{"id":18221742,"url":"https://github.com/kamirus/lambda-formalizations","last_synced_at":"2025-08-02T09:36:29.498Z","repository":{"id":43957293,"uuid":"362751252","full_name":"Kamirus/lambda-formalizations","owner":"Kamirus","description":"Lambda Calculi Formalizations in Coq using nested datatypes for a type-safe term representation","archived":false,"fork":false,"pushed_at":"2022-09-15T10:20:04.000Z","size":397,"stargazers_count":4,"open_issues_count":0,"forks_count":1,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-03-18T04:35:23.717Z","etag":null,"topics":["control-operators","coq-formalization","effect-handlers","effect-system","lambda-calculus","nested-datatypes","preservation","progress","stlc","theorem-proving"],"latest_commit_sha":null,"homepage":"","language":"Coq","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Kamirus.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2021-04-29T08:50:17.000Z","updated_at":"2023-07-28T10:01:03.000Z","dependencies_parsed_at":"2023-01-18T08:30:36.343Z","dependency_job_id":null,"html_url":"https://github.com/Kamirus/lambda-formalizations","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Kamirus%2Flambda-formalizations","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Kamirus%2Flambda-formalizations/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Kamirus%2Flambda-formalizations/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Kamirus%2Flambda-formalizations/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Kamirus","download_url":"https://codeload.github.com/Kamirus/lambda-formalizations/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":246925195,"owners_count":20855853,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["control-operators","coq-formalization","effect-handlers","effect-system","lambda-calculus","nested-datatypes","preservation","progress","stlc","theorem-proving"],"created_at":"2024-11-03T22:04:08.818Z","updated_at":"2025-04-03T02:30:47.106Z","avatar_url":"https://github.com/Kamirus.png","language":"Coq","readme":"# Lambda Calculi Formalizations\n\n- **Simply Typed Lambda Calculus**\n  - [Term representation using Nested Datatypes](Terms.v)\n    - [Progress and Preservation](STLC_Generic.v)\n  - [Legacy: Type-Level de Bruijn indices](stlc.v) (unnecessarily difficult approach)\n- **Delimited-Control Operators shift0/dollar**:\n  - Introduction : [Delimited Control](DelimitedControl.md)\n  - **Contribution**:\n    - Formalize `λ$` calculus with its **evaluation** strategy\n    - Introduce an **evaluation** strategy for `λc$` (a fine-grained version of `λ$`)\n    - Define **similarity** relations to prove **correspondance** between both calculi in a form of **simulations** which state that: *similar terms compute to similar values*\n  - [`λ$` calculus](LambdaDollar.v) (paper reference: [section 2.2](https://ii.uni.wroc.pl/~dabi/publications/APLAS12/materzok-biernacki-aplas12.pdf))\n  - [`λc$` calculus: a Fine-Grained version of `λ$`](LambdaLetDollar.v) (paper reference: [Figure 1](https://dl.acm.org/doi/10.1145/3479394.3479399))\n  - Correspondence between `λ$` and `λc$`:\n    - [Simulation: `λ$` to `λc$`](LambdaDollarToLet.v)\n    - [Simulation: `λc$` to `λ$`](LambdaLetToDollar.v)\n\nCreate Makefile with `coq_makefile -f _CoqProject *.v -o Makefile`\n\n\n## Future Work\n- Examine the potential of supporting the `control0` operator for the current evaluation strategy\n- Develop the alternative evaluation strategy - the hybrid (reduces differently when under the delimiter) one that aggressively duplicates `$`\n  - Simplify both calculi to the most common format to showcase the fine-grained difference - single term-tree `tm A`, two different reductions\n  - Remove call-by-value nature from both, let let-bindings do the rest\n  - Explore a different similarity relation strategy - instead of substituting similar terms try to work on common skeletons (`tm A`) with a substitution (`A → val`) of similar values\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fkamirus%2Flambda-formalizations","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fkamirus%2Flambda-formalizations","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fkamirus%2Flambda-formalizations/lists"}