xoa: new binary for the generation of multiple logical constants

[helm.git] / matita / components / binaries / xoa / engine.ml

diff --git a/matita/components/binaries/xoa/engine.ml b/matita/components/binaries/xoa/engine.ml
new file mode 100644 (file)
index 0000000..bc9a8be
--- /dev/null
+++ b/matita/components/binaries/xoa/engine.ml
@@ -0,0 +1,132 @@
+(*
+    ||M||  This file is part of HELM, an Hypertextual, Electronic        
+    ||A||  Library of Mathematics, developed at the Computer Science     
+    ||T||  Department, University of Bologna, Italy.                     
+    ||I||                                                                
+    ||T||  HELM is free software; you can redistribute it and/or         
+    ||A||  modify it under the terms of the GNU General Public License   
+    \   /  version 2 or (at your option) any later version.      
+     \ /   This software is distributed as is, NO WARRANTY.     
+      V_______________________________________________________________ *)
+
+module P = Printf
+module A = Ast
+
+let string_iter sep f n =
+   let rec aux = function
+      | n when n < 1 -> ""
+      | 1            -> f 1
+      | n            -> f n ^ sep ^ aux (pred n)
+   in
+   aux n
+
+let void_iter f n =
+   let rec aux = function
+      | n when n < 1 -> ()
+      | 1            -> f 1
+      | n            -> f n; aux (pred n)
+   in
+   aux n
+
+let mk_exists ooch noch c v =
+   let description = "multiple existental quantifier" in
+   let in_prec = "non associative with precedence 20\n" in
+(*   let out_prec = "right associative with precedence 20\n" in *)
+   let name s = P.sprintf "%s%u_%u" s c v in
+   let o_name = name "ex" in
+   let i_name = "'Ex" in
+
+   let set n      = P.sprintf "A%u" (v - n) 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_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_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 id n       = P.sprintf "ident x%u" (v - n) 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 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 full b n   = P.sprintf "(%s.$P%u)" (abst_clo b) (c - n) in 
+   let full_seq b = string_iter " " (full b) c in
+
+   P.fprintf ooch "(* %s (%u, %u) *)\n\n" description c v;
+
+   P.fprintf ooch "inductive %s (%s:Type[0]) (%s:%s→Prop) : Prop ≝\n" 
+      o_name set_list pre_list set_type;
+   P.fprintf ooch "   | %s_intro: ∀%s. %s → %s %s %s\n.\n\n"
+      o_name ele_list pre_type o_name qm_set qm_pre;
+
+   P.fprintf ooch "interpretation \"%s (%u, %u)\" %s %s = (%s %s %s).\n\n"
+      description c v i_name pre_seq o_name qm_set pre_seq;
+
+   P.fprintf noch "(* %s (%u, %u) *)\n\n" description c v;
+
+   P.fprintf noch "notation > \"hvbox(∃∃ %s break . %s)\"\n %s for @{ %s %s }.\n\n"
+      id_list term_conj in_prec i_name (full_seq false);
+
+   P.fprintf noch "notation < \"hvbox(∃∃ %s break . %s)\"\n %s for @{ %s %s }.\n\n"
+      id_list term_conj in_prec i_name (full_seq true)
+
+let mk_or ooch noch c =
+   let description = "multiple disjunction connective" in
+   let in_prec = "non associative with precedence 30\n" in
+   let name s = P.sprintf "%s%u" s c in
+   let o_name = name "or" in
+   let i_name = "'Or" in
+
+   let pre n      = P.sprintf "P%u" (c - n) in   
+   let pre_list   = string_iter "," pre c in
+   let pre_seq    = string_iter " " pre c in 
+
+   let qm n       = "?" in
+   let qm_pre     = string_iter " " qm c in 
+
+   let term n     = P.sprintf "term 29 P%u" (c - n) in
+   let term_disj  = string_iter " break | " term c in 
+
+   let par n     = P.sprintf "$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"
+                       o_name (c - n) (pre n) o_name qm_pre
+   in
+
+   P.fprintf ooch "(* %s (%u) *)\n\n" description c;
+
+   P.fprintf ooch "inductive %s (%s:Prop) : Prop ≝\n" 
+      o_name pre_list;
+   void_iter mk_con c;
+   P.fprintf ooch ".\n\n";
+
+   P.fprintf ooch "interpretation \"%s (%u)\" %s %s = (%s %s).\n\n"
+      description c i_name pre_seq o_name pre_seq;
+
+   P.fprintf noch "(* %s (%u) *)\n\n" description c;
+
+   P.fprintf noch "notation \"hvbox(∨∨ %s)\"\n %s for @{ %s %s }.\n\n"
+      term_disj in_prec i_name par_seq
+
+let generate ooch noch = function
+   | A.Exists (c, v) ->
+      if c > 0 && v > 0 then mk_exists ooch noch c v
+   | A.Or c          ->
+      if c > 1 then mk_or ooch noch c