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"row-type-primary:t10:String" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t11: " }, { "text": "×", "kind": "op", "key": "row-type-primary:t12:×" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t13: " }, { "text": "ℤ", "kind": "type", "key": "row-type-primary:t14:ℤ" }, { "text": ")", "kind": "plain", "key": "row-type-primary:t15:)" }, { "text": ")", "kind": "plain", "key": "row-type-primary:t16:)" } ] ], "code": "{-# OPTIONS --cubical --guardedness #-}\n\nmodule Gadget.ComplexTransformExample where\n\nopen import Cubical.Foundations.Prelude using (Type)\nopen import Cubical.Data.Nat using (ℕ; zero; suc)\nopen import Cubical.Data.Sigma using (_×_; _,_)\nopen import Cubical.Data.Sum using (_⊎_; inr)\nopen import Cubical.Data.Int using (ℤ; negsuc)\nopen import Agda.Builtin.String using (String)\n\nmutual\n data Expr : Type where\n litNat : ℕ -> Expr\n litString : String -> Expr\n litInt : ℤ -> Expr\n block : Stmts -> Expr\n\n data Stmts : Type where\n done : Stmts\n step : Expr -> Stmts -> Stmts\n\nprograms : Type _\nprograms = Expr × (ℕ ⊎ (String × ℤ))\n" }, { "title": "Data checking", "note": "One fetched record becomes an ordinary Agda definition checked at the row type.", "lines": [ [ { "text": "{-#", "kind": "plain", "key": "common:l0:t0:{-#" }, { "text": " ", "kind": "ws", "key": "common:l0:t1: " }, { "text": "OPTIONS", "kind": "type", "key": "common:l0:t2:OPTIONS" }, { "text": " ", "kind": "ws", "key": "common:l0:t3: " }, { "text": "--cubical", "kind": "plain", "key": "common:l0:t4:--cubical" }, { "text": " ", "kind": "ws", "key": "common:l0:t5: " }, { "text": "--guardedness", "kind": "plain", "key": "common:l0:t6:--guardedness" }, { "text": " ", "kind": "ws", "key": "common:l0:t7: " }, { "text": "#-}", "kind": "plain", "key": "common:l0:t8:#-}" } ], [], [ { "text": "module", "kind": "kw", "key": "common:l2:t0:module" }, { "text": " ", "kind": "ws", "key": "common:l2:t1: " }, { "text": "Gadget", "kind": "type", "key": "common:l2:t2:Gadget" 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", "kind": "ws", "key": "common:l4:t11: " }, { "text": "(", "kind": "plain", "key": "common:l4:t12:(" }, { "text": "Type", "kind": "kw", "key": "common:l4:t13:Type" }, { "text": ")", "kind": "plain", "key": "common:l4:t14:)" } ], [ { "text": "open", "kind": "kw", "key": "common:l5:t0:open" }, { "text": " ", "kind": "ws", "key": "common:l5:t1: " }, { "text": "import", "kind": "kw", "key": "common:l5:t2:import" }, { "text": " ", "kind": "ws", "key": "common:l5:t3: " }, { "text": "Cubical", "kind": "type", "key": "common:l5:t4:Cubical" }, { "text": ".", "kind": "plain", "key": "common:l5:t5:." }, { "text": "Data", "kind": "type", "key": "common:l5:t6:Data" }, { "text": ".", "kind": "plain", "key": "common:l5:t7:." }, { "text": "Nat", "kind": "type", "key": "common:l5:t8:Nat" }, { "text": " ", "kind": "ws", "key": "common:l5:t9: " }, { "text": "using", "kind": "kw", "key": "common:l5:t10:using" }, { "text": " ", "kind": "ws", "key": "common:l5:t11: " }, { "text": "(", "kind": "plain", "key": "common:l5:t12:(" }, { "text": "ℕ;", "kind": "type", "key": "common:l5:t13:ℕ;" }, { "text": " ", "kind": "ws", "key": "common:l5:t14: " }, { "text": "zero;", "kind": "plain", "key": "common:l5:t15:zero;" }, { "text": " ", "kind": "ws", "key": "common:l5:t16: " }, { "text": "suc", "kind": "plain", "key": "common:l5:t17:suc" }, { "text": ")", "kind": "plain", "key": "common:l5:t18:)" } ], [ { "text": "open", "kind": "kw", "key": "common:l6:t0:open" }, { "text": " ", "kind": "ws", "key": "common:l6:t1: " }, { "text": "import", "kind": "kw", "key": "common:l6:t2:import" }, { "text": " ", "kind": "ws", "key": "common:l6:t3: " }, { "text": "Cubical", "kind": "type", "key": "common:l6:t4:Cubical" }, { "text": ".", "kind": "plain", "key": "common:l6:t5:." }, { "text": "Data", "kind": "type", "key": "common:l6:t6:Data" }, { "text": ".", "kind": "plain", "key": "common:l6:t7:." }, { "text": "Sigma", "kind": "type", "key": "common:l6:t8:Sigma" }, { "text": " ", "kind": "ws", "key": "common:l6:t9: " }, { "text": "using", "kind": "kw", "key": "common:l6:t10:using" }, { "text": " ", "kind": "ws", "key": "common:l6:t11: " }, { "text": "(", "kind": "plain", "key": "common:l6:t12:(" }, { "text": "_", "kind": "op", "key": "common:l6:t13:_" }, { "text": "×", "kind": "op", "key": "common:l6:t14:×" }, { "text": "_", "kind": "op", "key": "common:l6:t15:_" }, { "text": ";", "kind": "plain", "key": "common:l6:t16:;" }, { "text": " ", "kind": "ws", "key": "common:l6:t17: " }, { "text": "_", "kind": "op", "key": "common:l6:t18:_" }, { "text": ",", "kind": "plain", "key": "common:l6:t19:," }, { "text": "_", "kind": "op", "key": "common:l6:t20:_" }, { "text": ")", "kind": "plain", "key": "common:l6:t21:)" } ], [ { "text": "open", "kind": "kw", "key": "common:l7:t0:open" }, { "text": " ", "kind": "ws", "key": "common:l7:t1: " }, { "text": "import", "kind": "kw", "key": "common:l7:t2:import" }, { "text": " ", "kind": "ws", "key": "common:l7:t3: " }, { "text": "Cubical", "kind": "type", "key": "common:l7:t4:Cubical" }, { "text": ".", "kind": "plain", "key": "common:l7:t5:." }, { "text": "Data", "kind": "type", "key": "common:l7:t6:Data" }, { "text": ".", "kind": "plain", "key": "common:l7:t7:." }, { "text": "Sum", "kind": "type", "key": "common:l7:t8:Sum" }, { "text": " ", "kind": "ws", "key": "common:l7:t9: " }, { "text": "using", "kind": "kw", "key": "common:l7:t10:using" }, { "text": " ", "kind": "ws", "key": "common:l7:t11: " }, { "text": "(", "kind": "plain", "key": "common:l7:t12:(" }, { "text": "_", "kind": "op", "key": "common:l7:t13:_" }, { "text": "⊎", "kind": "op", "key": "common:l7:t14:⊎" }, { "text": "_", "kind": "op", "key": "common:l7:t15:_" }, { "text": ";", "kind": "plain", "key": "common:l7:t16:;" }, { "text": " ", "kind": "ws", "key": "common:l7:t17: " }, { "text": "inr", "kind": "plain", "key": "common:l7:t18:inr" }, { "text": ")", "kind": "plain", "key": "common:l7:t19:)" } ], [ { "text": "open", "kind": "kw", "key": "common:l8:t0:open" }, { "text": " ", "kind": "ws", "key": "common:l8:t1: " }, { "text": "import", "kind": "kw", "key": "common:l8:t2:import" }, { "text": " ", "kind": "ws", "key": "common:l8:t3: " }, { "text": "Cubical", "kind": "type", "key": "common:l8:t4:Cubical" }, { "text": ".", "kind": "plain", "key": "common:l8:t5:." }, { "text": "Data", "kind": "type", "key": "common:l8:t6:Data" }, { "text": ".", "kind": "plain", "key": "common:l8:t7:." }, { "text": "Int", "kind": "type", "key": "common:l8:t8:Int" }, { "text": " ", "kind": "ws", "key": "common:l8:t9: " }, { "text": "using", "kind": "kw", "key": "common:l8:t10:using" }, { "text": " ", "kind": "ws", "key": "common:l8:t11: " }, { "text": "(", "kind": "plain", "key": "common:l8:t12:(" }, { "text": "ℤ;", "kind": "type", "key": "common:l8:t13:ℤ;" }, { "text": " ", "kind": "ws", "key": "common:l8:t14: " }, { "text": "negsuc", "kind": "plain", "key": "common:l8:t15:negsuc" }, { "text": ")", "kind": "plain", "key": "common:l8:t16:)" } ], [ { "text": "open", "kind": "kw", "key": "common:l9:t0:open" }, { "text": " ", "kind": "ws", "key": "common:l9:t1: " }, { "text": "import", "kind": "kw", "key": "common:l9:t2:import" }, { "text": " ", "kind": "ws", "key": "common:l9:t3: " }, { "text": "Agda", "kind": "type", "key": "common:l9:t4:Agda" }, { "text": ".", "kind": "plain", "key": "common:l9:t5:." }, { "text": "Builtin", "kind": "type", "key": "common:l9:t6:Builtin" }, { "text": ".", "kind": "plain", "key": "common:l9:t7:." }, { "text": "String", "kind": "type", "key": "common:l9:t8:String" }, { "text": " ", "kind": "ws", "key": "common:l9:t9: " }, { "text": "using", "kind": "kw", "key": "common:l9:t10:using" }, { "text": " ", "kind": "ws", "key": "common:l9:t11: " }, { "text": "(", "kind": "plain", "key": "common:l9:t12:(" }, { "text": "String", "kind": "type", "key": "common:l9:t13:String" }, { "text": ")", "kind": "plain", "key": "common:l9:t14:)" } ], [], [ { "text": "mutual", "kind": "kw", "key": "common:l11:t0:mutual" } ], [ { "text": " ", "kind": "ws", "key": "common:l12:t0: " }, { "text": "data", "kind": "kw", "key": "common:l12:t1:data" }, { "text": " ", "kind": "ws", "key": "common:l12:t2: " }, { "text": "Expr", "kind": "type", "key": "common:l12:t3:Expr" }, { "text": " ", "kind": "ws", "key": "common:l12:t4: " }, { "text": ":", "kind": "op", "key": "common:l12:t5::" }, { "text": " ", "kind": "ws", "key": "common:l12:t6: " }, { "text": "Type", "kind": "kw", "key": "common:l12:t7:Type" }, { "text": " ", "kind": "ws", "key": "common:l12:t8: " }, { "text": "where", "kind": "kw", "key": "common:l12:t9:where" } ], [ { "text": " ", "kind": "ws", "key": "common:l13:t0: " }, { "text": "litNat", "kind": "plain", "key": "common:l13:t1:litNat" }, { "text": " ", "kind": "ws", "key": "common:l13:t2: " }, { "text": ":", "kind": "op", "key": "common:l13:t3::" }, { "text": " ", "kind": "ws", "key": "common:l13:t4: " }, { "text": "ℕ", "kind": "type", "key": "common:l13:t5:ℕ" }, { "text": " ", "kind": "ws", "key": "common:l13:t6: " }, { "text": "->", "kind": "op", "key": "common:l13:t7:->" }, { "text": " ", "kind": "ws", "key": "common:l13:t8: " }, { "text": "Expr", "kind": "type", "key": "common:l13:t9:Expr" } ], [ { "text": " ", "kind": "ws", "key": "common:l14:t0: " }, { "text": "litString", "kind": "plain", "key": "common:l14:t1:litString" }, { "text": " ", "kind": "ws", "key": "common:l14:t2: " }, { "text": ":", "kind": "op", "key": "common:l14:t3::" }, { "text": " ", "kind": "ws", "key": "common:l14:t4: " }, { "text": "String", "kind": "type", "key": "common:l14:t5:String" }, { "text": " ", "kind": "ws", "key": "common:l14:t6: " }, { "text": "->", "kind": "op", "key": "common:l14:t7:->" }, { "text": " ", "kind": "ws", "key": "common:l14:t8: " }, { "text": "Expr", "kind": "type", "key": "common:l14:t9:Expr" } ], [ { "text": " ", "kind": "ws", "key": "common:l15:t0: " }, { "text": "litInt", "kind": "plain", "key": "common:l15:t1:litInt" }, { "text": " ", "kind": "ws", "key": "common:l15:t2: " }, { "text": ":", "kind": "op", "key": "common:l15:t3::" }, { "text": " ", "kind": "ws", "key": "common:l15:t4: " }, { "text": "ℤ", "kind": "type", "key": "common:l15:t5:ℤ" }, { "text": " ", "kind": "ws", "key": "common:l15:t6: " }, { "text": "->", "kind": "op", "key": "common:l15:t7:->" }, { "text": " ", "kind": "ws", "key": "common:l15:t8: " }, { "text": "Expr", "kind": "type", "key": "common:l15:t9:Expr" } ], [ { "text": " ", "kind": "ws", "key": "common:l16:t0: " }, { "text": "block", "kind": "plain", "key": "common:l16:t1:block" }, { "text": " ", "kind": "ws", "key": "common:l16:t2: " }, { "text": ":", "kind": "op", "key": "common:l16:t3::" }, { "text": " ", "kind": "ws", "key": "common:l16:t4: " }, { "text": "Stmts", "kind": "type", "key": "common:l16:t5:Stmts" }, { "text": " ", "kind": "ws", "key": "common:l16:t6: " }, { "text": "->", "kind": "op", "key": "common:l16:t7:->" }, { "text": " ", "kind": "ws", "key": "common:l16:t8: " }, { "text": "Expr", "kind": "type", "key": "common:l16:t9:Expr" } ], [], [ { "text": " ", "kind": "ws", "key": "common:l18:t0: " }, { "text": "data", "kind": "kw", "key": "common:l18:t1:data" }, { "text": " ", "kind": "ws", "key": "common:l18:t2: " }, { "text": "Stmts", "kind": "type", "key": "common:l18:t3:Stmts" }, { "text": " ", "kind": "ws", "key": "common:l18:t4: " }, { "text": ":", "kind": "op", "key": "common:l18:t5::" }, { "text": " ", "kind": "ws", "key": "common:l18:t6: " }, { "text": "Type", "kind": "kw", "key": "common:l18:t7:Type" }, { "text": " ", "kind": "ws", "key": "common:l18:t8: " }, { "text": "where", "kind": "kw", "key": "common:l18:t9:where" } ], [ { "text": " ", "kind": "ws", "key": "common:l19:t0: " }, { "text": "done", "kind": "plain", "key": "common:l19:t1:done" }, { "text": " ", "kind": "ws", "key": "common:l19:t2: " }, { "text": ":", "kind": "op", "key": "common:l19:t3::" }, { "text": " ", "kind": "ws", "key": "common:l19:t4: " }, { "text": "Stmts", "kind": "type", "key": "common:l19:t5:Stmts" } ], [ { "text": " ", "kind": "ws", "key": "common:l20:t0: " }, { "text": "step", "kind": "plain", "key": "common:l20:t1:step" }, { "text": " ", "kind": "ws", "key": "common:l20:t2: " }, { "text": ":", "kind": "op", "key": "common:l20:t3::" }, { "text": " ", "kind": "ws", "key": "common:l20:t4: " }, { "text": "Expr", "kind": "type", "key": "common:l20:t5:Expr" }, { "text": " ", "kind": "ws", "key": "common:l20:t6: " }, { "text": "->", "kind": "op", "key": "common:l20:t7:->" }, { "text": " ", "kind": "ws", "key": "common:l20:t8: " }, { "text": "Stmts", "kind": "type", "key": "common:l20:t9:Stmts" }, { "text": " ", "kind": "ws", "key": "common:l20:t10: " }, { "text": "->", "kind": "op", "key": "common:l20:t11:->" }, { "text": " ", "kind": "ws", "key": "common:l20:t12: " }, { "text": "Stmts", "kind": "type", "key": "common:l20:t13:Stmts" } ], [], [ { "text": "tdbUUIDb2000000000040008000000000000002", "kind": "uuid", "key": "record-name-primary" }, { "text": " ", "kind": "ws" }, { "text": ":", "kind": "op" }, { "text": " ", "kind": "ws" }, { "text": "Expr", "kind": "type", "key": "row-type-primary:t0:Expr" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t1: " }, { "text": "×", "kind": "op", "key": "row-type-primary:t2:×" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t3: " }, { "text": "(", "kind": "plain", "key": "row-type-primary:t4:(" }, { "text": "ℕ", "kind": "type", "key": "row-type-primary:t5:ℕ" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t6: " }, { "text": "⊎", "kind": "op", "key": "row-type-primary:t7:⊎" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t8: " }, { "text": "(", "kind": "plain", "key": "row-type-primary:t9:(" }, { "text": "String", "kind": "type", "key": "row-type-primary:t10:String" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t11: " }, { "text": "×", "kind": "op", "key": "row-type-primary:t12:×" }, { "text": " ", "kind": "ws", "key": "row-type-primary:t13: " }, { "text": "ℤ", "kind": "type", "key": "row-type-primary:t14:ℤ" }, { "text": ")", "kind": "plain", "key": "row-type-primary:t15:)" }, { "text": ")", "kind": "plain", "key": "row-type-primary:t16:)" } ], [ { "text": "tdbUUIDb2000000000040008000000000000002", "kind": "uuid", "key": "record-name-def" }, { "text": " ", "kind": "ws" }, { "text": "=", "kind": "op" }, { "text": " ", "kind": "ws" }, { "text": "block", "kind": "plain", "key": "record-body-primary:t0:block" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t1: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t2:(" }, { "text": "step", "kind": "plain", "key": "record-body-primary:t3:step" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t4: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t5:(" }, { "text": "litNat", "kind": "plain", "key": "record-body-primary:t6:litNat" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t7: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t8:(" }, { "text": "suc", "kind": "plain", "key": "record-body-primary:t9:suc" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t10: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t11:(" }, { "text": "suc", "kind": "plain", "key": "record-body-primary:t12:suc" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t13: " }, { "text": "zero", "kind": "plain", "key": "record-body-primary:t14:zero" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t15:)" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t16:)" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t17:)" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t18: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t19:(" }, { "text": "step", "kind": "plain", "key": "record-body-primary:t20:step" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t21: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t22:(" }, { "text": "litString", "kind": "plain", "key": "record-body-primary:t23:litString" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t24: " }, { "text": "\"mlttdb\"", "kind": "string", "key": "record-body-primary:t25:\"mlttdb\"" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t26:)" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t27: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t28:(" }, { "text": "step", "kind": "plain", "key": "record-body-primary:t29:step" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t30: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t31:(" }, { "text": "litInt", "kind": "plain", "key": "record-body-primary:t32:litInt" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t33: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t34:(" }, { "text": "negsuc", "kind": "plain", "key": "record-body-primary:t35:negsuc" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t36: " }, { "text": "0", "kind": "num", "key": "record-body-primary:t37:0" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t38:)" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t39:)" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t40: " }, { "text": "done", "kind": "plain", "key": "record-body-primary:t41:done" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t42:)" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t43:)" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t44:)" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t45: " }, { "text": ",", "kind": "plain", "key": "record-body-primary:t46:," }, { "text": " ", "kind": "ws", "key": "record-body-primary:t47: " }, { "text": "inr", "kind": "plain", "key": "record-body-primary:t48:inr" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t49: " }, { "text": "(", "kind": "plain", "key": "record-body-primary:t50:(" }, { "text": "\"mlttdb\"", "kind": "string", "key": "record-body-primary:t51:\"mlttdb\"" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t52: " }, { "text": ",", "kind": "plain", "key": "record-body-primary:t53:," }, { "text": " ", "kind": "ws", "key": "record-body-primary:t54: " }, { "text": "negsuc", "kind": "plain", "key": "record-body-primary:t55:negsuc" }, { "text": " ", "kind": "ws", "key": "record-body-primary:t56: " }, { "text": "0", "kind": "num", "key": "record-body-primary:t57:0" }, { "text": ")", "kind": "plain", "key": "record-body-primary:t58:)" } ] ], "code": "{-# OPTIONS --cubical --guardedness #-}\n\nmodule Gadget.ComplexTransformExample where\n\nopen import Cubical.Foundations.Prelude using (Type)\nopen import Cubical.Data.Nat using (ℕ; zero; suc)\nopen import Cubical.Data.Sigma using (_×_; _,_)\nopen import Cubical.Data.Sum using (_⊎_; inr)\nopen import Cubical.Data.Int using (ℤ; negsuc)\nopen import Agda.Builtin.String using (String)\n\nmutual\n data Expr : Type where\n litNat : ℕ -> Expr\n litString : String -> Expr\n litInt : ℤ -> Expr\n block : Stmts -> Expr\n\n data Stmts : Type where\n done : Stmts\n step : Expr -> Stmts -> Stmts\n\ntdbUUIDb2000000000040008000000000000002 : Expr × (ℕ ⊎ (String × ℤ))\ntdbUUIDb2000000000040008000000000000002 = block (step (litNat (suc (suc zero))) (step (litString \"mlttdb\") (step (litInt (negsuc 0)) done))) , inr (\"mlttdb\" , negsuc 0)\n" } ] }