of the trivial generating function from a kind of “semi-classical" formality theorem.

At last we plan to compare the formal construction carried out in this article with the non-formal construction coming from the Poisson-sigma model (see [@feldcat2000]) and with the local symplectic groupoid construction of [@CDW1987] and [@karasev1987].

The second author thanks Ernst Hairer for useful discussions, and suggestions.

Recovering the formal groupoid from the generating function {#recovering}
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In this section we show that one can recover formally the structure of symplectic groupoid from a generating function obeying the SGA equation.

\[formalgroupoid\] Let $S_h$ be a natural deformation of the trivial generating function which satisfies the SGA equation. Then the set $G_h = \mathbb R^{*d}[[h]]\times \mathbb R^d[[h]]$ can be given a structure of **formal symplectic groupoid**, i.e., the maps $$\begin{array}{cccc}
\epsilon_h(x) & = & (0,x)  &\textbf{unit map}\\
i_h(p,x)      & = & (-p,x) &\textbf{inverse map}\\
s_h(p,x)      & = & \nabla_{p_2}S_h(p,0,x) & \textbf{source map}\\
t_h(p,x)      & = & \nabla_{p_1}S_h(0,p,x) & \textbf{target map}
\end{array}$$ and the multiplication given by $$G_h^{(m)}= {\operatorname{graph}}(dS)$$ satisfy formally the axioms of a groupoid.

In particular, if we endow $G_h$ with the canonical symplectic form, then $G_h^{(m)}$ is formally Lagrangian in $\overline{G_h}\times \overline{G_h}\times G_h$.

The multiplication space being 