From program verification to program synthesis

Question

1. What are the contributions in "From program verification to program synthesis" ?

2. What future works have the authors mentioned in the paper "From program verification to program synthesis" ?

3. What is the function that expands a flowgraph?

4. Why does the solver not derive s2 + 1 s1?

Accepted Answer

This paper describes a novel technique for the synthesis of imperative programs.. In their approach, which the authors call proof-theoretic synthesis, the user provides an input-output functional specification, a description of the atomic operations in the programming language, and a specification of the synthesized program ’ s looping structure, allowed stack space, and bound on usage of certain operations.. The insight behind their approach is to interpret program synthesis as generalized program verification, which allows us to bring verification tools and techniques to program synthesis.. The authors demonstrate the feasibility of the proposed approach by synthesizing programs in three different domains: arithmetic, sorting, and dynamic programming.. Using verification tools that the authors previously built in the VS project they are able to synthesize programs for complicated arithmetic algorithms including Strassen ’ s matrix multiplication and Bresenham ’ s line drawing ; several sorting algorithms ; and several dynamic programming algorithms.. Automated program synthesis has the potential to make programming and the design of systems easier by allowing programs to be specified at a higher-level than executable code.. For these programs, the median time for synthesis is 14 seconds, and the ratio of synthesis to verification time ranges between 1× to 92× ( with an median of 7× ), illustrating the potential of the approach.

Accepted Answer

The authors envision that in the future, they can either augment synthesis conditions with constraints about relevance or use a postprocessing step to prioritize and pick relevant solutions from those enumerated.

Accepted Answer

Given a string for a flowgraph template, the authors define an expansion function Expand : int ×Dprf ×R ×D ×Rflow → TSL that introduces fresh unknowns for missing guards, statements and invariants that are to be synthesized.

Accepted Answer

because of the incompleteness in the handling of quadratic expressions, their solver cannot derive (s2 + 1)2 ≤ s21 from s2 + 1 ≤ s1.

Accepted Answer

The authors encode the synthesis problem as a verification problem by encoding program guards and statements as logical facts that need to be discovered.

Accepted Answer

The authors have demonstrated the viability of their approach by synthesizing difficult examples in the three domains of arithmetic, sorting, and dynamic programming, all in very reasonable time.

Accepted Answer

The synthesis conditions corresponding to a scaffold are satisfiable iff there exists a program (with a maximum of n transitions in each acyclic fragment where n is the parameter to the expansion) that is valid with respect to the scaffold.

Accepted Answer

The authors constrain the well-formedness of each transition system in the expanded scaffold exp = ExpandD,Rn,Dprf(Rflow) using Eq. (4).WellFormCond(exp) = ^choose {[]gi→si}i ∈cond(exp)WellFormTS({[]gi → si}i) (5)where cond(exp) recursively examines the expanded scaffold exp and returns the set of all choose statements in it.

Accepted Answer

Disjointedness is not required for correctness [11] because if multiple guards are triggered then arbitrarily choosing the body for any one suffices.

Accepted Answer

The authors then observe that they resemble verification conditions, and the authors can employ verification tools, if they have certain properties, to solve them (Section 4).

Accepted Answer

This assumption holds without loss of generality because it is always possible to collapse consecutive acyclic fragments, e.g., two consecutive acyclic fragments with n transitions each can be collapsed into a single acyclic fragment with n2 transitions.

From program verification to program synthesis

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Most frequently asked questions

1. What are the contributions in "From program verification to program synthesis" ?

2. What future works have the authors mentioned in the paper "From program verification to program synthesis" ?

3. What is the function that expands a flowgraph?

4. Why does the solver not derive s2 + 1 s1?

5. How do the authors encode program guards and statements?

6. How have the authors demonstrated the viability of their approach?

7. What are the synthesis conditions for an expanded scaffold?

8. How do the authors constrain the well-formedness of an expanded scaffold?

9. What is the way to ensure that the guards are not disjointed?

10. What are the constraints that are used to solve the synthesis conditions?

11. What is the simplest way to collapse acyclic fragments?

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References

Introduction to Algorithms

Introduction to algorithms: 4. Turtle graphics

Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

A Discipline of Programming

Introduction to Algorithms, 2nd edition.

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