Bidirectional Typing with Freezing, Skeletons, and Ghosts | Paper Citation Record

Observation d1f1178a-b863-4802-9617-27ffb307a730 · outbound

This paper cites https://github.com/4y8/modal-effect-types/tree/frost.

Bidirectional Typing with Freezing, Skeletons, and Ghosts https://github.com/4y8/modal-effect-types/tree/frost

Reference 1

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Observation f20c7686-f6ef-4ead-addd-834c1c0a8876 · outbound

This paper cites 1985.The lambda calculus - its syntax and semantics.

Bidirectional Typing with Freezing, Skeletons, and Ghosts 1985.The lambda calculus - its syntax and semantics

Reference 2

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Observation 2590e5f9-8cdc-44b0-b03b-b11343c27b53 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation eb43e11b-0000-4a7e-8845-44559032729d · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 9ea5eb80-e4ea-43b2-a066-8b125f749b25 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation c641d24d-9cfa-4686-ac9f-c5263add9f67 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 2218f7d0-b870-434a-b1a2-67f259dd5083 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 67defd80-a4a2-4cbb-a7f4-d3250f1f16ac · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 8

Resolution: verified exact; doi, observed 2026-08-01T21:38:35.519935Z

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Observation 627ac0da-16fa-4e18-b00c-75211fc66d8d · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 9

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Observation 290a3ea7-5e09-4cde-b5fa-0e9ea36a7247 · outbound

This paper cites Krishnaswami.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Krishnaswami

Reference 10

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Observation 9cc9c300-8b98-47d5-981b-7c2387bcbb6e · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 89c36e15-f3b2-427c-95fa-c57134c420dd · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation d91bcb03-e18d-4efc-ae92-8ee0aad36582 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 13

Resolution: verified exact; doi, observed 2026-08-01T21:38:35.412543Z

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Observation fd5b713c-14a6-4ad3-b181-c35655dd336e · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 714fc642-4c9c-42b2-ab32-d33376b3cd3f · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Resolution: verified exact; doi, observed 2026-08-01T21:38:35.301824Z

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Observation 1ed0aaf6-f8af-4fc1-a18b-897802cdd3a1 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 9d701e07-889d-4319-867a-d9721b83f24d · outbound

This paper cites 2013.Type inference, Haskell and dependent types.

Bidirectional Typing with Freezing, Skeletons, and Ghosts 2013.Type inference, Haskell and dependent types

Reference 17

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Observation e2478650-893d-47f0-ab69-4c621784f60b · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 9cd84a2f-a197-44dd-b24a-562830257b57 · outbound

This paper cites Peyton Jones, Dimitrios Vytiniotis, Stephanie Weirich, and Mark Shields.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Peyton Jones, Dimitrios Vytiniotis, Stephanie Weirich, and Mark Shields

Reference 19

Resolution: verified exact; doi, observed 2026-08-01T21:38:35.160056Z

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Observation b18b928a-0f0d-45f6-b304-fcf79b7636eb · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation cda4d7b2-8a37-44e2-a6b2-cc2584dcc9d5 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 21

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Observation 28368278-c818-4227-ab4a-7749b664fc31 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 96dabc0c-47b9-4da7-b547-c21b8e396b94 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 870f0651-7da0-436f-863b-664eee5caa24 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 24

Resolution: verified exact; doi, observed 2026-08-01T21:38:34.894465Z

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Observation 7e54a630-f6ec-4bcf-a5bb-79b274e1dc7b · outbound

This paper cites 1990.Definition of standard ML.

Bidirectional Typing with Freezing, Skeletons, and Ghosts 1990.Definition of standard ML

Reference 25

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Observation 10d0693a-6698-4508-a433-f7878dc4eabe · outbound

This paper cites Garrett Morris.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Garrett Morris

Reference 26

Resolution: verified exact; doi, observed 2026-08-01T21:38:34.773495Z

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Observation 7541c2b7-d17e-4a9a-bc14-a216e3f89ec8 · outbound

This paper cites Omnidirectional type inference for ML: principality any way.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Omnidirectional type inference for ML: principality any way

Reference 27

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Observation 6e773ff9-ecb0-4898-b16c-0401c7f39685 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 28

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Observation 223f59dd-d9d9-485f-9906-d5d8e8db628f · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 29

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Observation d1a03a2d-99ef-41b5-bfb8-98ad6d29af15 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 30

Resolution: verified exact; doi, observed 2026-08-01T21:38:34.636927Z

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Observation 8f694003-71d0-4431-b74c-a1d598c9bbcf · outbound

This paper cites Pierce and David N.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Pierce and David N

Reference 31

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Observation 69c257bd-59be-4fbd-9ef9-a246fd0075dd · outbound

This paper cites Plotkin and John Power.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Plotkin and John Power

Reference 32

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Observation efb4b9b0-4dae-4939-ac7c-17895aeae3bf · outbound

This paper cites Plotkin and Matija Pretnar.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Plotkin and Matija Pretnar

Reference 33

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Observation bf345aa5-0e92-4a8f-a410-018c5961fb57 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 34

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Observation 6a7de3d5-d006-4b91-ab78-81dba44b1f4b · outbound

This paper cites Russo and Dimitrios Vytiniotis.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Russo and Dimitrios Vytiniotis

Reference 35

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Observation deef33a0-980f-4c5e-866e-b0d9f7146128 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 4595b5ce-af1f-480c-9df0-cbed9fee92d8 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 2f14d729-e14c-4f2b-9ef4-0615d1047df5 · outbound

This paper cites Siek and Walid Taha.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Siek and Walid Taha

Reference 38

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Observation b33da978-7a83-47fe-ae5a-e635edef3c9a · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation eb2272a6-7e7d-4074-a2af-7381c5f9b06b · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation c09975e3-cbc9-4b2d-a51d-4edc152292c6 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 4d043261-c89e-465c-b230-19f4908de258 · outbound

This paper cites Peyton Jones.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Peyton Jones

Reference 42

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Observation 53fee70d-392b-480d-8b10-a2799745e8e0 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation bbfc7786-2e7b-47e5-a76f-1a2aee5db20f · outbound

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Observation 38cecab3-7e58-40ec-b8d2-8c0ecc611e64 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 3a979821-3c96-4787-94ed-436e1e56be4d · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 46

Resolution: verified exact; doi, observed 2026-08-01T21:38:34.440216Z

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Observation 4915fc25-b3f0-4f05-a01a-cc7cc4d1e915 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 47

Resolution: verified exact; doi, observed 2026-08-01T21:38:34.352019Z

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Observation 8b1f760c-e0b3-4426-8346-6bdf09a2bd3e · outbound

This paper cites A solution to it is a tuple(𝜃1 :: Θ0⊑Θ 1;𝑃1) such that Θ1⊢𝜃 1𝑃∼𝑃 1 where Θ1⊢𝜃 1𝑃0 ▶𝑃1.

Bidirectional Typing with Freezing, Skeletons, and Ghosts A solution to it is a tuple(𝜃1 :: Θ0⊑Θ 1;𝑃1) such that Θ1⊢𝜃 1𝑃∼𝑃 1 where Θ1⊢𝜃 1𝑃0 ▶𝑃1

Reference 48

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Observation b2b1f002-7a94-4b09-bbbf-6567477b687c · outbound

This paper cites A solution to it is a metasubstitution𝜃1 :: Θ0⊑Θ 1 such that Θ1⊢𝜃 1 ˆ𝛼∼𝜃 1 ˆ𝛽.

Bidirectional Typing with Freezing, Skeletons, and Ghosts A solution to it is a metasubstitution𝜃1 :: Θ0⊑Θ 1 such that Θ1⊢𝜃 1 ˆ𝛼∼𝜃 1 ˆ𝛽

Reference 49

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Observation 18cb9f90-9b29-476b-8c90-8b823e408729 · outbound

This paper cites A solution to it is a metasubstitution𝜃1 :: Θ0,Ξ⊑Θ 1 such that Θ1⊢𝜃 1𝑃∼𝜃 1 ˆ𝛼.

Bidirectional Typing with Freezing, Skeletons, and Ghosts A solution to it is a metasubstitution𝜃1 :: Θ0,Ξ⊑Θ 1 such that Θ1⊢𝜃 1𝑃∼𝜃 1 ˆ𝛼

Reference 50

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Observation 98515dc2-cb83-4243-bc1d-18638849c010 · outbound

This paper cites Lemma C.7 (Completeness and optimality of consistency).

Bidirectional Typing with Freezing, Skeletons, and Ghosts Lemma C.7 (Completeness and optimality of consistency)

Reference 53

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Observation bd463151-8958-4267-a70a-8235281480fe · outbound

This paper cites 40 Wenhao Tang, Shengyi Jiang, Aghilas Y.

Bidirectional Typing with Freezing, Skeletons, and Ghosts 40 Wenhao Tang, Shengyi Jiang, Aghilas Y

Reference 56

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Observation 7f28d32b-441a-4736-89b7-b3081be57233 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 7c198b1a-bd5c-4a78-a699-b26a79bd0d17 · outbound

This paper cites By 10 , we have𝑃=𝑃 1→𝑃 2.

Bidirectional Typing with Freezing, Skeletons, and Ghosts By 10 , we have𝑃=𝑃 1→𝑃 2

Reference 58

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Observation 8208c01a-84c6-4bd7-8294-b445061fc8f3 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation 19c81267-fcab-4e02-9f90-62e7992972ee · outbound

This paper cites We proceed by case analysis on𝑃𝑖.

Bidirectional Typing with Freezing, Skeletons, and Ghosts We proceed by case analysis on𝑃𝑖

Reference 60

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Observation 9794efe8-18af-403f-a115-e40f41588dbb · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 61

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Observation aaa07337-a871-4b95-8e23-4109add35abb · outbound

This paper cites We proceed by case analysis on𝑃𝑖.

Bidirectional Typing with Freezing, Skeletons, and Ghosts We proceed by case analysis on𝑃𝑖

Reference 62

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Observation 3bc309c6-5557-47a5-bcb7-179d136c7f6f · outbound

This paper cites We proceed by case analysis on𝑃𝑖.

Bidirectional Typing with Freezing, Skeletons, and Ghosts We proceed by case analysis on𝑃𝑖

Reference 63

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Observation b9fadd19-3952-4914-885f-3119bf9ea85d · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

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Observation ba7d7bf5-39d8-41f0-9d5c-4167fd4c5ec4 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 65

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Observation 361c5232-c4af-4095-8c35-38b7d6b70bb9 · outbound

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Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 66

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Observation 6ce048e5-811c-44d3-b1c4-b6c44a35f070 · outbound

This paper cites Case U-Flex-Flex-Id ˆ𝛼∈dom(Θ 0) Θ0⊢ ˆ𝛼≃ ˆ𝛼⊣Θ 0 Trivial.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Case U-Flex-Flex-Id ˆ𝛼∈dom(Θ 0) Θ0⊢ ˆ𝛼≃ ˆ𝛼⊣Θ 0 Trivial

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:44.665559Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8128164-1153-4d61-94a9-bb31919c9293 · outbound

This paper cites CaseU-Assign-UnivGhost-Id.

Bidirectional Typing with Freezing, Skeletons, and Ghosts CaseU-Assign-UnivGhost-Id

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:44.771681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9753ffff-d266-44c9-b706-1124a177105d · outbound

This paper cites Case U-Ghost Δ2∩ftv(𝑃 0)=∅ Θ0[𝑃0]- -Δ1|Δ 2 ∼𝑃 0⊣Θ 0 We haveΘ 0⊑Θ 0 by reflexivity.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Case U-Ghost Δ2∩ftv(𝑃 0)=∅ Θ0[𝑃0]- -Δ1|Δ 2 ∼𝑃 0⊣Θ 0 We haveΘ 0⊑Θ 0 by reflexivity

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:44.874820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52dbd681-8c48-4cd7-a7c2-841cf4172db2 · outbound

This paper cites an unresolved cited work.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:44.997081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a94890ad-22ae-49b9-91f4-ccc192ca41c0 · outbound

This paper cites an unresolved cited work.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.063793Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation efa5a5b0-fd28-41c5-bc8e-d471b63dcd42 · outbound

This paper cites an unresolved cited work.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Unresolved cited work

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.147842Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0f7ab62-8004-4e74-857e-a0d249b084ef · outbound

This paper cites By induction on the context Θ0 and case analysis on which algorithmic unification rule to use.

Bidirectional Typing with Freezing, Skeletons, and Ghosts By induction on the context Θ0 and case analysis on which algorithmic unification rule to use

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.244598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d2e5e5a-fcf6-43cd-9042-e90da47a90e6 · outbound

This paper cites there existΘ 1 and𝜃 1 such that Θ0|Ξ⊢ ˆ𝛼≔𝑃⊣Θ 1 𝜃1 :: Θ1⊑Θ𝜃≡𝜃 1 :: Θ0,Ξ⊑Θ.

Bidirectional Typing with Freezing, Skeletons, and Ghosts there existΘ 1 and𝜃 1 such that Θ0|Ξ⊢ ˆ𝛼≔𝑃⊣Θ 1 𝜃1 :: Θ1⊑Θ𝜃≡𝜃 1 :: Θ0,Ξ⊑Θ

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.343884Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c023a4dc-90ec-405e-87e2-9852aa4a88e4 · outbound

This paper cites We prove by induction on the declarative consistency derivation Ψ|Θ⊢𝜃𝑆∼𝑄.

Bidirectional Typing with Freezing, Skeletons, and Ghosts We prove by induction on the declarative consistency derivation Ψ|Θ⊢𝜃𝑆∼𝑄

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.506446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 251cf4b3-3e8d-40bf-b787-626109a77dc5 · outbound

This paper cites Case C-Ghost ·|Θ⊢ ∼𝑄 In this case𝑆= and𝑃=.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Case C-Ghost ·|Θ⊢ ∼𝑄 In this case𝑆= and𝑃=

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.595435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae9668f8-c9d9-4633-8af4-b0d45203d2ab · outbound

This paper cites Bidirectional Typing with Freezing, Skeletons, and Ghosts 117 By inversion on 4 , we have Θ,𝛼|Δ 2,𝛼⊢𝜃𝑃 ′ ▶𝑄 6.

Bidirectional Typing with Freezing, Skeletons, and Ghosts Bidirectional Typing with Freezing, Skeletons, and Ghosts 117 By inversion on 4 , we have Θ,𝛼|Δ 2,𝛼⊢𝜃𝑃 ′ ▶𝑄 6

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.690878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2190744-a3da-4960-ab41-35f9fef41e5f · outbound

This paper cites By guardedness of𝑄, inversion on 4 gives Θ|Δ 2⊢𝜃𝑃 ′ ▶𝑄 6.

Bidirectional Typing with Freezing, Skeletons, and Ghosts By guardedness of𝑄, inversion on 4 gives Θ|Δ 2⊢𝜃𝑃 ′ ▶𝑄 6

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-01T21:35:45.798463Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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