docs.json

{"reExports":[],"name":"Data.HeytingAlgebra","comments":null,"declarations":[{"kind":null,"children":[{"comments":null,"title":"ff","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeVar","contents":"a"}},"sourceSpan":{"start":[53,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[53,10]}},{"comments":null,"title":"tt","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeVar","contents":"a"}},"sourceSpan":{"start":[54,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[54,10]}},{"comments":null,"title":"implies","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}]}},"sourceSpan":{"start":[55,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[55,25]}},{"comments":null,"title":"conj","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}]}},"sourceSpan":{"start":[56,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[56,22]}},{"comments":null,"title":"disj","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}]}},"sourceSpan":{"start":[57,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[57,22]}},{"comments":null,"title":"not","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}},"sourceSpan":{"start":[58,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[58,16]}},{"comments":null,"title":"heytingAlgebraBoolean","info":{"declType":"instance","dependencies":[],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebra"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Boolean"]}]}},"sourceSpan":{"start":[63,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[69,16]}},{"comments":null,"title":"heytingAlgebraUnit","info":{"declType":"instance","dependencies":[],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebra"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Data","Unit"],"Unit"]}]}},"sourceSpan":{"start":[71,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[77,15]}},{"comments":null,"title":"heytingAlgebraFunction","info":{"declType":"instance","dependencies":[{"constraintAnn":[],"constraintClass":[["Data","HeytingAlgebra"],"HeytingAlgebra"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"b"}],"constraintKindArgs":[],"constraintData":null}],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebra"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"b"}]}]}},"sourceSpan":{"start":[79,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[85,22]}},{"comments":null,"title":"heytingAlgebraProxy","info":{"declType":"instance","dependencies":[],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebra"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}]}},"sourceSpan":{"start":[87,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[93,13]}},{"comments":null,"title":"heytingAlgebraRecord","info":{"declType":"instance","dependencies":[{"constraintAnn":[],"constraintClass":[["Prim","RowList"],"RowToList"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"row"},{"annotation":[],"tag":"TypeVar","contents":"list"}],"constraintKindArgs":[],"constraintData":null},{"constraintAnn":[],"constraintClass":[["Data","HeytingAlgebra"],"HeytingAlgebraRecord"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"list"},{"annotation":[],"tag":"TypeVar","contents":"row"},{"annotation":[],"tag":"TypeVar","contents":"row"}],"constraintKindArgs":[],"constraintData":null}],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebra"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]}},"sourceSpan":{"start":[95,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[101,40]}}],"comments":"The `HeytingAlgebra` type class represents types that are bounded lattices with\nan implication operator such that the following laws hold:\n\n- Associativity:\n  - `a || (b || c) = (a || b) || c`\n  - `a && (b && c) = (a && b) && c`\n- Commutativity:\n  - `a || b = b || a`\n  - `a && b = b && a`\n- Absorption:\n  - `a || (a && b) = a`\n  - `a && (a || b) = a`\n- Idempotent:\n  - `a || a = a`\n  - `a && a = a`\n- Identity:\n  - `a || ff = a`\n  - `a && tt = a`\n- Implication:\n  - ``a `implies` a = tt``\n  - ``a && (a `implies` b) = a && b``\n  - ``b && (a `implies` b) = b``\n  - ``a `implies` (b && c) = (a `implies` b) && (a `implies` c)``\n- Complemented:\n  - ``not a = a `implies` ff``\n","title":"HeytingAlgebra","info":{"fundeps":[],"arguments":[["a",null]],"declType":"typeClass","superclasses":[]},"sourceSpan":{"start":[52,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[58,16]}},{"kind":null,"children":[],"comments":null,"title":"(&&)","info":{"declType":"alias","alias":[["Data","HeytingAlgebra"],{"Right":{"Left":{"Ident":"conj"}}}],"fixity":{"associativity":"infixr","precedence":3}},"sourceSpan":{"start":[60,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[60,20]}},{"kind":null,"children":[],"comments":null,"title":"(||)","info":{"declType":"alias","alias":[["Data","HeytingAlgebra"],{"Right":{"Left":{"Ident":"disj"}}}],"fixity":{"associativity":"infixr","precedence":2}},"sourceSpan":{"start":[61,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[61,20]}},{"kind":{"kind":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim","RowList"],"RowList"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Type"]}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Row"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Type"]}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Row"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Type"]}]}]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Constraint"]}]}]}]},"keyword":"class"},"children":[{"comments":null,"title":"ffRecord","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"rowlist"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}]}]}},"sourceSpan":{"start":[111,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[111,58]}},{"comments":null,"title":"ttRecord","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"rowlist"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}]}]}},"sourceSpan":{"start":[112,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[112,58]}},{"comments":null,"title":"impliesRecord","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"rowlist"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}]}]}]}},"sourceSpan":{"start":[113,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[113,78]}},{"comments":null,"title":"disjRecord","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"rowlist"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}]}]}]}},"sourceSpan":{"start":[114,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[114,75]}},{"comments":null,"title":"conjRecord","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"rowlist"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}]}]}]}},"sourceSpan":{"start":[115,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[115,75]}},{"comments":null,"title":"notRecord","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Type","Proxy"],"Proxy"]},{"annotation":[],"tag":"TypeVar","contents":"rowlist"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"row"}]}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Record"]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}]}]}},"sourceSpan":{"start":[116,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[116,60]}},{"comments":null,"title":"heytingAlgebraRecordNil","info":{"declType":"instance","dependencies":[],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebraRecord"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim","RowList"],"Nil"]}]},{"annotation":[],"tag":"TypeVar","contents":"row"}]},{"annotation":[],"tag":"REmpty"}]}},"sourceSpan":{"start":[118,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[124,20]}},{"comments":null,"title":"heytingAlgebraRecordCons","info":{"declType":"instance","dependencies":[{"constraintAnn":[],"constraintClass":[["Data","Symbol"],"IsSymbol"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"key"}],"constraintKindArgs":[],"constraintData":null},{"constraintAnn":[],"constraintClass":[["Prim","Row"],"Cons"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"key"},{"annotation":[],"tag":"TypeVar","contents":"focus"},{"annotation":[],"tag":"TypeVar","contents":"subrowTail"},{"annotation":[],"tag":"TypeVar","contents":"subrow"}],"constraintKindArgs":[],"constraintData":null},{"constraintAnn":[],"constraintClass":[["Data","HeytingAlgebra"],"HeytingAlgebraRecord"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"rowlistTail"},{"annotation":[],"tag":"TypeVar","contents":"row"},{"annotation":[],"tag":"TypeVar","contents":"subrowTail"}],"constraintKindArgs":[],"constraintData":null},{"constraintAnn":[],"constraintClass":[["Data","HeytingAlgebra"],"HeytingAlgebra"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"focus"}],"constraintKindArgs":[],"constraintData":null}],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","HeytingAlgebra"],"HeytingAlgebraRecord"]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim","RowList"],"Cons"]},{"annotation":[],"tag":"TypeVar","contents":"key"}]},{"annotation":[],"tag":"TypeVar","contents":"focus"}]},{"annotation":[],"tag":"TypeVar","contents":"rowlistTail"}]}]},{"annotation":[],"tag":"TypeVar","contents":"row"}]},{"annotation":[],"tag":"TypeVar","contents":"subrow"}]}},"sourceSpan":{"start":[126,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[171,53]}}],"comments":"A class for records where all fields have `HeytingAlgebra` instances, used\nto implement the `HeytingAlgebra` instance for records.\n","title":"HeytingAlgebraRecord","info":{"fundeps":[[["rowlist"],["subrow"]]],"arguments":[["rowlist",null],["row",null],["subrow",null]],"declType":"typeClass","superclasses":[]},"sourceSpan":{"start":[110,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/HeytingAlgebra.purs","end":[116,60]}}]}