let mk_exists ooch noch c v =
let description = "multiple existental quantifier" in
let prec = "non associative with precedence 20\n" in
- let name s = P.sprintf "%s%u_%u" s c v in
+ let name s =
+ if v = 1 then P.sprintf "%s%u" s c else P.sprintf "%s%u_%u" s c v
+ in
let o_name = name "ex" in
- let i_name = "'Ex" in
-
+ let i_name =
+ if v = 1 then "'Ex" else P.sprintf "'Ex%u" v
+ in
let set n = P.sprintf "A%u" (v - n) in
- let set_list = string_iter "," set v in
+ let set_list = string_iter "," set v in
let set_type = string_iter "→" set v in
-
+
let ele n = P.sprintf "x%u" (v - n) in
let ele_list = string_iter "," ele v in
let ele_seq = string_iter " " ele v in
-
- let pre n = P.sprintf "P%u" (c - n) in
+
+ let pre n = P.sprintf "P%u" (c - n) in
let pre_list = string_iter "," pre c in
- let pre_seq = string_iter " " pre c in
- let pre_appl n = P.sprintf "%s %s" (pre n) ele_seq in
+ let pre_seq = string_iter " " pre c in
+ let pre_appl n = P.sprintf "%s %s" (pre n) ele_seq in
let pre_type = string_iter " → " pre_appl c in
let qm n = "?" in
- let qm_set = string_iter " " qm v in
- let qm_pre = string_iter " " qm c in
+ let qm_set = string_iter " " qm v in
+ let qm_pre = string_iter " " qm c in
let id n = P.sprintf "ident x%u" (v - n) in
- let id_list = string_iter " , " id v in
+ let id_list = string_iter " , " id v in
let term n = P.sprintf "term 19 P%u" (c - n) in
- let term_conj = string_iter " break & " term c in
+ let term_conj = string_iter " break & " term c in
let abst b n = let xty = if b then P.sprintf ":$T%u" (v - n) else "" in
P.sprintf "λ${ident x%u}%s" (v - n) xty in
- let abst_clo b = string_iter "." (abst b) v in
+ let abst_clo b = string_iter "." (abst b) v in
- let full b n = P.sprintf "(%s.$P%u)" (abst_clo b) (c - n) in
+ let full b n = P.sprintf "(%s.$P%u)" (abst_clo b) (c - n) in
let full_seq b = string_iter " " (full b) c in
P.fprintf ooch "(* %s (%u, %u) *)\n\n" description c v;
- P.fprintf ooch "inductive %s (%s:Type[0]) (%s:%s→Prop) : Prop ≝\n"
+ P.fprintf ooch "inductive %s (%s:Type[0]) (%s:%s→Prop) : Prop ≝\n"
o_name set_list pre_list set_type;
P.fprintf ooch " | %s_intro: ∀%s. %s → %s %s %s\n.\n\n"
o_name ele_list pre_type o_name qm_set qm_pre;
let o_name = name "or" in
let i_name = "'Or" in
- let pre n = P.sprintf "P%u" (c - n) in
+ let pre n = P.sprintf "P%u" (c - n) in
let pre_list = string_iter "," pre c in
- let pre_seq = string_iter " " pre c in
+ let pre_seq = string_iter " " pre c in
let qm n = "?" in
- let qm_pre = string_iter " " qm c in
+ let qm_pre = string_iter " " qm c in
let term n = P.sprintf "term 29 P%u" (c - n) in
- let term_disj = string_iter " break | " term c in
+ let term_disj = string_iter " break | " term c in
- let par n = P.sprintf "$P%u" (c - n) in
+ let par n = P.sprintf "$P%u" (c - n) in
let par_seq = string_iter " " par c in
let mk_con n = P.fprintf ooch " | %s_intro%u: %s → %s %s\n"
P.fprintf ooch "(* %s (%u) *)\n\n" description c;
- P.fprintf ooch "inductive %s (%s:Prop) : Prop ≝\n"
+ P.fprintf ooch "inductive %s (%s:Prop) : Prop ≝\n"
o_name pre_list;
void_iter mk_con c;
P.fprintf ooch ".\n\n";
let o_name = name "and" in
let i_name = "'And" in
- let pre n = P.sprintf "P%u" (c - n) in
+ let pre n = P.sprintf "P%u" (c - n) in
let pre_list = string_iter "," pre c in
- let pre_type = string_iter " → " pre c in
- let pre_seq = string_iter " " pre c in
+ let pre_type = string_iter " → " pre c in
+ let pre_seq = string_iter " " pre c in
let qm n = "?" in
- let qm_pre = string_iter " " qm c in
+ let qm_pre = string_iter " " qm c in
let term n = P.sprintf "term 34 P%u" (c - n) in
- let term_conj = string_iter " break & " term c in
+ let term_conj = string_iter " break & " term c in
- let par n = P.sprintf "$P%u" (c - n) in
+ let par n = P.sprintf "$P%u" (c - n) in
let par_seq = string_iter " " par c in
P.fprintf ooch "(* %s (%u) *)\n\n" description c;
- P.fprintf ooch "inductive %s (%s:Prop) : Prop ≝\n"
+ P.fprintf ooch "inductive %s (%s:Prop) : Prop ≝\n"
o_name pre_list;
P.fprintf ooch " | %s_intro: %s → %s %s\n.\n\n"
o_name pre_type o_name qm_pre;