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theory_hol.lp: rename T into ⊤ and F into ⊥ #161

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Jan 10, 2025
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theory_hol.lp: rename T into ⊤ and F into ⊥ #161

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theory_hol.lp: rename T into ⊤ and F into ⊥
fblanqui Jan 10, 2025
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fblanqui Jan 10, 2025
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fblanqui Jan 10, 2025
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fblanqui Jan 10, 2025
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2 changes: 0 additions & 2 deletions TODO.md
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Expand Up @@ -7,8 +7,6 @@ TODO

- why the mapping of ITLIST does not work anymore ?

- in lp output, replace T by ⊤ ?

- write progress in an ocaml program, and estimate time wrt size of files

- use a single term_abbrev file for each theorem, and split it
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10 changes: 5 additions & 5 deletions erasing.lp
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Expand Up @@ -29,17 +29,17 @@ builtin "ex_def" ≔ ∃_def;
builtin "not" ≔ ¬;
builtin "not_def" ≔ ¬_def;

builtin "True" ≔ T;
builtin "T_def" ≔ T_def;
builtin "True" ≔ ⊤;
builtin "T_def" ≔ ⊤_def;

builtin "False" ≔ F;
builtin "F_def" ≔ F_def;
builtin "False" ≔ ⊥;
builtin "F_def" ≔ ⊥_def;

builtin "ex1" ≔ ∃₁;
builtin "ex1_def" ≔ ∃₁_def;

// natural deduction rules
builtin "Logic.I" ≔ Tᵢ;
builtin "Logic.I" ≔ ⊤ᵢ;
builtin "conj" ≔ ∧ᵢ;
builtin "proj1" ≔ ∧ₑ₁;
builtin "proj2" ≔ ∧ₑ₂;
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6 changes: 3 additions & 3 deletions theory_hol.lp
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Expand Up @@ -26,18 +26,18 @@ opaque symbol SYM [a] [x y : El a] (xy: Prf (= x y)) : Prf (= y x) ≔
/* HOL-Light derived connectives */
constant symbol ∃₁ [A] : El (fun (fun A bool) bool);
constant symbol ¬ : El (fun bool bool);
constant symbol F : El bool;
constant symbol ⊥ : El bool;
constant symbol ∨ : El (fun bool (fun bool bool));
constant symbol ∃ [A] : El (fun (fun A bool) bool);
constant symbol ∀ [A] : El (fun (fun A bool) bool);
constant symbol ⇒ : El (fun bool (fun bool bool));
constant symbol ∧ : El (fun bool (fun bool bool));
constant symbol T : El bool;
constant symbol ⊤ : El bool;

/* Natural deduction rules */
rule Prf (⇒ $p $q) ↪ Prf $p → Prf $q;
rule Prf (∀ $p) ↪ Π x, Prf ($p x);
symbol Tᵢ : Prf T;
symbol ⊤ᵢ : Prf ⊤;
symbol ∧ᵢ [p : El bool] : Prf p → Π [q : El bool], Prf q → Prf (∧ p q);
symbol ∧ₑ₁ [p q : El bool] : Prf (∧ p q) → Prf p;
symbol ∧ₑ₂ [p q : El bool] : Prf (∧ p q) → Prf q;
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4 changes: 3 additions & 1 deletion xlp.ml
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Expand Up @@ -32,6 +32,8 @@ let name =
| "==>" -> "⇒"
| "!" -> "∀"
| "?" -> "∃"
| "F" -> "⊥"
| "T" -> "⊤"
| "?!" -> "∃₁"
| "~" -> "¬"
| "-->" -> "⟶" (* 27F6 *)
Expand Down Expand Up @@ -504,7 +506,7 @@ let proof tvs rmap =
int oc (pos_first (fun th -> concl th = t) !the_axioms);
list_prefix " " typ oc (type_vars_in_term t);
list_prefix " " term oc (frees t)
| Ptruth -> string oc "Tᵢ"
| Ptruth -> string oc "⊤ᵢ"
| Pconj(k1,k2) -> string oc "∧ᵢ "; sub_at oc k1; char oc ' '; sub_at oc k2
| Pconjunct1 k -> string oc "∧ₑ₁ "; sub_at oc k
| Pconjunct2 k -> string oc "∧ₑ₂ "; sub_at oc k
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