6893913683
This PR replaces `List.lt` with `List.Lex`, from Mathlib, and adds the new `Bool` valued lexicographic comparatory function `List.lex`. This subtly changes the definition of `<` on Lists in some situations. `List.lt` was a weaker relation: in particular if `l₁ < l₂`, then `a :: l₁ < b :: l₂` may hold according to `List.lt` even if `a` and `b` are merely incomparable (either neither `a < b` nor `b < a`), whereas according to `List.Lex` this would require `a = b`. When `<` is total, in the sense that `¬ · < ·` is antisymmetric, then the two relations coincide. Mathlib was already overriding the order instances for `List α`, so this change should not be noticed by anyone already using Mathlib. We simultaneously add the boolean valued `List.lex` function, parameterised by a `BEq` typeclass and an arbitrary `lt` function. This will support the flexibility previously provided for `List.lt`, via a `==` function which is weaker than strict equality.
82 lines
2.3 KiB
Text
82 lines
2.3 KiB
Text
import Lean
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open Lean Meta
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def ex1 (declName : Name) : MetaM Unit := do
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let info ← getConstInfo declName
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IO.println s!"{declName} : {← ppExpr info.type}"
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if let some val := info.value? then
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IO.println s!"{declName} : {← ppExpr val}"
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#eval ex1 ``Nat
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def ex2 (declName : Name) : MetaM Unit := do
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let info ← getConstInfo declName
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trace[Meta.debug] "{declName} : {info.type}"
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if let some val := info.value? then
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trace[Meta.debug] "{declName} : {val}"
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#eval ex2 ``Add.add
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set_option trace.Meta.debug true in
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#eval ex2 ``Add.add
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def ex3 (declName : Name) : MetaM Unit := do
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let info ← getConstInfo declName
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forallTelescope info.type fun xs type => do
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trace[Meta.debug] "hypotheses : {xs}"
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trace[Meta.debug] "resultType : {type}"
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for x in xs do
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trace[Meta.debug] "{x} : {← inferType x}"
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def myMin [LT α] [DecidableLT α] (a b : α) : α :=
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if a < b then
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a
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else
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b
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set_option trace.Meta.debug true in
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#eval ex3 ``myMin
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def ex4 : MetaM Unit := do
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let nat := mkConst ``Nat
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withLocalDeclD `a nat fun a =>
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withLocalDeclD `b nat fun b => do
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let e ← mkAppM ``HAdd.hAdd #[a, b]
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trace[Meta.debug] "{e} : {← inferType e}"
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let e ← mkAdd a (mkNatLit 5)
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trace[Meta.debug] "added 5: {e}"
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let e ← whnf e
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trace[Meta.debug] "whnf: {e}"
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let e ← reduce e
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trace[Meta.debug] "reduced: {e}"
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let a_plus_1 ← mkAdd a (mkNatLit 1)
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let succ_a := mkApp (mkConst ``Nat.succ) a
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trace[Meta.debug] "({a_plus_1} =?= {succ_a}) == {← isDefEq a_plus_1 succ_a}"
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let m ← mkFreshExprMVar nat
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let m_plus_1 ← mkAdd m (mkNatLit 1)
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trace[Meta.debug] "m_plus_1: {m_plus_1}"
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unless (← isDefEq m_plus_1 succ_a) do throwError "isDefEq failed"
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trace[Meta.debug] "m_plus_1: {m_plus_1}"
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set_option trace.Meta.debug true in
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#eval ex4
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open Elab Term
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def ex5 : TermElabM Unit := do
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let nat := Lean.mkConst ``Nat
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withLocalDeclD `a nat fun a => do
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withLocalDeclD `b nat fun b => do
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let ab ← mkAppM ``HAdd.hAdd #[a, b]
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let abStx ← exprToSyntax ab
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let aStx ← exprToSyntax a
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let stx ← `(fun x => if x < 10 then $abStx + x else x + $aStx)
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let e ← elabTerm stx none
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trace[Meta.debug] "{e} : {← inferType e}"
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let e := mkApp e (mkNatLit 5)
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let e ← whnf e
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trace[Meta.debug] "{e}"
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set_option trace.Meta.debug true in
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#eval ex5
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