fact
stringlengths 2
32.6k
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stringclasses 10
values | library
stringclasses 5
values | imports
stringclasses 205
values | filename
stringclasses 216
values | symbolic_name
stringlengths 1
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10.5k
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(m : mfixpoint term) : context := List.rev (mapi (fun i d => vass d.(dname) (lift0 i d.(dtype))) m).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
fix_context
| 10,100 |
(na : aname) (decl : context_decl) : context_decl := {| decl_name := na; decl_type := decl_type decl; decl_body := decl_body decl |}.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
rename_decl
| 10,101 |
(ind : inductive) (oib : one_inductive_body) (pred : predicate term) : option context := (* Decompose the type.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
build_return_context
| 10,102 |
(Γ : list ident) (Γ' : context) : list ident := let fix aux Γids Γ := match Γ with | [] => Γids | decl :: Γ => aux (fresh_name Γids (binder_name (decl_name decl)) (Some (decl_type decl)) :: Γids) Γ end in aux Γ (MCList.rev Γ').
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
fresh_names
| 10,103 |
{A} (f : A -> t) (g : A -> t) (def : def A) := string_of_name (binder_name (dname def)) ^ " { struct " ^ string_of_nat (rarg def) ^ " }" ^ " : " ^ f (dtype def) ^ " := " ^ nl ^ g (dbody def).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_def
| 10,104 |
(print_term : list ident -> bool -> term -> t) Γ (defs : mfixpoint term) := let ctx' := fix_context defs in print_list (print_def (print_term Γ true) (print_term (fresh_names Σ Γ ctx') true)) (nl ^ " with ") defs.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_defs
| 10,105 |
(s : sort) := match s with | sProp => "Prop" | sSProp => "SProp" | sType l => if with_universes then ("Type(" ++ MCString.string_of_list string_of_level_expr (LevelExprSet.elements l) ++ ")")%bs else "Type" end.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_sort
| 10,106 |
(Γ : list ident) (top : bool) (t : term) {struct t} : Tree.t := match t with | tRel n => match nth_error Γ n with | Some id => id | None => "UnboundRel(" ^ string_of_nat n ^ ")" end | tVar n => "Var(" ^ n ^ ")" | tEvar ev args => "Evar(" ^ string_of_nat ev ^ "[]" ^ ")" | tSort s => print_sort s | tCast c k t => parens top (print_term Γ true c ^ ":" ^ print_term Γ true t) | tProd na dom codom => let na' := (fresh_name Σ Γ na.(binder_name) (Some dom)) in if (noccur_between 0 1 codom) then parens top (print_term Γ false dom ^ " → " ^ print_term (na' :: Γ) true codom) else parens top ("∀ " ^ na' ^ " : " ^ print_term Γ false dom ^ ", " ^ print_term (na' :: Γ) true codom) | tLambda na dom body => let na' := (fresh_name Σ Γ na.(binder_name) (Some dom)) in parens top ("fun " ^ na' ^ " : " ^ print_term Γ true dom ^ " ⇒ " ^ print_term (na' :: Γ) true body) | tLetIn na def dom body => let na' := (fresh_name Σ Γ na.(binder_name) (Some dom)) in parens top ("let " ^ na' ^ " : " ^ print_term Γ true dom ^ " := " ^ print_term Γ true def ^ " in " ^ nl ^ print_term (na' :: Γ) true body) | tApp f l => parens top (print_term Γ false f ^ " " ^ print_list (print_term Γ false) " " l) | tConst c u => string_of_kername c ^ print_universe_instance u | tInd (mkInd i k) u => match lookup_ind_decl Σ i k with | Some oib => oib.(ind_name) ^ print_universe_instance u | None => "UnboundInd(" ^ string_of_inductive (mkInd i k) ^ "," ^ string_of_universe_instance u ^ ")" end | tConstruct (mkInd i k as ind) l u => match lookup_ind_decl Σ i k with | Some oib => match nth_error oib.(ind_ctors) l with | Some cb => cb.(cstr_name) ^ print_universe_instance u | None => "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ "," ^ string_of_universe_instance u ^ ")" end | None => "UnboundConstruct(" ^ string_of_inductive ind ^ "," ^ string_of_nat l ^ "," ^ string_of_universe_instance u ^ ")" end | tCase {| ci_ind := mkInd mind i as ind; ci_npar := pars |} p t brs => match lookup_ind_decl Σ mind i with | Some oib => match build_return_context ind oib p with | None => "Case(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_term t ^ "," ^ string_of_predicate string_of_term p ^ "," ^ string_of_list (pretty_string_of_branch string_of_term) brs ^ ")" | Some Γret => let Γret := fresh_names Σ Γ Γret in let ret_binders := firstn #|pcontext p| Γret in let (as_name, indices) := (hd "_" ret_binders, MCList.rev (tail ret_binders)) in let in_args := (repeat "_" #|pparams p| ++ indices)%list in let in_str := oib.(ind_name) ^ concat "" (map (fun a : bytestring.string => " " ^ a) in_args) in let fix print_branch Γ names prbr {struct names} := match names with | [] => "⇒ " ^ prbr Γ | na :: l => let na' := (fresh_name Σ Γ na.(binder_name) None) in na' ^ " " ^ print_branch (na' :: Γ) l prbr end in let brs := map (fun br => print_branch Γ (List.rev br.(bcontext)) (fun Γ => print_term Γ true br.(bbody))) brs in let brs := combine brs oib.(ind_ctors) in parens top ("match " ^ print_term Γ true t ^ " as " ^ as_name ^ " in " ^ in_str ^ " return " ^ print_term Γret true (preturn p) ^ " with " ^ nl ^ print_list (fun '(b, cb) => cb.(cstr_name) ^ " " ^ b) (nl ^ " | ") brs ^ nl ^ "end" ^ nl) end | None => "Case(" ^ string_of_inductive ind ^ "," ^ string_of_nat i ^ "," ^ string_of_term t ^ "," ^ string_of_predicate string_of_term p ^ "," ^ string_of_list (pretty_string_of_branch string_of_term) brs ^ ")" end | tProj p c => match lookup_projection Σ p with | Some (mdecl, idecl, cdecl, pdecl) => print_term Γ false c ^ ".(" ^ pdecl.(proj_name) ^ ")" | None => "UnboundProj(" ^ string_of_inductive p.(proj_ind) ^ "," ^ string_of_nat p.(proj_npars) ^ "," ^ string_of_nat p.(proj_arg) ^ "," ^ print_term Γ true c ^ ")" end | tFix l n => parens top ("let fix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ binder_name ∘ dname) l) n) | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ binder_name ∘ dname) l) n) | tInt i => "Int(" ^ string_of_prim_int i ^ ")" | tFloat f => "Float(" ^ string_of_float f ^ ")" | tString s => "Float(" ^ string_of_pstring s ^ ")" | tArray u arr def ty => "Array(" ^ string_of_level u ^ "," ^ string_of_list string_of_term arr ^ "," ^ string_of_term def ^ "," ^ string_of_term ty ^ ")" end.
|
Fixpoint
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_term
| 10,107 |
Γ (c : context_decl) : ident * t := match c with | {| decl_name := na; decl_type := ty; decl_body := None |} => let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in (na', ("(" ^ na' ^ " : " ^ print_term Γ true ty ^ ")")) | {| decl_name := na; decl_type := ty; decl_body := Some b |} => let na' := (fresh_name Σ Γ na.(binder_name) (Some ty)) in (na', ("(" ^ na' ^ " : " ^ print_term Γ true ty ^ " := " ^ print_term Γ true b ^ ")")) end.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
pr_context_decl
| 10,108 |
Γ Δ : list ident * t := match Δ with | [] => (Γ, "" : t) | d :: decls => let '(Γ, s) := print_context Γ decls in let '(na, s') := pr_context_decl Γ d in match decls with | [] => (na :: Γ, s ^ s') | _ => (na :: Γ, s ^ " " ^ s') end end.
|
Fixpoint
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_context
| 10,109 |
Γ (mib : mutual_inductive_body) (c : constructor_body) : t := let '(Γargs, s) := print_context Γ c.(cstr_args) in c.(cstr_name) ^ " : " ^ s ^ "_" ^ print_list (print_term Γargs true) " " c.(cstr_indices).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_one_cstr
| 10,110 |
(short : bool) Γ (mib : mutual_inductive_body) (oib : one_inductive_body) : t := let '(Γpars, spars) := print_context Γ mib.(ind_params) in let '(Γinds, sinds) := print_context Γpars oib.(ind_indices) in oib.(ind_name) ^ spars ^ sinds ^ print_term Γinds true (tSort oib.(ind_sort)) ^ ":=" ^ nl ^ if short then "..." else print_list (print_one_cstr Γpars mib) nl oib.(ind_ctors).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_one_ind
| 10,111 |
Γ (mie : mutual_inductive_entry) (c : ident × term) : t := c.1 ^ " : " ^ print_term Γ true c.2.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_one_cstr_entry
| 10,112 |
(short : bool) Γ (mie : mutual_inductive_entry) (oie : one_inductive_entry) : t := let '(Γpars, spars) := print_context Γ mie.(mind_entry_params) in oie.(mind_entry_typename) ^ spars ^ print_term Γpars true oie.(mind_entry_arity) ^ ":=" ^ nl ^ if short then "..." else print_list (print_one_cstr_entry Γpars mie) nl (combine oie.(mind_entry_consnames) oie.(mind_entry_lc)).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_one_ind_entry
| 10,113 |
e := match e with | Monomorphic_entry ctx => Monomorphic_ctx | Polymorphic_entry uctx => Polymorphic_ctx (fst uctx, snd (snd uctx)) end.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
universes_decl_of_universes_entry
| 10,114 |
k := match k with | Finite => "Inductive" | CoFinite => "CoInductive" | BiFinite => "Variant" end.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_recursivity_kind
| 10,115 |
Σ with_universes (short : bool) (mib : mutual_inductive_body) : t := let Σ' := (Σ, mib.(ind_universes)) in let names := fresh_names Σ' [] (arities_context mib.(ind_bodies)) in (print_recursivity_kind mib.(ind_finite) ^ " " ^ print_list (print_one_ind Σ' with_universes short names mib) (nl ^ "with ") mib.(ind_bodies) ^ "." ^ nl).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_mib
| 10,116 |
mie := rev_map (fun ind => vass (mkBindAnn (nNamed ind.(mind_entry_typename)) Relevant) (it_mkProd_or_LetIn mie.(mind_entry_params) ind.(mind_entry_arity))) mie.(mind_entry_inds).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
mie_arities_context
| 10,117 |
Σ with_universes (short : bool) (mie : mutual_inductive_entry) : t := let Σ' := (Σ, universes_decl_of_universes_entry mie.(mind_entry_universes)) in let names := fresh_names Σ' [] (mie_arities_context mie) in (print_recursivity_kind mie.(mind_entry_finite) ^ " " ^ print_list (print_one_ind_entry Σ' with_universes short names mie) (nl ^ "with ") mie.(mind_entry_inds) ^ "." ^ nl).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_mie
| 10,118 |
with_universes (short : bool) (prefix : nat) (Σ : global_env) (acc : t) : t := match prefix with | 0 => match Σ.(declarations) with [] => acc | _ => ("..." ^ nl ^ acc) end | S n => let univs := Σ.(Env.universes) in let retro := Σ.(Env.retroknowledge) in match Σ.(declarations) with | [] => acc | (kn, InductiveDecl mib) :: Σ => let Σ := {| Env.universes := univs; declarations := Σ; retroknowledge := retro |} in print_env_aux with_universes short n Σ (print_mib Σ with_universes short mib ^ acc) | (kn, ConstantDecl cb) :: Σ => let Σ' := ({| Env.universes := univs; declarations := Σ; retroknowledge := retro |}, cb.(cst_universes)) in print_env_aux with_universes short n Σ'.1 ((match cb.(cst_body) with | Some _ => "Definition " | None => "Axiom " end) ^ string_of_kername kn ^ " : " ^ print_term Σ' with_universes nil true cb.(cst_type) ^ match cb.(cst_body) with | Some b => if short then ("..." ^ nl) else (" := " ^ nl ^ print_term Σ' with_universes nil true b ^ "." ^ nl) | None => "." end ^ acc) end end.
|
Fixpoint
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_env_aux
| 10,119 |
with_universes (short : bool) (prefix : nat) Σ := print_env_aux with_universes short prefix Σ (Tree.string "").
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_env
| 10,120 |
with_universes (short : bool) (prefix : nat) (p : program) : t := print_env with_universes short prefix (fst p) ^ nl ^ print_term (empty_ext (fst p)) with_universes nil true (snd p).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_program
| 10,121 |
Σ with_universes short := Tree.to_string ∘ PrintTermTree.print_mie Σ with_universes short.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_mie
| 10,122 |
Σ with_universes short := Tree.to_string ∘ PrintTermTree.print_mib Σ with_universes short.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_mib
| 10,123 |
Σ Γ top := Tree.to_string ∘ PrintTermTree.print_term Σ true Γ top.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_term
| 10,124 |
(short : bool) (prefix : nat) Σ := Tree.to_string (PrintTermTree.print_env true short prefix Σ).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_env
| 10,125 |
(short : bool) (prefix : nat) (p : program) : string := Tree.to_string (PrintTermTree.print_program true short prefix p).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import Primitive Environment Universes. From MetaCoq.Template Require Import Ast AstUtils LiftSubst. Import bytestring.Tree.
|
template-coq\theories\Pretty.v
|
print_program
| 10,126 |
Σ Γ M1 N1 M2 : red1 Σ Γ M1 N1 -> red1 Σ Γ (tApp M1 M2) (mkApps N1 M2). Proof. constructor. auto. Qed.
|
Lemma
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config. From MetaCoq.Template Require Import Ast AstUtils WfAst Induction LiftSubst From Equations Require Import Equations. Require Import ssreflect.
|
template-coq\theories\Reduction.v
|
red1_tApp_mkApps_l
| 10,127 |
Σ Γ M1 N1 M2 : red1 Σ Γ M1 N1 -> red1 Σ Γ (tApp M1 [M2]) (mkApp N1 M2). Proof. intros. change (mkApp N1 M2) with (mkApps N1 [M2]). apply app_red_l. auto. Qed.
|
Lemma
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config. From MetaCoq.Template Require Import Ast AstUtils WfAst Induction LiftSubst From Equations Require Import Equations. Require Import ssreflect.
|
template-coq\theories\Reduction.v
|
red1_tApp_mkApp
| 10,128 |
Σ Γ M1 N1 M2 : WfAst.wf Σ M1 -> red1 Σ Γ M1 N1 -> red1 Σ Γ (mkApp M1 M2) (mkApp N1 M2). Proof. intros wfM1 H. destruct (isApp M1) eqn:Heq. destruct M1; try discriminate. simpl. revert wfM1. inv H. simpl. intros. rewrite mkApp_mkApps. constructor. intros. rewrite mkApp_mkApps. econstructor; eauto. inv wfM1. simpl. clear -H1. unfold is_constructor in *. destruct (nth_error args narg) eqn:Heq. eapply nth_error_app_left in Heq. now rewrite -> Heq. discriminate. intros. rewrite mkApp_mkApps. now constructor. intros. simpl. constructor. clear -X. induction X; constructor; auto. rewrite mkApp_tApp; auto. now apply red1_tApp_mkApp. Qed.
|
Lemma
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config. From MetaCoq.Template Require Import Ast AstUtils WfAst Induction LiftSubst From Equations Require Import Equations. Require Import ssreflect.
|
template-coq\theories\Reduction.v
|
red1_mkApp
| 10,129 |
Σ Γ M1 N1 M2 : WfAst.wf Σ M1 -> All (WfAst.wf Σ) M2 -> red1 Σ Γ M1 N1 -> red1 Σ Γ (mkApps M1 M2) (mkApps N1 M2). Proof. induction M2 in M1, N1 |- *. simpl; auto. intros. specialize (IHM2 (mkApp M1 a) (mkApp N1 a)). inv X0. forward IHM2. apply wf_mkApp; auto. forward IHM2. auto. rewrite <- !mkApps_mkApp; auto. apply IHM2. apply red1_mkApp; auto. Qed.
|
Lemma
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config. From MetaCoq.Template Require Import Ast AstUtils WfAst Induction LiftSubst From Equations Require Import Equations. Require Import ssreflect.
|
template-coq\theories\Reduction.v
|
red1_mkApps_l
| 10,130 |
Σ Γ M1 M2 N2 : WfAst.wf Σ M1 -> All (WfAst.wf Σ) M2 -> OnOne2 (red1 Σ Γ) M2 N2 -> red1 Σ Γ (mkApps M1 M2) (mkApps M1 N2). Proof. intros. induction X1 in M1, X, X0 |- *. inv X0. destruct (isApp M1) eqn:Heq. destruct M1; try discriminate. simpl. constructor. apply OnOne2_app. constructor. auto. rewrite mkApps_tApp; try congruence. rewrite mkApps_tApp; try congruence. constructor. constructor. auto. inv X0. specialize (IHX1 (mkApp M1 hd)). forward IHX1. apply wf_mkApp; auto. forward IHX1; auto. now rewrite !mkApps_mkApp in IHX1. Qed.
|
Lemma
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config. From MetaCoq.Template Require Import Ast AstUtils WfAst Induction LiftSubst From Equations Require Import Equations. Require Import ssreflect.
|
template-coq\theories\Reduction.v
|
red1_mkApps_r
| 10,131 |
{term} `{EqDec term} : EqDec (predicate term). Proof. intros [] []. fcase (eq_dec pparams pparams0). fcase (eq_dec puinst puinst0). fcase (eq_dec pcontext pcontext0). fcase (eq_dec preturn preturn0). Defined.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eq_predicate
| 10,132 |
EqDec PrimString.string. Proof. intros s1 s2. destruct (PrimString.compare s1 s2) eqn:Hcmp; [left|right|right]. - by apply PString.compare_eq. - intros Heq%PString.compare_eq. rewrite Heq in Hcmp. discriminate Hcmp. - intros Heq%PString.compare_eq. rewrite Heq in Hcmp. discriminate Hcmp. Qed.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
EqDec_pstring
| 10,133 |
EqDec term. Proof. intro x; induction x using term_forall_list_rect ; intro t ; destruct t ; try (right ; discriminate). all: term_dec_tac term_dec. - induction X in args |- *. + destruct args. * left. reflexivity. * right. discriminate. + destruct args. * right. discriminate. * destruct (IHX args) ; nodec. destruct (p t) ; nodec. subst. left. inversion e. reflexivity. - destruct (IHx1 t1) ; nodec. destruct (IHx2 t2) ; nodec. subst. left. reflexivity. - destruct (IHx1 t1) ; nodec. destruct (IHx2 t2) ; nodec. subst. left. reflexivity. - destruct (IHx1 t1) ; nodec. destruct (IHx2 t2) ; nodec. subst. left. reflexivity. - destruct (IHx1 t1) ; nodec. destruct (IHx2 t2) ; nodec. destruct (IHx3 t3) ; nodec. subst. left. reflexivity. - destruct (IHx t) ; nodec. subst. induction X in args |- *. + destruct args. all: nodec. left. reflexivity. + destruct args. all: nodec. destruct (IHX args). all: nodec. destruct (p t0). all: nodec. subst. inversion e. subst. left. reflexivity. - destruct (IHx t) ; nodec. destruct p0, type_info; subst; cbn. term_dec_tac term_dec. destruct X as (?&?). destruct (s preturn0); cbn in * ; nodec. subst. assert ({pparams = pparams0} + {pparams <> pparams0}) as []; nodec. { revert pparams0. clear -a. induction a. - intros []; [left; reflexivity|right; discriminate]. - intros []; [right; discriminate|]. destruct (p t) ; nodec. destruct (IHa l0) ; nodec. subst; left; reflexivity. } subst. revert branches. clear -X0. induction X0 ; intro l0. + destruct l0. * left. reflexivity. * right. discriminate. + destruct l0. * right. discriminate. * destruct (IHX0 l0) ; nodec. destruct (p (bbody b)) ; nodec. destruct (eq_dec (bcontext x) (bcontext b)) ; nodec. destruct x, b. left. cbn in *. subst. inversion e. reflexivity. - destruct (IHx t) ; nodec. left. subst. reflexivity. - revert mfix. induction X ; intro m0. + destruct m0. * left. reflexivity. * right. discriminate. + destruct p as [p1 p2]. destruct m0. * right. discriminate. * destruct (p1 (dtype d)) ; nodec. destruct (p2 (dbody d)) ; nodec. destruct (IHX m0) ; nodec. destruct x, d ; subst. cbn in *. destruct (eq_dec dname dname0) ; nodec. subst. inversion e1. subst. destruct (eq_dec rarg rarg0) ; nodec. subst. left. reflexivity. - revert mfix. induction X ; intro m0. + destruct m0. * left. reflexivity. * right. discriminate. + destruct p as [p1 p2]. destruct m0. * right. discriminate. * destruct (p1 (dtype d)) ; nodec. destruct (p2 (dbody d)) ; nodec. destruct (IHX m0) ; nodec. destruct x, d ; subst. cbn in *. destruct (eq_dec dname dname0) ; nodec. subst. inversion e1. subst. destruct (eq_dec rarg rarg0) ; nodec. subst. left. reflexivity. - destruct (eq_dec i i0) ; nodec. subst. left. reflexivity. - destruct (eq_dec f f0) ; nodec. subst. left. reflexivity. - destruct (eq_dec s s0) ; nodec. subst. left. reflexivity. - destruct (IHx1 t1); subst; nodec. destruct (IHx2 t2); subst; nodec. destruct (eq_dec u u0); nodec; subst. revert arr0. induction X. + intros []; auto. nodec. + intros []; auto. nodec. destruct (IHX l0). noconf e. destruct (p t); nodec. subst. left; auto. nodec. Defined.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
EqDec_term
| 10,134 |
ReflectEq term := let h := EqDec_ReflectEq term in _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_term
| 10,135 |
ReflectEq context := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_ctx
| 10,136 |
(x y : constant_body) := let (tyx, bodyx, univx, relx) := x in let (tyy, bodyy, univy, rely) := y in eqb tyx tyy && eqb bodyx bodyy && eqb univx univy && eqb relx rely.
|
Definition
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_constant_body
| 10,137 |
ReflectEq constant_body.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_constant_body
| 10,138 |
(x y : constructor_body) := x.(cstr_name) ==? y.(cstr_name) && x.(cstr_args) ==? y.(cstr_args) && x.(cstr_indices) ==? y.(cstr_indices) && x.(cstr_type) ==? y.(cstr_type) && x.(cstr_arity) ==? y.(cstr_arity).
|
Definition
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_constructor_body
| 10,139 |
ReflectEq constructor_body.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_constructor_body
| 10,140 |
(x y : projection_body) := x.(proj_name) ==? y.(proj_name) && x.(proj_type) ==? y.(proj_type) && x.(proj_relevance) ==? y.(proj_relevance).
|
Definition
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_projection_body
| 10,141 |
ReflectEq projection_body.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_projection_body
| 10,142 |
(x y : one_inductive_body) := x.(ind_name) ==? y.(ind_name) && x.(ind_indices) ==? y.(ind_indices) && x.(ind_sort) ==? y.(ind_sort) && x.(ind_type) ==? y.(ind_type) && x.(ind_kelim) ==? y.(ind_kelim) && x.(ind_ctors) ==? y.(ind_ctors) && x.(ind_projs) ==? y.(ind_projs) && x.(ind_relevance) ==? y.(ind_relevance).
|
Definition
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_one_inductive_body
| 10,143 |
ReflectEq one_inductive_body.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_one_inductive_body
| 10,144 |
(x y : mutual_inductive_body) := let (f, n, p, b, u, v) := x in let (f', n', p', b', u', v') := y in eqb f f' && eqb n n' && eqb b b' && eqb p p' && eqb u u' && eqb v v'.
|
Definition
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_mutual_inductive_body
| 10,145 |
ReflectEq mutual_inductive_body.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_mutual_inductive_body
| 10,146 |
x y := match x, y with | ConstantDecl cst, ConstantDecl cst' => eqb cst cst' | InductiveDecl mib, InductiveDecl mib' => eqb mib mib' | _, _ => false end.
|
Definition
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
eqb_global_decl
| 10,147 |
ReflectEq global_decl.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
reflect_global_decl
| 10,148 |
#[export] : EqDec term := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
term_eq_dec
| 10,149 |
#[export] : EqDec context := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
context_eq_dec
| 10,150 |
#[export] : EqDec constructor_body := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
constructor_body_eq_dec
| 10,151 |
#[export] : EqDec projection_body := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
projection_body_eq_dec
| 10,152 |
#[export] : EqDec one_inductive_body := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
one_inductive_body_eq_dec
| 10,153 |
#[export] : EqDec mutual_inductive_body := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
mutual_inductive_body_eq_dec
| 10,154 |
#[export] : EqDec constant_body := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
constant_body_eq_dec
| 10,155 |
#[export] : EqDec global_decl := _.
|
Instance
|
template-coq
|
From Coq Require Numbers.Cyclic.Int63.Uint63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import BasicAst Reflect Environment EnvironmentReflect. From MetaCoq.Template Require Import AstUtils Ast Induction. Require Import ssreflect. From Equations Require Import Equations.
|
template-coq\theories\ReflectAst.v
|
global_decl_eq_dec
| 10,156 |
p := EtaExpand.eta_expand_program p.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
eta_expand
| 10,157 |
(d : kername × global_decl) : TemplateMonad unit := match d.2 with | ConstantDecl cb => match cb.(cst_body) with | Some body => tmMsg ("Unquoting eta-expanded " ++ string_of_kername d.1)%bs ;; tmUnquote body ;; tmMsg ("Succeeded") | None => ret tt end | InductiveDecl idecl => ret tt end.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
check_def
| 10,158 |
{A} (l : list A) := match l with | [] => true | _ :: _ => false end.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
is_nil
| 10,159 |
(t : term) : bool := match t with | tRel i => true | tEvar ev args => List.forallb (wfterm) args | tLambda _ T M | tProd _ T M => wfterm T && wfterm M | tApp u v => wfterm u && List.forallb (wfterm) v && negb (isApp u) && negb (is_nil v) | tCast c kind t => wfterm c && wfterm t | tLetIn na b t b' => wfterm b && wfterm t && wfterm b' | tCase ind p c brs => let p' := test_predicate (fun _ => true) (wfterm) (wfterm) p in let brs' := forallb (wfterm ∘ bbody) brs in p' && wfterm c && brs' | tProj p c => wfterm c | tFix mfix idx => List.forallb (test_def wfterm wfterm) mfix | tCoFix mfix idx => List.forallb (test_def wfterm wfterm) mfix | _ => true end.
|
Fixpoint
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
wfterm
| 10,160 |
d := match d with | ConstantDecl cb => wfterm cb.(cst_type) && option_default wfterm cb.(cst_body) true | InductiveDecl idecl => true end.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
wf_global_decl
| 10,161 |
global_declarations -> bool := forallb (wf_global_decl ∘ snd).
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
wf_global_declarations
| 10,162 |
(g : global_env) := wf_global_declarations g.(declarations).
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
wf_global_env
| 10,163 |
p := wf_global_env p.1 && wfterm p.2.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
wf_program
| 10,164 |
(g : Ast.Env.program) : TemplateMonad unit := monad_map check_def g.1.(declarations) ;; tmMsg "Wellformed global environment" ;; ret tt.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
check_wf
| 10,165 |
forall p : Ast.Env.program, ∥ wt_template_program p ∥.
|
Axiom
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
assume_wt_template_program
| 10,166 |
(p : Ast.Env.program) : TemplateMonad unit := monad_map check_def (eta_expand (make_template_program_env p (assume_wt_template_program p))).1.(declarations) ;; tmMsg "Wellformed eta-expanded global environment" ;; ret tt.
|
Definition
|
template-coq
|
From Coq Require Import List. From MetaCoq.Common Require Import config Transform. From MetaCoq.Template Require Import TemplateProgram Pretty EtaExpand All Loader. Import ListNotations. Import MCMonadNotation. Import bytestring. From Coq Require Import ssrbool.
|
template-coq\theories\TemplateCheckWf.v
|
check_wf_eta
| 10,167 |
{Σ : global_declarations} {d} : EnvMap.fresh_globals (d :: Σ) -> EnvMap.fresh_globals Σ. Proof. intros H; now depelim H. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
fresh_globals_cons_inv
| 10,168 |
{cf : checker_flags} (Σ : global_env) : wf Σ -> EnvMap.fresh_globals Σ.(declarations). Proof. destruct Σ as [univs Σ]; cbn. move=> [] onu; cbn. induction 1; try destruct o; constructor; auto; constructor; eauto. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
wf_fresh_globals
| 10,169 |
{ env :> global_env; map : EnvMap.t global_decl; repr : EnvMap.repr env.(declarations) map; wf : EnvMap.fresh_globals env.(declarations) }.
|
Record
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
t
| 10,170 |
Σ kn := EnvMap.lookup kn Σ.(map).
|
Definition
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_env
| 10,171 |
(Σ : t) kn : lookup_env Σ kn = Env.lookup_env Σ kn. Proof. rewrite /lookup_env /Env.lookup_env. apply (EnvMap.lookup_spec Σ.(env).(declarations)); apply Σ. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_env_spec
| 10,172 |
Σ kn : option mutual_inductive_body := decl <- lookup_env Σ kn;; match decl with | ConstantDecl _ => None | InductiveDecl mdecl => ret mdecl end.
|
Definition
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_minductive
| 10,173 |
Σ kn : lookup_minductive Σ kn = Ast.lookup_minductive Σ kn. Proof. rewrite /lookup_minductive /Ast.lookup_minductive. rewrite lookup_env_spec //. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_minductive_spec
| 10,174 |
Σ kn : option (mutual_inductive_body * one_inductive_body) := mdecl <- lookup_minductive Σ (inductive_mind kn) ;; idecl <- nth_error mdecl.(ind_bodies) (inductive_ind kn) ;; ret (mdecl, idecl).
|
Definition
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_inductive
| 10,175 |
Σ kn : lookup_inductive Σ kn = Ast.lookup_inductive Σ kn. Proof. rewrite /lookup_inductive /Ast.lookup_inductive. rewrite lookup_minductive_spec //. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_inductive_spec
| 10,176 |
Σ kn c : option (mutual_inductive_body * one_inductive_body * constructor_body) := '(mdecl, idecl) <- lookup_inductive Σ kn ;; cdecl <- nth_error idecl.(ind_ctors) c ;; ret (mdecl, idecl, cdecl).
|
Definition
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_constructor
| 10,177 |
Σ kn : lookup_constructor Σ kn = Ast.lookup_constructor Σ kn. Proof. rewrite /lookup_constructor /Ast.lookup_constructor. rewrite lookup_inductive_spec //. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_constructor_spec
| 10,178 |
Σ (p : projection) : option (mutual_inductive_body * one_inductive_body * constructor_body * projection_body) := '(mdecl, idecl, cdecl) <- lookup_constructor Σ p.(proj_ind) 0 ;; pdecl <- nth_error idecl.(ind_projs) p.(proj_arg) ;; ret (mdecl, idecl, cdecl, pdecl).
|
Definition
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_projection
| 10,179 |
Σ kn : lookup_projection Σ kn = Ast.lookup_projection Σ kn. Proof. rewrite /lookup_projection /Ast.lookup_projection. rewrite lookup_constructor_spec //. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import ssreflect ssrbool. From Equations Require Import Equations. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Kernames EnvMap. From MetaCoq.Template Require Import Ast Typing. Import MCMonadNotation.
|
template-coq\theories\TemplateEnvMap.v
|
lookup_projection_spec
| 10,180 |
Ast.Env.program.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
template_program
| 10,181 |
(TemplateEnvMap.GlobalEnvMap.t * Ast.term).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
template_program_env
| 10,182 |
{cf : checker_flags} (p : template_program) := let Σ := Ast.Env.empty_ext p.1 in wf_ext Σ × ∑ T, Σ ;;; [] |- p.2 : T.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
wt_template_program
| 10,183 |
(p : Ast.Env.program) (v : Ast.term) := ∥ WcbvEval.eval p.1 p.2 v ∥.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
eval_template_program
| 10,184 |
{cf : checker_flags} (p : template_program_env) := let Σ := Ast.Env.empty_ext p.1 in wf_ext Σ × ∑ T, Σ ;;; [] |- p.2 : T.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
wt_template_program_env
| 10,185 |
(p : template_program_env) (v : Ast.term) := ∥ WcbvEval.eval p.1 p.2 v ∥.
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
eval_template_program_env
| 10,186 |
{cf : checker_flags} p : ∥ wt_template_program p ∥ -> EnvMap.EnvMap.fresh_globals (declarations p.1). Proof. intros [[wfΣ _]]. eapply TemplateEnvMap.wf_fresh_globals, wfΣ. Qed.
|
Lemma
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
wt_template_program_fresh
| 10,187 |
{cf : checker_flags} (p : template_program) (wtp : ∥ wt_template_program p ∥) : template_program_env := (GlobalEnvMap.make p.1 (wt_template_program_fresh p wtp), p.2).
|
Definition
|
template-coq
|
From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Export config Transform. From MetaCoq.Template Require Import Import Transform.
|
template-coq\theories\TemplateProgram.v
|
make_template_program_env
| 10,188 |
(cmp_univ : Universe.t -> Universe.t -> Prop) : Instance.t -> Instance.t -> Prop := Forall2 (on_rel cmp_univ Universe.make').
|
Definition
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_universe_instance
| 10,189 |
(cmp_univ : conv_pb -> Universe.t -> Universe.t -> Prop) pb v u u' := match v with | Variance.Irrelevant => True | Variance.Covariant => on_rel (cmp_univ pb) Universe.make' u u' | Variance.Invariant => on_rel (cmp_univ Conv) Universe.make' u u' end.
|
Definition
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_universe_variance
| 10,190 |
cmp_univ pb v u u' := Forall3 (cmp_universe_variance cmp_univ pb) v u u'.
|
Definition
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_universe_instance_variance
| 10,191 |
lookup gr napp := match gr with | IndRef ind => match lookup_inductive_gen lookup ind with | Some (mdecl, idecl) => match destArity [] idecl.(ind_type) with | Some (ctx, _) => if (context_assumptions ctx) <=? napp then match mdecl.(ind_variance) with | Some var => Variance var | None => AllEqual end else AllEqual | None => AllEqual end | None => AllEqual end | ConstructRef ind k => match lookup_constructor_gen lookup ind k with | Some (mdecl, idecl, cdecl) => if (cdecl.(cstr_arity) + mdecl.(ind_npars))%nat <=? napp then (** Fully applied constructors are always compared at the same supertype, which implies that no universe ws_cumul_pb needs to be checked here.
|
Definition
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
global_variance_gen
| 10,192 |
cmp_univ pb v := match v with | AllEqual => cmp_universe_instance (cmp_univ Conv) | AllIrrelevant => fun l l' => #|l| = #|l'| | Variance v => fun u u' => cmp_universe_instance (cmp_univ Conv) u u' \/ cmp_universe_instance_variance cmp_univ pb v u u' end.
|
Definition
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_opt_variance
| 10,193 |
cmp_univ pb v : RelationClasses.subrelation (cmp_opt_variance cmp_univ pb AllEqual) (cmp_opt_variance cmp_univ pb v). Proof. intros u u' H. destruct v as [| |v] => //=. 1: now apply Forall2_length in H. now left. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_instance_opt_variance
| 10,194 |
(cmp_univ : conv_pb -> Universe.t -> Universe.t -> Prop) pb v u u' : RelationClasses.subrelation (cmp_univ Conv) (cmp_univ pb) -> on_rel (cmp_univ Conv) Universe.make' u u' -> cmp_universe_variance cmp_univ pb v u u'. Proof. destruct v => //=. intros H H1; apply H, H1. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_universe_universe_variance
| 10,195 |
cmp_univ pb v u u' : RelationClasses.subrelation (cmp_univ Conv) (cmp_univ pb) -> #|v| = #|u| -> cmp_universe_instance (cmp_univ Conv) u u' -> cmp_universe_instance_variance cmp_univ pb v u u'. Proof. intros Hsub Hlen Hu. apply Forall2_triv in Hlen. eapply Forall2_Forall2_Forall3 in Hu; tea. apply Forall3_impl with (1 := Hu) => v1 u1 u1' [] _ H1. now apply cmp_universe_universe_variance. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_instance_variance
| 10,196 |
cmp_univ pb v ui ui' : RelationClasses.subrelation (cmp_univ Conv) (cmp_univ pb) -> cmp_universe_instance (cmp_univ Conv) ui ui' \/ cmp_universe_instance_variance cmp_univ pb v ui ui' -> { cmp_universe_instance (cmp_univ Conv) ui ui' } + { cmp_universe_instance_variance cmp_univ pb v ui ui' }. Proof. intros subr H. elim:(eq_dec #|v| #|ui|). - right. destruct H as [|]; tas. now eapply cmp_instance_variance. - left. destruct H as [|]; tas. eapply @Forall3_Forall2_left with (Q := fun _ _ => True) in H => //. apply Forall2_length in H. now exfalso. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_opt_variance_var_dec
| 10,197 |
Σ cmp_universe pb gr napp := cmp_opt_variance cmp_universe pb (global_variance_gen Σ gr napp).
|
Definition
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_global_instance_gen
| 10,198 |
R R' : RelationClasses.subrelation R R' -> RelationClasses.subrelation (cmp_universe_instance R) (cmp_universe_instance R'). Proof. intros H x y xy. eapply Forall2_impl; tea; unfold on_rel; auto. Qed.
|
Lemma
|
template-coq
|
From Coq Require Import CMorphisms. From MetaCoq.Utils Require Import utils. From MetaCoq.Common Require Import config Reflect Environment EnvironmentTyping. From MetaCoq.Template Require Import Ast AstUtils Induction. Require Import ssreflect ssrbool. From Equations.Prop Require Import DepElim. From Equations Require Import Equations.
|
template-coq\theories\TermEquality.v
|
cmp_universe_instance_impl
| 10,199 |
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