docs: sumcheck documentation

barretenberg/cpp/docs/src/honk.md

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+# Honk
+
+Honk is a sumcheck-based SNARK protocol which is similar to HyperPlonk [HyperPlonk]. A theory paper, based on the thesis [H], is forthcoming. This spec described what is currently implemented in Barretenberg.
+
+The variants of Honk that we build will be heavily optimized. As a warm-up, we describe a basic, unoptimized version of the protocol [here](honk-outline.md).
+
+# Preliminaries
+
+# Flavors
+
+# Prover's algorithm
+This is outlined in `proof_system::honk::UltraProver::construct_proof()`:
+ \snippet cpp/src/barretenberg/ultra_honk/ultra_prover.cpp ConstructProof
+
+## Sumcheck
+Sumcheck protocol is a proof system allowing to efficiently prove claims about the sums of values of multilinear polynomials in \f$ d \f$ variables over the Boolean hypercube \f$ \{0,1\}^d \f$ as well as more elaborate relations between such polynomials. Our implementation of Sumcheck including is described [here](sumcheck-outline.md).
+# Verifier's algorithm