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Diffstat (limited to 'spartan/lib/tactics.ML')
| -rw-r--r-- | spartan/lib/tactics.ML | 233 |
1 files changed, 0 insertions, 233 deletions
diff --git a/spartan/lib/tactics.ML b/spartan/lib/tactics.ML deleted file mode 100644 index f23bfee..0000000 --- a/spartan/lib/tactics.ML +++ /dev/null @@ -1,233 +0,0 @@ -(* Title: tactics.ML - Author: Joshua Chen - -General tactics for dependent type theory. -*) - -structure Tactics(* : -sig - -val assumptions_tac: Proof.context -> int -> tactic -val known_tac: Proof.context -> int -> tactic -val typechk_tac: Proof.context -> int -> tactic -val auto_typechk: bool Config.T -val SIDE_CONDS: (int -> tactic) -> Proof.context -> int -> tactic -val rule_tac: thm list -> Proof.context -> int -> tactic -val dest_tac: int option -> thm list -> Proof.context -> int -> tactic -val intro_tac: Proof.context -> int -> tactic -val intros_tac: Proof.context -> int -> tactic -val old_elims_tac: term option -> Proof.context -> int -> tactic - -end *) = struct - -(*An assumption tactic that only solves typing goals with rigid terms and - judgmental equalities without schematic variables*) -fun assumptions_tac ctxt = SUBGOAL (fn (goal, i) => - let - val concl = Logic.strip_assums_concl goal - in - if - Lib.is_typing concl andalso Lib.is_rigid (Lib.term_of_typing concl) - orelse not ((exists_subterm is_Var) concl) - then assume_tac ctxt i - else no_tac - end) - -(*Solves typing goals with rigid term by resolving with context facts and - simplifier premises, or arbitrary goals by *non-unifying* assumption*) -fun known_tac ctxt = SUBGOAL (fn (goal, i) => - let - val concl = Logic.strip_assums_concl goal - in - ((if Lib.is_typing concl andalso Lib.is_rigid (Lib.term_of_typing concl) - then - let val ths = map fst (Facts.props (Proof_Context.facts_of ctxt)) - in resolve_tac ctxt (ths @ Simplifier.prems_of ctxt) end - else K no_tac) - ORELSE' assumptions_tac ctxt) i - end) - -(*Typechecking: try to solve goals of the form "a: A" where a is rigid*) -fun typechk_tac ctxt = - let - val tac = SUBGOAL (fn (goal, i) => - if Lib.rigid_typing_concl goal - then - let val net = Tactic.build_net - ((Named_Theorems.get ctxt \<^named_theorems>\<open>typechk\<close>) - @(Named_Theorems.get ctxt \<^named_theorems>\<open>intros\<close>) - @(map #1 (Elim.rules ctxt))) - in (resolve_from_net_tac ctxt net) i end - else no_tac) - in - REPEAT_ALL_NEW (known_tac ctxt ORELSE' tac) - end - -(*Many methods try to automatically discharge side conditions by typechecking. - Switch this flag off to discharge by non-unifying assumption instead.*) -val auto_typechk = Attrib.setup_config_bool \<^binding>\<open>auto_typechk\<close> (K true) - -fun side_cond_tac ctxt = CHANGED o REPEAT o - (if Config.get ctxt auto_typechk then typechk_tac ctxt else known_tac ctxt) - -(*Combinator runs tactic and tries to discharge all new typing side conditions*) -fun SIDE_CONDS tac ctxt = tac THEN_ALL_NEW (TRY o side_cond_tac ctxt) - -local -fun mk_rules _ ths [] = ths - | mk_rules n ths ths' = - let val ths'' = foldr1 (op @) - (map (fn th => [rotate_prems n (th RS @{thm PiE})] handle THM _ => []) ths') - in - mk_rules n (ths @ ths') ths'' - end -in - -(*Resolves with given rules, discharging as many side conditions as possible*) -fun rule_tac ths ctxt = resolve_tac ctxt (mk_rules 0 [] ths) - -(*Attempts destruct-resolution with the n-th premise of the given rules*) -fun dest_tac opt_n ths ctxt = dresolve_tac ctxt - (mk_rules (case opt_n of NONE => 0 | SOME 0 => 0 | SOME n => n-1) [] ths) - -end - -(*Applies some introduction rule*) -fun intro_tac ctxt = SUBGOAL (fn (_, i) => SIDE_CONDS - (resolve_tac ctxt (Named_Theorems.get ctxt \<^named_theorems>\<open>intros\<close>)) ctxt i) - -fun intros_tac ctxt = SUBGOAL (fn (_, i) => - (CHANGED o REPEAT o CHANGED o intro_tac ctxt) i) - -(*Basic elimination tactic, only uses existing type judgments from the context - (performs no type synthesis)*) -fun old_elims_tac opt_tm ctxt = case opt_tm of - NONE => SUBGOAL (fn (_, i) => eresolve_tac ctxt (map #1 (Elim.rules ctxt)) i) - | SOME tm => SUBGOAL (fn (goal, i) => - let - fun elim_rule typing = - let - val hd = head_of (Lib.type_of_typing typing) - val opt_rl = Elim.lookup_rule ctxt hd - in - case opt_rl of - NONE => Drule.dummy_thm - | SOME (rl, _) => Drule.infer_instantiate' ctxt - [SOME (Thm.cterm_of ctxt tm)] rl - end - - val template = Lib.typing_of_term tm - - val facts = Proof_Context.facts_of ctxt - val candidate_typings = Facts.could_unify facts template - val candidate_rules = - map (elim_rule o Thm.prop_of o #1) candidate_typings - - val prems = Logic.strip_assums_hyp goal - val candidate_typings' = - filter (fn prem => Term.could_unify (template, prem)) prems - val candidate_rules' = map elim_rule candidate_typings' - in - (resolve_tac ctxt candidate_rules - ORELSE' eresolve_tac ctxt candidate_rules') i - end) - -(* Revamped general induction/elimination *) - -(*Pushes a context/goal premise typing t:T into a \<Prod>-type*) -fun internalize_fact_tac t = - Subgoal.FOCUS_PARAMS (fn {context = ctxt, concl = raw_concl, ...} => - let - val concl = Logic.strip_assums_concl (Thm.term_of raw_concl) - val C = Lib.type_of_typing concl - val B = Thm.cterm_of ctxt (Lib.lambda_var t C) - val a = Thm.cterm_of ctxt t - (*The resolvent is PiE[where ?B=B and ?a=a]*) - val resolvent = - Drule.infer_instantiate' ctxt [NONE, NONE, SOME B, SOME a] @{thm PiE} - in - HEADGOAL (resolve_tac ctxt [resolvent]) - (*known_tac infers the correct type T inferred by unification*) - THEN SOMEGOAL (known_tac ctxt) - end) - -(*Premises that have already been pushed into the \<Prod>-type*) -structure Inserts = Proof_Data ( - type T = term Item_Net.T - val init = K (Item_Net.init Term.aconv_untyped single) -) - -local - -fun elim_core_tac tms types ctxt = SUBGOAL (K ( - let - val rule_insts = map ((Elim.lookup_rule ctxt) o Term.head_of) types - val rules = flat (map - (fn rule_inst => case rule_inst of - NONE => [] - | SOME (rl, idxnames) => [Drule.infer_instantiate ctxt - (idxnames ~~ map (Thm.cterm_of ctxt) tms) rl]) - rule_insts) - in - HEADGOAL (resolve_tac ctxt rules) - THEN RANGE (replicate (length tms) (typechk_tac ctxt)) 1 - end handle Option => no_tac)) - -in - -fun elim_context_tac tms ctxt = case tms of - [] => CONTEXT_SUBGOAL (K (Context_Tactic.CONTEXT_TACTIC (HEADGOAL ( - SIDE_CONDS (eresolve_tac ctxt (map #1 (Elim.rules ctxt))) ctxt)))) - | major::_ => CONTEXT_SUBGOAL (fn (goal, _) => - let - val facts = Proof_Context.facts_of ctxt - val prems = Logic.strip_assums_hyp goal - val template = Lib.typing_of_term major - val types = - map (Thm.prop_of o #1) (Facts.could_unify facts template) - @ filter (fn prem => Term.could_unify (template, prem)) prems - |> map Lib.type_of_typing - in case types of - [] => Context_Tactic.CONTEXT_TACTIC no_tac - | _ => - let - val inserts = map (Thm.prop_of o fst) (Facts.props facts) @ prems - |> filter Lib.is_typing - |> map Lib.dest_typing - |> filter_out (fn (t, _) => - Term.aconv (t, major) orelse Item_Net.member (Inserts.get ctxt) t) - |> map (fn (t, T) => ((t, T), Lib.subterm_count_distinct tms T)) - |> filter (fn (_, i) => i > 0) - (*`t1: T1` comes before `t2: T2` if T1 contains t2 as subterm. - If they are incomparable, then order by decreasing - `subterm_count [p, x, y] T`*) - |> sort (fn (((t1, _), i), ((_, T2), j)) => - Lib.cond_order (Lib.subterm_order T2 t1) (int_ord (j, i))) - |> map (#1 o #1) - val record_inserts = Inserts.map (fold Item_Net.update inserts) - val tac = - (*Push premises having a subterm in `tms` into a \<Prod>*) - fold (fn t => fn tac => - tac THEN HEADGOAL (internalize_fact_tac t ctxt)) - inserts all_tac - (*Apply elimination rule*) - THEN (HEADGOAL ( - elim_core_tac tms types ctxt - (*Pull pushed premises back out*) - THEN_ALL_NEW (SUBGOAL (fn (_, i) => - REPEAT_DETERM_N (length inserts) - (resolve_tac ctxt @{thms PiI} i))) - )) - (*Side conditions*) - THEN ALLGOALS (TRY o side_cond_tac ctxt) - in - fn (ctxt, st) => Context_Tactic.TACTIC_CONTEXT - (record_inserts ctxt) (tac st) - end - end) - -end - -end - -open Tactics |