134 lines
4.5 KiB
Text
134 lines
4.5 KiB
Text
import Lean.Meta
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open Lean
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open Lean.Meta
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unsafe def tstInferType (mods : List Name) (e : Expr) : IO Unit :=
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withImportModules (mods.map $ fun m => {module := m}) {} 0 fun env => do
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let (type, _, _) ← (inferType e : MetaM _).toIO {} { env := env } {} {};
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IO.println (toString e ++ " : " ++ toString type)
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unsafe def tstWHNF (mods : List Name) (e : Expr) (t := TransparencyMode.default) : IO Unit :=
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withImportModules (mods.map $ fun m => {module := m}) {} 0 fun env => do
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let (s, _, _) ← (whnf e : MetaM _).toIO {} { env := env };
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IO.println (toString e ++ " ==> " ++ toString s)
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unsafe def tstIsProp (mods : List Name) (e : Expr) : IO Unit :=
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withImportModules (mods.map $ fun m => {module := m}) {} 0 fun env => do
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let (b, _, _) ← (isProp e : MetaM _).toIO {} { env := env };
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IO.println (toString e ++ ", isProp: " ++ toString b)
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def t1 : Expr :=
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let map := mkConst `List.map [levelOne, levelOne];
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let nat := mkConst `Nat [];
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let bool := mkConst `Bool [];
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mkAppN map #[nat, bool]
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#eval tstInferType [`Init.Data.List] t1
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def t2 : Expr :=
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let prop := mkSort levelZero;
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mkForall `x BinderInfo.default prop prop
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#eval tstInferType [`Init.Core] t2
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def t3 : Expr :=
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let nat := mkConst `Nat [];
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let natLe := mkConst `Nat.le [];
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let zero := mkLit (Literal.natVal 0);
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let p := mkAppN natLe #[mkBVar 0, zero];
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mkForall `x BinderInfo.default nat p
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#eval tstInferType [`Init.Data.Nat] t3
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def t4 : Expr :=
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let nat := mkConst `Nat [];
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let p := mkAppN (mkConst `Nat.succ []) #[mkBVar 0];
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mkLambda `x BinderInfo.default nat p
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#eval tstInferType [`Init.Core] t4
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def t5 : Expr :=
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let add := mkConst `Nat.add [];
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mkAppN add #[mkLit (Literal.natVal 3), mkLit (Literal.natVal 5)]
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#eval tstWHNF [`Init.Data.Nat] t5
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#eval tstWHNF [`Init.Data.Nat] t5 TransparencyMode.reducible
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set_option pp.all true
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#check @List.cons Nat
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def t6 : Expr :=
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let map := mkConst `List.map [levelOne, levelOne];
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let nat := mkConst `Nat [];
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let add := mkConst `Nat.add [];
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let f := mkLambda `x BinderInfo.default nat (mkAppN add #[mkBVar 0, mkLit (Literal.natVal 1)]);
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let cons := mkApp (mkConst `List.cons [levelZero]) nat;
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let nil := mkApp (mkConst `List.nil [levelZero]) nat;
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let one := mkLit (Literal.natVal 1);
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let four := mkLit (Literal.natVal 4);
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let xs := mkApp (mkApp cons one) (mkApp (mkApp cons four) nil);
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mkAppN map #[nat, nat, f, xs]
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#eval tstInferType [`Init.Data.List] t6
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#eval tstWHNF [`Init.Data.List] t6
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#eval tstInferType [] $ mkSort levelZero
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#eval tstInferType [`Init.Data.List] $ mkLambda `a BinderInfo.implicit (mkSort levelOne) (mkLambda `x BinderInfo.default (mkBVar 0) (mkLambda `xs BinderInfo.default (mkApp (mkConst `List [levelZero]) (mkBVar 1)) (mkBVar 0)))
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def t7 : Expr :=
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let nat := mkConst `Nat [];
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let one := mkLit (Literal.natVal 1);
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mkLet `x nat one one
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#eval tstInferType [`Init.Core] $ t7
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#eval tstWHNF [`Init.Core] $ t7
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def t8 : Expr :=
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let nat := mkConst `Nat [];
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let one := mkLit (Literal.natVal 1);
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let add := mkConst `Nat.add [];
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mkLet `x nat one (mkAppN add #[one, mkBVar 0])
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#eval tstInferType [`Init.Core] $ t8
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#eval tstWHNF [`Init.Core] $ t8
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def t9 : Expr :=
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let nat := mkConst `Nat [];
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mkLet `a (mkSort levelOne) nat (mkForall `x BinderInfo.default (mkBVar 0) (mkBVar 1))
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#eval tstInferType [`Init.Core] $ t9
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#eval tstWHNF [`Init.Core] $ t9
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#eval tstInferType [`Init.Core] $ mkLit (Literal.natVal 10)
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#eval tstInferType [`Init.Core] $ mkLit (Literal.strVal "hello")
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#eval tstInferType [`Init.Core] $ mkMData {} $ mkLit (Literal.natVal 10)
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def t10 : Expr :=
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let nat := mkConst `Nat [];
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let refl := mkApp (mkConst `Eq.refl [levelOne]) nat;
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mkLambda `a BinderInfo.default nat (mkApp refl (mkBVar 0))
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#eval tstInferType [`Init.Core] t10
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#eval tstIsProp [`Init.Core] t10
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#eval tstIsProp [`Init.Core] (mkAppN (mkConst `And []) #[mkConst `True [], mkConst `True []])
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#eval tstIsProp [`Init.Core] (mkConst `And [])
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-- Example where isPropQuick fails
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#eval tstIsProp [`Init.Core] (mkAppN (mkConst `id [levelZero]) #[mkSort levelZero, mkAppN (mkConst `And []) #[mkConst `True [], mkConst
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`True []]])
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#eval tstIsProp [`Init.Core] (mkAppN (mkConst `Eq [levelOne]) #[mkConst `Nat [], mkLit (Literal.natVal 0), mkLit (Literal.natVal 1)])
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#eval tstIsProp [`Init.Core] $
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mkForall `x BinderInfo.default (mkConst `Nat [])
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(mkAppN (mkConst `Eq [levelOne]) #[mkConst `Nat [], mkBVar 0, mkLit (Literal.natVal 1)])
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#eval tstIsProp [`Init.Core] $
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mkApp
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(mkLambda `x BinderInfo.default (mkConst `Nat [])
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(mkAppN (mkConst `Eq [levelOne]) #[mkConst `Nat [], mkBVar 0, mkLit (Literal.natVal 1)]))
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(mkLit (Literal.natVal 0))
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