{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JMFY7VVLAYPCZNOKCZZPDBSDLH","short_pith_number":"pith:JMFY7VVL","canonical_record":{"source":{"id":"1711.04718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-13T17:30:12Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"08d0735b5a54806ade69288f58c1aef026ff5873abf2e4d0dd07a9ee481087a8","abstract_canon_sha256":"6aba6f3595c5e79a2b79732c734edcf4eafade1849c6a2d4f170c207cd61bc18"},"schema_version":"1.0"},"canonical_sha256":"4b0b8fd6ab061e2cb5ca1672f1864359d33fd1253d577411e6561bd5e9a76b91","source":{"kind":"arxiv","id":"1711.04718","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04718","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04718v1","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04718","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"JMFY7VVLAYPC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JMFY7VVLAYPCZNOK","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JMFY7VVL","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JMFY7VVLAYPCZNOKCZZPDBSDLH","target":"record","payload":{"canonical_record":{"source":{"id":"1711.04718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-13T17:30:12Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"08d0735b5a54806ade69288f58c1aef026ff5873abf2e4d0dd07a9ee481087a8","abstract_canon_sha256":"6aba6f3595c5e79a2b79732c734edcf4eafade1849c6a2d4f170c207cd61bc18"},"schema_version":"1.0"},"canonical_sha256":"4b0b8fd6ab061e2cb5ca1672f1864359d33fd1253d577411e6561bd5e9a76b91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:35.857277Z","signature_b64":"Bmj/JQSJUKGr7yi8halXlfT6Mjvq2fRxy/f11NSARMQMpI0gRXsGV91rdWV/wjq/3oJIQ58IvrdWjhn2t7deBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0b8fd6ab061e2cb5ca1672f1864359d33fd1253d577411e6561bd5e9a76b91","last_reissued_at":"2026-05-18T00:30:35.856729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:35.856729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.04718","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTozdsrRindN3weAFVqpIBOx3Yne6B4jrU245lhRvlgp6gJ4u+jTlD+T3NB7utmeCNWmqfDJJvhU7dNfqEgPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:15:57.836874Z"},"content_sha256":"dd86170b9f6e128207f3ae2ccf2c4950ce2a65ec623a4304ffaa9bbcc557d0a8","schema_version":"1.0","event_id":"sha256:dd86170b9f6e128207f3ae2ccf2c4950ce2a65ec623a4304ffaa9bbcc557d0a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JMFY7VVLAYPCZNOKCZZPDBSDLH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Type Checking Algorithm for Higher-rank, Impredicative and Second-order Types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Peng Fu","submitted_at":"2017-11-13T17:30:12Z","abstract_excerpt":"We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is before each function declaration. We prove the soundness of the type checking algorithm with respect to System $\\mathbf{F}_{\\omega}$, i.e. if the program is type checked, then the type checker will produce a well-typed annotated System $\\mathbf{F}_{\\omega}$ term. We extend the basic algorithm to handle pattern matching and let-bindings. We implement a proto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04718","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYK/xIzOS+NrCPmg2uumBDlDXhJ/S79e+Ahb1Ry+Dn1OLv8/xbZSA45foEYNGH7smdrxGZfRkuOHCGPJmTroAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:15:57.837507Z"},"content_sha256":"6e1fcbedad54411a3e1d56ecfa0737d5c03b4087aae74e48b1441eaf4e745af6","schema_version":"1.0","event_id":"sha256:6e1fcbedad54411a3e1d56ecfa0737d5c03b4087aae74e48b1441eaf4e745af6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH/bundle.json","state_url":"https://pith.science/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T23:15:57Z","links":{"resolver":"https://pith.science/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH","bundle":"https://pith.science/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH/bundle.json","state":"https://pith.science/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMFY7VVLAYPCZNOKCZZPDBSDLH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JMFY7VVLAYPCZNOKCZZPDBSDLH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6aba6f3595c5e79a2b79732c734edcf4eafade1849c6a2d4f170c207cd61bc18","cross_cats_sorted":["cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-13T17:30:12Z","title_canon_sha256":"08d0735b5a54806ade69288f58c1aef026ff5873abf2e4d0dd07a9ee481087a8"},"schema_version":"1.0","source":{"id":"1711.04718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04718","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04718v1","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04718","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"JMFY7VVLAYPC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JMFY7VVLAYPCZNOK","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JMFY7VVL","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:6e1fcbedad54411a3e1d56ecfa0737d5c03b4087aae74e48b1441eaf4e745af6","target":"graph","created_at":"2026-05-18T00:30:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is before each function declaration. We prove the soundness of the type checking algorithm with respect to System $\\mathbf{F}_{\\omega}$, i.e. if the program is type checked, then the type checker will produce a well-typed annotated System $\\mathbf{F}_{\\omega}$ term. We extend the basic algorithm to handle pattern matching and let-bindings. We implement a proto","authors_text":"Peng Fu","cross_cats":["cs.PL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-13T17:30:12Z","title":"A Type Checking Algorithm for Higher-rank, Impredicative and Second-order Types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04718","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dd86170b9f6e128207f3ae2ccf2c4950ce2a65ec623a4304ffaa9bbcc557d0a8","target":"record","created_at":"2026-05-18T00:30:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6aba6f3595c5e79a2b79732c734edcf4eafade1849c6a2d4f170c207cd61bc18","cross_cats_sorted":["cs.PL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-13T17:30:12Z","title_canon_sha256":"08d0735b5a54806ade69288f58c1aef026ff5873abf2e4d0dd07a9ee481087a8"},"schema_version":"1.0","source":{"id":"1711.04718","kind":"arxiv","version":1}},"canonical_sha256":"4b0b8fd6ab061e2cb5ca1672f1864359d33fd1253d577411e6561bd5e9a76b91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0b8fd6ab061e2cb5ca1672f1864359d33fd1253d577411e6561bd5e9a76b91","first_computed_at":"2026-05-18T00:30:35.856729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:35.856729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bmj/JQSJUKGr7yi8halXlfT6Mjvq2fRxy/f11NSARMQMpI0gRXsGV91rdWV/wjq/3oJIQ58IvrdWjhn2t7deBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:35.857277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd86170b9f6e128207f3ae2ccf2c4950ce2a65ec623a4304ffaa9bbcc557d0a8","sha256:6e1fcbedad54411a3e1d56ecfa0737d5c03b4087aae74e48b1441eaf4e745af6"],"state_sha256":"0c704f88cdab941f3a442380c008b6c9c3d13f18299cf0097d7cbd8e957d096b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82JNKwJhjd/jqYGUI/EMbnU4friLIVCTzy0kxfaagjQMek5kLmvMteSB63k2Ksy1FBkSfI30Vy22fwt5R6FJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:15:57.841068Z","bundle_sha256":"ba3cce5188e9c5f52193be9cd18a524acf545f6f4c5cea33908fa433d24ca49e"}}