads model + sample + N, checks validity (onehot or binary domain), computes energy
• Decoder — reads sample + N, extracts the solution into output vectors

The verifier automatically selects the right validity check:

• ROWSUM/COLSUM loops when onehot constraints are present
• Binary domain check (GETLINE + 0-or-1 test) when no onehot constraints exist

Specification

Authoritative specification: ../spec/xqcp/SPEC.md. The spec is the source of truth; any divergence in this reference implementation is a bug.

Examples

See the working XQCP programs in top-level runnable examples:

• TSP: examples/tsp/runner.py — 2D grid model, onehot constraints, COLFIND decoder
• Max-Cut: examples/maxcut/runner.py — 1D model, edge iteration, GETLINE decoder

Each runner inlines the CP DSL, compiles to XQVM assembly, and runs the encoder → SA → verifier → decoder pipeline on either the Python reference VM or the Rust VM (via --interpreter).