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Composition and Merging of Assume-Guarantee Contracts Are Tensor Products

Inigo Incer

Abstract

We show that the operations of composition and merging of contracts are part of the tensor product structure of the algebra of contracts.

Composition and Merging of Assume-Guarantee Contracts Are Tensor Products

Abstract

We show that the operations of composition and merging of contracts are part of the tensor product structure of the algebra of contracts.
Paper Structure (9 sections, 6 theorems, 18 equations)

This paper contains 9 sections, 6 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Assume-guarantee contracts
  3. Conjunction and disjunction
  4. Axioms for composition and merging
  5. Tensor products of contracts
  6. Tensor products of bimodules over monoids
  7. The tensor product of conjunctive monoids of contracts
  8. The tensor product of disjunctive monoids of contracts
  9. Discussion and concluding remarks

Key Result

corollary 1

The contracts $0 \coloneq (1_\mathbf{B}, 0_\mathbf{B})$ and $1 \coloneq (0_\mathbf{B}, 1_\mathbf{B})$ are, respectively, the bottom and top of $\mathbb{C}(\mathbf{B})$.

Theorems & Definitions (12)

  • definition 1
  • corollary 1
  • proposition 1
  • proof
  • definition 2
  • corollary 2
  • proposition 2
  • proof
  • theorem 1
  • proof
  • ...and 2 more