lean4-htt/tests/lean/run/meta1.lean
2020-10-25 09:16:38 -07:00

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Text

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