104 lines
3.3 KiB
Text
104 lines
3.3 KiB
Text
import Lean.MetavarContext
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open Lean
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def check (b : Bool) : IO Unit :=
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unless b do throw $ IO.userError "error"
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def f := mkConst `f []
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def g := mkConst `g []
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def a := mkConst `a []
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def b := mkConst `b []
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def c := mkConst `c []
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def b0 := mkBVar 0
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def b1 := mkBVar 1
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def b2 := mkBVar 2
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def u := mkLevelParam `u
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def typeE := mkSort levelOne
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def natE := mkConst `Nat []
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def boolE := mkConst `Bool []
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def vecE := mkConst `Vec [levelZero]
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instance : Coe Name FVarId where
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coe n := { name := n }
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instance : Coe Name MVarId where
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coe n := { name := n }
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def α := mkFVar `α
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def x := mkFVar `x
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def y := mkFVar `y
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def z := mkFVar `z
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def w := mkFVar `w
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def m1 := mkMVar `m1
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def m2 := mkMVar `m2
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def m3 := mkMVar `m3
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def m4 := mkMVar `m4
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def m5 := mkMVar `m5
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def m6 := mkMVar `m6
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def bi := BinderInfo.default
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def arrow (d b : Expr) := mkForall `_ bi d b
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def lctx1 : LocalContext := {}
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def lctx2 := lctx1.mkLocalDecl `α `α typeE
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def lctx3 := lctx2.mkLocalDecl `x `x natE
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def lctx4 := lctx3.mkLocalDecl `y `y α
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def lctx5 := lctx4.mkLocalDecl `z `z (mkAppN vecE #[x])
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def lctx6 := lctx5.mkLocalDecl `w `w (arrow natE (mkAppN m6 #[α, x, y]))
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def t1 := lctx5.mkLambda #[α, x, y] $ mkAppN f #[α, mkAppN g #[x, y], lctx5.mkLambda #[z] (mkApp f z)]
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#eval check (!t1.hasFVar)
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#eval toString t1
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def mctx1 : MetavarContext := {}
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def mctx2 := mctx1.addExprMVarDecl `m1 `m1 lctx3 #[] natE
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def mctx3 := mctx2.addExprMVarDecl `m2 `m2 lctx4 #[] α
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def mctx4 := mctx3.addExprMVarDecl `m3 `m3 lctx4 #[] natE
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def mctx5 := mctx4.addExprMVarDecl `m4 `m4 lctx1 #[] (arrow typeE (arrow natE (arrow α natE)))
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def mctx6 := mctx5.addExprMVarDecl `m5 `m5 lctx5 #[] typeE
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def mctx7 := mctx5.addExprMVarDecl `m6 `m6 lctx5 #[] (arrow typeE (arrow natE (arrow α natE)))
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def mctx8 := mctx7.assignDelayed `m4 lctx4 #[α, x, y] m3
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def mctx9 := mctx8.assignExpr `m3 (mkAppN g #[x, y])
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def mctx10 := mctx9.assignExpr `m1 a
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def t2 := lctx5.mkLambda #[α, x, y] $ mkAppN f #[mkAppN m4 #[α, x, y], x]
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#eval t2
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#eval check (!t2.hasFVar)
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#eval toString t2
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#eval toString (mctx6.instantiateMVars t2).1
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#eval check (!(mctx9.instantiateMVars t2).1.hasMVar)
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#eval check (!(mctx9.instantiateMVars t2).1.hasFVar)
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#eval toString (mctx9.instantiateMVars t2).1
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-- t3 is ill-formed since m3's localcontext contains ‵α`, `x` and `y`
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def t3 := lctx5.mkLambda #[α, x, y] $ mkAppN f #[m3, x]
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#eval check (mctx10.instantiateMVars t3).1.hasFVar
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#eval toString (mctx7.instantiateMVars t3).1
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partial def mkDiamond : Nat → Expr
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| 0 => m1
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| (n+1) => mkAppN f #[mkDiamond n, mkDiamond n]
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#eval toString (mctx7.instantiateMVars (mkDiamond 3)).1
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#eval toString (mctx10.instantiateMVars (mkDiamond 3)).1
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#eval toString (mctx7.instantiateMVars (mkDiamond 100)).1.getAppFn
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#eval toString (mctx10.instantiateMVars (mkDiamond 100)).1.getAppFn
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def mctx11 := mctx10.assignDelayed `m6 lctx5 #[α, x, y] m5
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def mctx12 := mctx11.assignExpr `m5 (arrow α α)
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def t4 := lctx6.mkLambda #[α, x, y, w] $ mkAppN f #[mkAppN m4 #[α, x, y], x]
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#eval toString t4
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#eval toString (mctx9.instantiateMVars t4).1
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#eval toString (mctx12.instantiateMVars t4).1
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#eval check (mctx9.instantiateMVars t4).1.hasMVar
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#eval check (!((mctx9.instantiateMVars t4).1.hasFVar))
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#eval check (!(mctx12.instantiateMVars t4).1.hasMVar)
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#eval check (!((mctx12.instantiateMVars t4).1.hasFVar))
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