diff options
| -rw-r--r-- | HoTT_Base.thy | 53 | ||||
| -rw-r--r-- | HoTT_Methods.thy | 5 | ||||
| -rw-r--r-- | HoTT_Typing.thy (renamed from typing.ML) | 104 | ||||
| -rw-r--r-- | util.ML | 72 |
4 files changed, 125 insertions, 109 deletions
diff --git a/HoTT_Base.thy b/HoTT_Base.thy index 1eaed12..9dcf6d0 100644 --- a/HoTT_Base.thy +++ b/HoTT_Base.thy @@ -1,64 +1,21 @@ (******** -Isabelle/HoTT: Foundational definitions and notation +Isabelle/HoTT: Basic logical definitions and notation Feb 2019 -This file is the starting point of the Isabelle/HoTT object logic, and contains the basic setup and definitions. +This file completes the basic logical and functional setup of the HoTT logic. Among other things, it: -* Calls the setup of object-level type inference functionality. * Defines the universe hierarchy and its governing rules. * Defines named theorems for later use by proof methods. ********) theory HoTT_Base -imports Pure -keywords "assume_type" "assume_types" :: thy_decl +imports HoTT_Typing begin -section \<open>Terms and typing\<close> - -typedecl t \<comment> \<open>Type of object-logic terms (which includes the types)\<close> - -judgment has_type :: "[t, t] \<Rightarrow> prop" ("(3_:/ _)") - -section \<open>Setup non-core logic functionality\<close> - -declare[[eta_contract=false]] \<comment> \<open>Do not eta-contract\<close> - -ML \<open>val trace = Attrib.setup_config_bool @{binding "trace"} (K false)\<close> - \<comment> \<open>Context attribute for tracing; use declare[[trace=true]] at any point in a theory to turn on.\<close> - -text \<open>Set up type assumption and inference functionality:\<close> - -ML_file "util.ML" -ML_file "typing.ML" -ML \<open> -val _ = - let - fun store_typing ctxt = Typing.put_declared_typing o (Syntax.read_prop ctxt) - in - Outer_Syntax.local_theory - @{command_keyword "assume_type"} - "Declare typing assumptions" - (Parse.prop >> - (fn prop => fn lthy => Local_Theory.background_theory (store_typing lthy prop) lthy)) - end - -val _ = - let - val parser = Parse.and_list (Parse.prop) - fun store_typings ctxt = fold (Typing.put_declared_typing o (Syntax.read_prop ctxt)) - in - Outer_Syntax.local_theory - @{command_keyword "assume_types"} - "Declare typing assumptions" - (parser >> - (fn props => fn lthy => Local_Theory.background_theory (store_typings lthy props) lthy)) - end -\<close> - + section \<open>Universes\<close> typedecl ord \<comment> \<open>Type of meta-numerals\<close> @@ -92,6 +49,7 @@ Instead use @{method elim}, or instantiate the rules suitably. @{thm U_cumulative'} is an alternative rule used by the method @{theory_text cumulativity} in @{file HoTT_Methods.thy}. \<close> + section \<open>Type families\<close> abbreviation (input) constraint :: "[t \<Rightarrow> t, t, t] \<Rightarrow> prop" ("(1_:/ _ \<leadsto> _)") @@ -99,6 +57,7 @@ where "f: A \<leadsto> B \<equiv> (\<And>x. x: A \<Longrightarrow> f x: B)" text \<open>We use the notation @{prop "B: A \<leadsto> U i"} to abbreviate type families.\<close> + section \<open>Named theorems\<close> named_theorems form diff --git a/HoTT_Methods.thy b/HoTT_Methods.thy index 99f3446..088c1fa 100644 --- a/HoTT_Methods.thy +++ b/HoTT_Methods.thy @@ -9,6 +9,7 @@ imports HoTT_Base "HOL-Eisbach.Eisbach" "HOL-Eisbach.Eisbach_Tools" begin + section \<open>Substitution and simplification\<close> ML_file "~~/src/Tools/misc_legacy.ML" @@ -25,6 +26,7 @@ Premises of the rule(s) applied are added as new subgoals. method compute declares comp = (subst comp) + section \<open>Handling universes\<close> text \<open> @@ -46,6 +48,7 @@ method cumulativity declares form = ( ((elim U_cumulative | (rule U_cumulative, rule form)), provelt) ) + section \<open>Deriving typing judgments\<close> method routine uses add = (assumption | rule add | rule)+ @@ -54,6 +57,7 @@ text \<open> The method @{method routine} proves typing judgments @{prop "a: A"} using the rules declared @{attribute intro} in the respective theory files, as well as any additional lemmas provided with the modifier @{theory_text add}. \<close> + section \<open>Derivation search\<close> text \<open> @@ -63,6 +67,7 @@ It also handles universes using @{method hierarchy} and @{method cumulativity}. method derive uses lems = (routine add: lems | compute comp: lems | cumulativity form: lems | hierarchy)+ + section \<open>Induction\<close> text \<open> diff --git a/typing.ML b/HoTT_Typing.thy index 8c3d42c..6433139 100644 --- a/typing.ML +++ b/HoTT_Typing.thy @@ -1,11 +1,40 @@ (******** -Isabelle/HoTT: typing.ML +Isabelle/HoTT: Core typing judgment form and associated automation Feb 2019 -Functionality for object-level type inference. +This file is the starting point of the definition of Isabelle/HoTT. +It declares the fundamental typing judgment form and sets up various +ML functionality to automate type inference. ********) +theory HoTT_Typing +imports Pure +keywords "assume_type" "assume_types" :: thy_decl + +begin + + +section \<open>Initial settings\<close> + +declare[[eta_contract=false]] \<comment> \<open>Do not eta-contract\<close> + +ML \<open>val trace = Attrib.setup_config_bool @{binding "trace"} (K false)\<close> + \<comment> \<open>Context attribute for tracing; use declare[[trace=true]] at any point in a theory to turn on.\<close> + + +section \<open>Terms and typing\<close> + +typedecl t \<comment> \<open>Type of object-logic terms (which includes the types)\<close> + +judgment has_type :: "[t, t] \<Rightarrow> prop" ("(3_:/ _)") + + +section \<open>Typing functionality\<close> + +ML_file "util.ML" + +ML \<open> signature TYPING = sig type jmt = term @@ -18,10 +47,11 @@ sig val typing_all: Proof.context -> jmt list val get_typing_in: term -> jmt list -> term option + val get_local_typing: Proof.context -> term -> term option - val get_declared_typing: theory -> term -> term option - val put_declared_typing: term -> theory -> theory + val put_theory_typing: term -> theory -> theory + val get_theory_typing: theory -> term -> term option val get_typing: Proof.context -> term -> term option end @@ -32,23 +62,23 @@ struct type jmt = term (* Determine if a term is a typing judgment *) -fun is_typing_jmt (@{const HoTT_Base.has_type} $ _ $ _) = true +fun is_typing_jmt (@{const has_type} $ _ $ _) = true | is_typing_jmt _ = false (* Functions to extract a and A from propositions "a: A" *) -fun term_of_jmt (@{const HoTT_Base.has_type} $ t $ _) = t +fun term_of_jmt (@{const has_type} $ t $ _) = t | term_of_jmt _ = Exn.error "Not a typing judgment" -fun type_of_jmt (@{const HoTT_Base.has_type} $ _ $ T) = T +fun type_of_jmt (@{const has_type} $ _ $ T) = T | type_of_jmt _ = Exn.error "Not a typing judgment" (* Get typing assumptions in "this" *) fun typing_this ctxt = Util.get_this ctxt |> map Thm.prop_of |> filter is_typing_jmt -(* Get the typing assumptions in the current context *) +(* Get the typing assumptions in the current proof context *) val typing_assms = Util.get_assms #> map Thm.prop_of #> filter is_typing_jmt -(* Get all visible typing judgments—Quick hack for now; should record them separately *) +(* Search the context and return all visible typing judgments *) fun typing_all ctxt = Util.get_all_thms ctxt |> map (Thm.prop_of o snd) |> filter is_typing_jmt @@ -84,36 +114,56 @@ fun get_local_typing ctxt tm = NONE => get_typing_in tm (typing_assms ctxt) | res => res -(* Storage space for declared typings *) -structure Declared_Typings = Theory_Data +(* Dedicated theory data for proven typing judgments *) +structure Theory_Typings = Theory_Data ( type T = term Symtab.table val empty = Symtab.empty val extend = I - val merge = K Symtab.empty -) + val merge = Symtab.join (fn key => fn (x, y) => y) +) (* Accessor for the above data *) -fun get_declared_typing thy tm = - case tm of - (Free (v, _)) => Symtab.lookup (Declared_Typings.get thy) v - | _ => NONE - -(* Store new typing information for free variables only - (constants should have their types declared at the moment of definition). - End users should use the "typing" keyword instead. -*) -fun put_declared_typing jmt = +fun get_theory_typing thy tm = + Symtab.lookup (Theory_Typings.get thy) (Util.string_of_term tm) + +fun put_theory_typing jmt = case jmt of Const("HoTT_Base.has_type", _) $ term $ typing => - (case term of - Free (v, _) => Declared_Typings.map (Symtab.update (v, typing)) - | _ => Exn.error "Cannot declare typing assumption (not a free variable)") + Theory_Typings.map (Symtab.update (Util.string_of_term term, typing)) | _ => Exn.error "Not a typing judgment" (* Get the typing of a term *) fun get_typing ctxt tm = case get_local_typing ctxt tm of - NONE => get_declared_typing (Proof_Context.theory_of ctxt) tm + NONE => get_theory_typing (Proof_Context.theory_of ctxt) tm | res => res end +\<close> + +ML \<open> +val _ = + let + fun store_typing ctxt = Typing.put_theory_typing o (Syntax.read_prop ctxt) + in + Outer_Syntax.local_theory + @{command_keyword "assume_type"} + "Declare typing assumptions" + (Parse.prop >> + (fn prop => fn lthy => Local_Theory.background_theory (store_typing lthy prop) lthy)) + end + +val _ = + let + val parser = Parse.and_list (Parse.prop) + fun store_typings ctxt = fold (Typing.put_theory_typing o (Syntax.read_prop ctxt)) + in + Outer_Syntax.local_theory + @{command_keyword "assume_types"} + "Declare typing assumptions" + (parser >> + (fn props => fn lthy => Local_Theory.background_theory (store_typings lthy props) lthy)) + end +\<close> + +end @@ -28,6 +28,7 @@ end structure Util: UTIL = struct +(* Unmark a name string identifier *) fun unmark s = Lexicon.unmark_class s handle Fail "unprefix" => @@ -39,40 +40,6 @@ fun unmark s = handle Fail "unprefix" => s -fun name_and_thm (fact, thm) = - ((case fact of - Facts.Named ((name, _), _) => name - | Facts.Fact name => name), - thm) - -fun get_all_thms ctxt = - let val (_, ref_thms) = Find_Theorems.find_theorems ctxt NONE NONE true [] - in ref_thms |> (map name_and_thm) - end - -(* Search all visible theorems (including local assumptions) containing a given name *) -fun find_thm ctxt name = - let val (_, ref_thms) = - Find_Theorems.find_theorems ctxt NONE NONE true [(true, Find_Theorems.Name name)] - in - ref_thms |> (map name_and_thm) - end - -(* Get the fact corresponding to the Isar term "this" in the current proof scope *) -fun get_this ctxt = - Name_Space.full_name (Proof_Context.naming_of ctxt) (Binding.name Auto_Bind.thisN) - |> Proof_Context.lookup_fact ctxt |> the |> #thms - handle Option.Option => ( - if (Config.get ctxt trace) then warning "\"this\" undefined in the context" else (); - [] - ) - -(* Get all visible assumptions in the current proof scope. - This includes the facts introduced in the statement of the goal using "assumes", - as well as all facts introduced using "assume" that are visible in the current block. - *) -val get_assms = Assumption.all_prems_of - (* Prepare a Pure pre-term, converting it to a (unchecked) term *) fun prep_term ctxt ptm = let val ptm = Term_Position.strip_positions ptm @@ -119,4 +86,39 @@ fun string_of_term tm = | Abs (_, typ, body) => "Abs (_, " ^ string_of_typ typ ^ ", " ^ string_of_term body ^ ")" | t1 $ t2 => "(" ^ string_of_term t1 ^ ") $ (" ^ string_of_term t2 ^ ")" -end
\ No newline at end of file +fun name_and_thm (fact, thm) = + ((case fact of + Facts.Named ((name, _), _) => name + | Facts.Fact name => name), + thm) + +(* Return all visible theorems *) +fun get_all_thms ctxt = + let val (_, ref_thms) = Find_Theorems.find_theorems ctxt NONE NONE true [] + in ref_thms |> (map name_and_thm) + end + +(* Search all visible theorems (including local assumptions) containing a given name *) +fun find_thm ctxt name = + let val (_, ref_thms) = + Find_Theorems.find_theorems ctxt NONE NONE true [(true, Find_Theorems.Name name)] + in + ref_thms |> (map name_and_thm) + end + +(* Get the fact corresponding to the Isar term "this" in the current proof scope *) +fun get_this ctxt = + Name_Space.full_name (Proof_Context.naming_of ctxt) (Binding.name Auto_Bind.thisN) + |> Proof_Context.lookup_fact ctxt |> the |> #thms + handle Option.Option => ( + if (Config.get ctxt trace) then warning "\"this\" undefined in the context" else (); + [] + ) + +(* Get all visible assumptions in the current proof scope. + This includes the facts introduced in the statement of the goal using "assumes", + as well as all facts introduced using "assume" that are visible in the current block. + *) +val get_assms = Assumption.all_prems_of + +end |