DisCoPy provides Python implementations of string diagrams and monoidal categories for compositional NLP.
Installation
pip install discopy
Core Categorical Structures
Types and Morphisms
from discopy import Ty, Box, Id, Diagram
n = Ty('n') # noun s = Ty('s') # sentence
Morphisms (boxes between types)john = Box('John', Ty(), n) # John: I → n sleeps = Box('sleeps', n, s) # sleeps: n → s
### Composition and Tensor
```python
# Sequential composition (;)
john_sleeps = john >> sleeps # John sleeps: I → s
# Parallel composition (⊗)
mary = Box('Mary', Ty(), n)
john_and_mary = john @ mary # John ⊗ Mary: I → n ⊗ n
String Diagrams
# Create and draw diagram
diagram = john >> sleeps
diagram.draw()
# Export formats
diagram.draw(path="diagram.png")
Pregroup Grammar
from discopy.grammar.pregroup import Ty, Word, Cup, Id
# Pregroup types with adjoints
n = Ty('n')
s = Ty('s')
n_r = n.r # right adjoint
n_l = n.l # left adjoint
# Words with grammatical types
john = Word('John', n)
sleeps = Word('sleeps', n.r @ s)
loves = Word('loves', n.r @ s @ n.l)
# Parse "John sleeps"
sentence = john @ sleeps >> Cup(n, n.r) @ Id(s)
Functorial Semantics
import numpy as np
from discopy.tensor import Tensor, Dim
# Meaning functor: Grammar → Vect
d = Dim(2)
john_vec = Tensor(dom=Dim(1), cod=d, array=np.array([1, 0]))
sleeps_mat = Tensor(dom=d, cod=Dim(1), array=np.array([0.8, 0.2]))
# Compose to get sentence meaning
result = john_vec >> sleeps_mat
Quantum Circuit Semantics
from discopy.quantum import Circuit, Ket, Bra, H, CX
# Map words to quantum circuits
john_circuit = Ket(0)
mary_circuit = Ket(1)
entangle = CX >> (H @ Circuit.id(1))
Categorical Guarantees
DisCoPy ensures:
- Monoidal Laws: Associativity and unit laws for ⊗
- Functoriality: Semantic maps preserve composition
- String Diagram Correctness: Diagrams represent valid morphisms
- Type Safety: Composition only when types match