feat: add examples

src/examples.md

@@ -1,2 +1,128 @@
 # Examples
-> Examples of PODs at the conceptual level (ie. ZuKYC, ETHDos, etc).
+
+Examples of POD2 use cases
+
+## EthDos
+
+Original in prolog https://gist.github.com/ludns/f84b379ec8c53c97b7f95630e16cc39c#file-eth_dos-pl
+
+An EthDos Pod exposes a single custom statement with two custom deduction
+rules, the inductive case and the base case.
+
+```
+statement eth_dos_distance(src: PubKey, dst: PubKey, distance: Int):
+   - OR():
+      - AND(attestation_pod: Pod, intermediate: PubKey, n: int):
+         - eq(attetation_pod.attestation, dst)
+         - eq(attetation_pod.type, SIGNATURE)
+         - sum_of(distance, 1, n)
+         - eth_dos_distance(src, attetation_pod.signer, n)
+      - AND():
+         - eq(src, dst)
+         - eq(distance, 0)
+```
+
+## ZuKYC (classic)
+
+Original using GPC https://github.com/proofcarryingdata/zukyc
+
+Authority public keys:
+- `ZOO_GOV`: PubKey, issues IDs
+- `ZOO_DEEL`: PubKey, issues bank statements
+Authority lists:
+- `SANCTION_LIST`: Hash, Merkle Tree Root of set of sanctioned public keys
+    - values: `["G2345678", "G1987654", "G1657678"]`
+Date values:
+- `NOW_MINUS_18Y`: Int, 18 years ago
+- `NOW_MINUS_1Y`: Int, 1 year ago
+- `NOW_MINUS_7D`: Int, 7 days ago
+
+A ZuKYC Pod exposes a single custom statement with one custom deduction rule.
+
+```
+statement loan_check(receiver: PubKey):
+   - OR():
+      - AND(gov_id: Pod, paystub: Pod):
+         - eq(gov_id.pk, receiver)
+         # Not in the sanction list
+         - does_not_contain(SANCTION_LIST, gov_id.pk)
+         # Valid government-issued ID
+         - eq(gov_id.signer, ZOO_GOV)
+         - eq(gov_id.type, SIGNATURE)
+         # At least 18 years old
+         - lt(gov_id.date_of_birth, NOW_MINUS_18Y) # date_of_birdth is more than 18y old
+         - eq(paystub.signer, ZOO_DEEL)
+         - eq(paystub.type, SIGNATURE)
+         - eq(paystub.ssn, gov_id.ssn)
+         # At least one year of consistent employment with your current employer
+         - lt(paystub.start_date, NOW_MINUS_1Y) # start_date is more than 1y old
+         - gt(paystub.issue_date, NOW_MINUS_7D) # issue_date is less than 7d old
+         # Annual salary is at least $20,000
+         - gt(paystub.anual_salary, 20000)
+```
+
+## ZuKYC (simplified for P1)
+
+This simplified version uses less statements but requires a very similar set of
+features.
+
+Authority lists:
+- `SANCTION_LIST`: Hash, Merkle Tree Root of set of sanctioned public keys
+    - values: `["G2345678", "G1987654", "G1657678"]`
+Date values:
+- `NOW_MINUS_18Y`: Int, 18 years ago
+- `NOW_MINUS_1Y`: Int, 1 year ago
+
+A ZuKYC Pod exposes a single custom statement with one custom deduction rule.
+
+```
+statement loan_check(receiver: string):
+   - OR():
+      - AND(gov_id: Pod, paystub: Pod):
+         - eq(gov_id.id_number, receiver)
+         # Not in the sanction list
+         - does_not_contain(SANCTION_LIST, gov_id.id_number)
+         # Valid government-issued ID
+         - reveal(gov_id.signer)
+         - eq(gov_id.type, SIGNATURE)
+         # At least 18 years old
+         - lt(gov_id.date_of_birth, NOW_MINUS_18Y) # date_of_birdth is more than 18y old
+         - reveal(paystub.signer)
+         - eq(paystub.type, SIGNATURE)
+         - eq(paystub.ssn, gov_id.ssn)
+         # At least one year of consistent employment with your current employer
+         - lt(paystub.start_date, NOW_MINUS_1Y) # start_date is more than 1y old
+```
+
+## GreatBoy
+
+A Good Boy Pod exposes one custom statement with one custom deduction rule.
+
+```
+statement good_boy(receiver: PubKey, good_boy_issuers: MerkleTree):
+   - OR():
+      - AND(pod: Pod):
+         # A good boy issuer is my friend
+         - eq(pod.type, SIGNATURE)
+         - contains(good_boy_issuers, pod.signer)
+         - eq(pod.friend, receiver)
+```
+
+A Great Boy Pod exposes (in addition to the above) one new custom statement
+with one custom deduction rule.
+
+```
+statement great_boy(receiver: PubKey, good_boy_issuers: MerkleTree):
+   - OR():
+      - AND(friend_pod_0: Pod, friend_pod_1: Pod):
+         # good boy 0 is my friend
+         - eq(friend_pod_0.type, SIGNATURE)
+         - good_boy(friend_pod_0.signer, good_boy_issuers)
+         - eq(friend_pod_0.friend, receiver)
+         # good boy 1 is my friend
+         - eq(friend_pod_1.type, SIGNATURE)
+         - good_boy(friend_pod_1.signer, good_boy_issuers)
+         - eq(friend_pod_1.friend, receiver)
+         # good boy 0 != good boy 1
+         - neq(friend_pod_0.signer, friend_pod_1.signer)
+```