CicNotationPt.Theorem (`Definition,srec_name,CicNotationPt.Implicit,Some res)
;;
+let ast_of_sort s =
+ match s with
+ NCic.Prop -> `Prop,"ind"
+ | NCic.Type u ->
+ let u = NCicPp.ppterm ~metasenv:[] ~subst:[] ~context:[] (NCic.Sort s) in
+ (try
+ if String.sub u 0 4 = "Type" then
+ `NType (String.sub u 4 (String.length u - 4)), "rect_" ^ u
+ else if String.sub u 0 5 = "CProp" then
+ `NCProp (String.sub u 5 (String.length u - 5)), "rect_" ^ u
+ else
+ (prerr_endline u;
+ assert false)
+ with Failure _ -> assert false)
+;;
+
let mk_elims (uri,_,_,_,obj) =
- let ast_of_sort s =
- match s with
- NCic.Prop -> `Prop,"ind"
- | NCic.Type u ->
- let u = NCicPp.ppterm ~metasenv:[] ~subst:[] ~context:[] (NCic.Sort s) in
- (try
- if String.sub u 0 4 = "Type" then
- `NType (String.sub u 4 (String.length u - 4)), "rect_" ^ u
- else if String.sub u 0 5 = "CProp" then
- `NCProp (String.sub u 5 (String.length u - 5)), "rect_" ^ u
- else
- (prerr_endline u;
- assert false)
- with Failure _ -> assert false)
- in
match obj with
NCic.Inductive (true,leftno,itl,_) ->
List.map (fun s -> mk_elim uri leftno itl (ast_of_sort s))
List.map (fun s -> NCic.Type s) (NCicEnvironment.get_universes ()))
| _ -> []
;;
+
+(********************* Projections **********************)
+
+let mk_lambda =
+ function
+ [] -> assert false
+ | [t] -> t
+ | l -> CicNotationPt.Appl l
+;;
+
+let rec count_prods = function NCic.Prod (_,_,t) -> 1 + count_prods t | _ -> 0;;
+
+let rec nth_prod projs n ty =
+ match ty with
+ NCic.Prod (_,s,_) when n=0 -> projs, s
+ | NCic.Prod (name,_,t) -> nth_prod (name::projs) (n-1) t
+ | _ -> assert false
+;;
+
+let rec pp rels =
+ function
+ NCic.Rel i -> List.nth rels (i - 1)
+ | NCic.Const _ as t ->
+ CicNotationPt.Ident
+ (NCicPp.ppterm ~metasenv:[] ~subst:[] ~context:[] t,None)
+ | NCic.Sort s -> CicNotationPt.Sort (fst (ast_of_sort s))
+ | NCic.Appl l -> CicNotationPt.Appl (List.map (pp rels) l)
+ | NCic.Prod (n,s,t) ->
+ let n = mk_id n in
+ CicNotationPt.Binder (`Pi, (n,Some (pp rels s)), pp (n::rels) t)
+ | _ -> assert false (* not implemented yet *)
+;;
+
+let mk_projection leftno tyname consname consty (projname,_,_) i =
+ let argsno = count_prods consty - leftno in
+ let rec aux names ty leftno =
+ match leftno,ty with
+ | 0,_ ->
+ let arg = mk_id "xxx" in
+ let arg_ty = mk_appl (mk_id tyname :: List.rev names) in
+ let bvar = mk_id "yyy" in
+ let underscore = CicNotationPt.Ident ("_",None),None in
+ let bvars =
+ HExtlib.mk_list underscore i @ [bvar,None] @
+ HExtlib.mk_list underscore (argsno - i -1) in
+ let branch = CicNotationPt.Pattern (consname,None,bvars), bvar in
+ let projs,outtype = nth_prod [] i ty in
+prerr_endline ("outtype[" ^ string_of_int i ^ "]: " ^ NCicPp.ppterm ~metasenv:[] ~subst:[] ~context:[] ty);
+prerr_endline ("XXX[" ^ string_of_int i ^ "]: " ^ NCicPp.ppterm ~metasenv:[] ~subst:[] ~context:[] outtype);
+ let rels =
+ List.map
+ (fun name -> mk_appl (mk_id name :: List.rev names @ [arg])) projs
+ @ names in
+ let outtype = pp rels outtype in
+ let outtype= CicNotationPt.Binder (`Lambda, (arg, Some arg_ty), outtype) in
+ CicNotationPt.Binder
+ (`Lambda, (arg,Some arg_ty),
+ CicNotationPt.Case (arg,None,Some outtype,[branch]))
+ | _,NCic.Prod (name,_,t) ->
+ let name = mk_id name in
+ CicNotationPt.Binder
+ (`Lambda, (name,None), aux (name::names) t (leftno - 1))
+ | _,_ -> assert false
+ in
+ let res = aux [] consty leftno in
+(* prerr_endline
+ (BoxPp.render_to_string
+ ~map_unicode_to_tex:false
+ (function x::_ -> x | _ -> assert false)
+ 80 (CicNotationPres.render (fun _ -> None)
+ (TermContentPres.pp_ast res)));*)
+ CicNotationPt.Theorem (`Definition,projname,CicNotationPt.Implicit,Some res)
+;;
+
+let mk_projections (_,_,_,_,obj) =
+ match obj with
+ NCic.Inductive
+ (true,leftno,[_,tyname,_,[_,consname,consty]],(_,`Record fields))
+ ->
+ HExtlib.list_mapi (mk_projection leftno tyname consname consty) fields
+ | _ -> []
+;;
{ carr: Type;
op: carr → carr → carr
}.
-(* this is a projection *)
-ndefinition carr: pre_magma → Type
- ≝ λM: pre_magma. match M with [ mk_pre_magma carr _ ⇒ carr ].
ncoercion carr: ∀M:pre_magma. Type ≝ carr on _M: pre_magma to Type.
-ndefinition op ≝
- λM: pre_magma. match M return λM:pre_magma. M → M → M with [ mk_pre_magma _ op ⇒ op ].
nrecord magma (A: pre_magma) : Type[1] ≝
{ mcarr: Ω \sup A;
op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
}.
-(* this is a projection *)
-ndefinition mcarr ≝ λA.λM: magma A. match M with [ mk_magma mcarr _ ⇒ mcarr ].
ncoercion mcarr: ∀A.∀M: magma A. Ω \sup A ≝ mcarr
on _M: magma ? to Ω \sup ?.
-ndefinition op_closed ≝
- λA.λM: magma A.
- match M return λM: magma A.∀x,y. x ∈ M → y ∈ M → op ? x y ∈ M with
- [ mk_magma _ opc ⇒ opc ].
nrecord pre_magma_morphism (A,B: pre_magma) : Type ≝
{ mmcarr: A → B;
mmprop: ∀x,y. mmcarr (op ? x y) = op ? (mmcarr x) (mmcarr y)
}.
-(* this is a projection *)
-ndefinition mmcarr ≝
- λA,B.λf: pre_magma_morphism A B. match f with [ mk_pre_magma_morphism f _ ⇒ f ].
ncoercion mmcarr: ∀A,B.∀M: pre_magma_morphism A B. A → B ≝ mmcarr
on _M: pre_magma_morphism ? ? to ∀_.?.
-ndefinition mmprop ≝
- λA,B,M.
- match M return λM:pre_magma_morphism A B.∀x,y. M (op ? x y) = op ? (M x) (M y) with
- [ mk_pre_magma_morphism _ p ⇒ p ].
nrecord magma_morphism (A) (B) (Ma: magma A) (Mb: magma B) : Type ≝
{ mmmcarr: pre_magma_morphism A B;
mmclosed: ∀x. x ∈ Ma → mmmcarr x ∈ Mb
}.
-(* this is a projection *)
-ndefinition mmmcarr ≝
- λA,B,Ma,Mb.λf: magma_morphism A B Ma Mb. match f with [ mk_magma_morphism f _ ⇒ f ].
ncoercion mmmcarr : ∀A,B,Ma,Mb.∀f: magma_morphism A B Ma Mb. pre_magma_morphism A B
≝ mmmcarr
on _f: magma_morphism ???? to pre_magma_morphism ??.
-ndefinition mmclosed ≝
- λA,B,Ma,Mb.λf: magma_morphism A B Ma Mb.
- match f return λf: magma_morphism A B Ma Mb.∀x. x ∈ Ma → f x ∈ Mb with
- [ mk_magma_morphism _ p ⇒ p ].
ndefinition sub_magma ≝
λA.λM1,M2: magma A. M1 ⊆ M2.
| nrewrite < Hx1;
nrewrite < Hy1;
napply (mmprop ?? f ??)]##]
-nqed.
\ No newline at end of file
+nqed.
+
+ndefinition counter_image: ∀A,B. (A → B) → Ω \sup B → Ω \sup A ≝
+ λA,B,f,Sb. {x | ∃y. y ∈ Sb ∧ f x = y}.
+
+ndefinition mm_counter_image:
+ ∀A,B. ∀Ma: magma A. ∀Mb: magma B. magma_morphism ?? Ma Mb → magma A.
+ #A; #B; #Ma; #Mb; #f;
+ napply (mk_magma ???)
+ [ napply (counter_image ?? f Mb)
+ | #x; #y; nwhd in ⊢ (% → % → ?); *; #y0; *; #Hy0; #H
projects / helm.git / commitdiff