407a59d697
This PR modifies the pretty printing of pi types. Now `∀` will be preferred over `→` for propositions if the domain is not a proposition. For example, `∀ (n : Nat), True` pretty prints as `∀ (n : Nat), True` rather than as `Nat → True`. There is also now an option `pp.foralls` (default true) that when false disables using `∀` at all, for pedagogical purposes. This PR also adjusts instance implicit binder pretty printing — nondependent pi types won't show the instance binder name. Closes #1834. The linked RFC also suggests using `_` for binder names in case of non-dependance. We're tabling that idea. Potentially it is useful for hygienic names; this could improve how `Nat → True` pretty prints as `∀ (a : Nat), True`, with this `a` that's chosen by implication notation elaboration. Relatedly, this PR exposes even further the issue where binder names are reused in a confusing way. Consider: `Nat → Nat → (a : Nat) → a = a` pretty prints as `∀ (a a a : Nat), a = a`.
144 lines
4 KiB
Text
144 lines
4 KiB
Text
/-!
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# Pretty print with `∀` instead of `→` when domain is type
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https://github.com/leanprover/lean4/issues/1834
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-/
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set_option linter.unusedVariables false
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/-!
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Tests of various pi types.
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-/
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section
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variable (α : Nat → Type) (p q : Prop) (P : Nat → Prop)
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-- default nondep
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/-- info: Nat → Nat : Type -/
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#guard_msgs in #check (i : Nat) → Nat
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-- implicit nondep
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/-- info: {i : Nat} → Nat : Type -/
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#guard_msgs in #check {i : Nat} → Nat
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-- instance implicit nondep
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/-- info: [Inhabited Nat] → Nat : Type -/
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#guard_msgs in #check [Inhabited Nat] → Nat
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-- default nondep, both prop
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/-- info: p → q : Prop -/
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#guard_msgs in #check (h : p) → q
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-- default nondep, only codomain prop
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/-- info: ∀ (i : Nat), p : Prop -/
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#guard_msgs in #check (i : Nat) → p
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-- implicit nondep, only codomain prop
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/-- info: ∀ {i : Nat}, p : Prop -/
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#guard_msgs in #check {i : Nat} → p
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-- instance implicit nondep, only codomain prop, hygienic name
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/-- info: ∀ [Inhabited Nat], p : Prop -/
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#guard_msgs in #check [Inhabited Nat] → p
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-- instance implicit nondep, only codomain prop, user-provided name
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/-- info: ∀ [instNat : Inhabited Nat], p : Prop -/
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#guard_msgs in #check [instNat : Inhabited Nat] → p
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-- default dep
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/-- info: (i : Nat) → α i : Type -/
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#guard_msgs in #check (i : Nat) → α i
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-- implicit dep
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/-- info: {i : Nat} → α i : Type -/
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#guard_msgs in #check {i : Nat} → α i
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-- instance implicit dep
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/-- info: [inst : Inhabited Nat] → α default : Type -/
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#guard_msgs in #check [Inhabited Nat] → α default
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-- default dep, codomain prop
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/-- info: ∀ (i : Nat), P i : Prop -/
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#guard_msgs in #check (i : Nat) → P i
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-- implicit dep, codomain prop
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/-- info: ∀ {i : Nat}, P i : Prop -/
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#guard_msgs in #check {i : Nat} → P i
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-- instance implicit dep, codomain prop, hygienic name
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/-- info: ∀ [inst : Inhabited Nat], P default : Prop -/
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#guard_msgs in #check [Inhabited Nat] → P default
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-- instance implicit dep, codomain prop, user-provided name
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/-- info: ∀ [instNat : Inhabited Nat], P default : Prop -/
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#guard_msgs in #check [instNat : Inhabited Nat] → P default
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-- Same tests but with `pp.foralls` set to false.
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set_option pp.foralls false
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-- default nondep
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/-- info: Nat → Nat : Type -/
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#guard_msgs in #check (i : Nat) → Nat
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-- implicit nondep
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/-- info: {i : Nat} → Nat : Type -/
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#guard_msgs in #check {i : Nat} → Nat
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-- default nondep, both prop
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/-- info: p → q : Prop -/
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#guard_msgs in #check (h : p) → q
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-- default nondep, only codomain prop
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/-- info: Nat → p : Prop -/
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#guard_msgs in #check (i : Nat) → p
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-- default dep
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/-- info: (i : Nat) → α i : Type -/
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#guard_msgs in #check (i : Nat) → α i
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-- implicit dep
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/-- info: {i : Nat} → α i : Type -/
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#guard_msgs in #check {i : Nat} → α i
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-- default dep, codomain prop
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/-- info: (i : Nat) → P i : Prop -/
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#guard_msgs in #check (i : Nat) → P i
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-- implicit dep, codomain prop
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/-- info: {i : Nat} → P i : Prop -/
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#guard_msgs in #check {i : Nat} → P i
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-- implicit nondep, only codomain prop
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/-- info: {i : Nat} → p : Prop -/
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#guard_msgs in #check {i : Nat} → p
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end
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/-!
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Rewrote forall, remains a forall, since domain is `Nat`.
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-/
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/--
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info: P : Nat → Prop
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q : Prop
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h : ∀ (n : Nat), P n = q
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hq : q
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⊢ ∀ (n : Nat), q
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-/
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#guard_msgs in
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example (P : Nat → Prop) (q : Prop) (h : ∀ n, P n = q) (hq : q) :
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∀ n, P n := by
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conv => enter [n]; rw [h]
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trace_state
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exact fun _ => hq
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/-!
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When `pp.foralls` is false, uses non-dependent `→`.
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-/
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/--
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info: P : Nat → Prop
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q : Prop
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h : (n : Nat) → P n = q
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hq : q
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⊢ Nat → q
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-/
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#guard_msgs in
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set_option pp.foralls false in
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example (P : Nat → Prop) (q : Prop) (h : ∀ n, P n = q) (hq : q) :
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∀ n, P n := by
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conv => enter [n]; rw [h]
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trace_state
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exact fun _ => hq
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/-!
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Rewrote forall, turns into an implication, since domain is a proposition.
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-/
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/--
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info: p : Prop
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P : p → Prop
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q : Prop
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h : ∀ (n : p), P n = q
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hq : q
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⊢ p → q
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-/
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#guard_msgs in
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example (p : Prop) (P : p → Prop) (q : Prop) (h : ∀ n, P n = q) (hq : q) :
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∀ n, P n := by
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conv => enter [n]; rw [h]
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trace_state
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exact fun _ => hq
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