Tatjana Winter

Elen Le Foll

Testing the Pedagogical Norm: Comparing If-conditionals in EFL Textbooks, Learner Writing and English Outside the Classroom

Keywords: coursebooks, learner corpus, conditionals, pedagogical grammar, English Language Teaching

English as a foreign language (EFL) textbooks typically present a prescriptive typology of three or four conditional types. We examine the extent to which this long-established English Language Teaching (ELT) typology is reflected in four varieties of English by comparing the forms and functions of four samples of 620 if-conditionals from French school EFL textbooks (TEC-Fr), French L1 Learner English (OpenCLC-Fr), Web English (EnTenTen15-S), and British English (BNC-S).

The ELT typology accounts for considerably less than half of if-sentences in the reference data. Even in the EFL textbooks, only 57% of if-conditionals match the typology explicitly taught in their grammar sections. For many formal and functional features, the learner data sits half-way between the distributions of the textbook and reference data. We conclude that the ELT typology needs to be adapted to provide a more representative account of if-conditionals that focuses on L1 and L2 usage and meaning over form.

Introduction

European foreign language curricula for primary and secondary schools claim to adopt a communicative approach. Communication and interaction in the target language are thus both the primary goal of language learning and the means by which this communicative proficiency is to be developed in the first place. Consequently, grammar is to take on a functional role in the classroom: no longer to be taught and learnt for its own sake, but for genuine communicative purposes. It follows that language models and grammar descriptions in teaching materials ought to reflect how language is most typically used in real, communicative contexts. However, corpus studies have revealed significant discrepancies between well-established pedagogical norms and language use outside the English classroom with regard to many grammatical features (Keck & Kim, 2014: 43-46;cf. Römer, 2011).

This study explores the representations of if-conditionals in contemporary EFL textbooks used at lower secondary school levelwhere textbooks are known to make up "a considerable part of the input that learners actually get in the first six years of English instruction" (Römer, 2007: 355-356). The aim is twofold. First, we critically examine the adequacy of the representations of if-conditionals in school EFL textbooks by comparing them to two corpora of naturally occurring English, and second, we examine the impact of the long-established ELT typology of conditionals on EFL textbooks and learner language. To this end, we adopt a triangular approach, comparing the forms and meanings of if-conditionals in four corpus samples representing: a. modern EFL textbooks used in France, b. texts produced by French L1 learners of English and c. naturally-occurring English as a target language reference. This paper is organised as follows: section 2 gives an account of the current state of research on conditionals in ELT. Section 3 describes the corpora used in this study and outlines the procedure for collecting, annotating and analysing our data. In section 4, we first report our findings concerning the extent to which the explicitly taught ELT typology is reflected in our corpus samples before turning to the formal variety of conditionals and the range of meanings expressed by these structures. In section 5, we discuss the results in light of our research questions and, in section 6, conclude by considering the implications of our results for the EFL classroom.

Conditionals in English Language Teaching

In the following, we provide a brief overview of previous corpus-based analyses of ifconditionals in EFL pedagogical materials and learner writing. Many of these studies examine the traditional ELT typology of conditionals which is followed by most EFL textbooks and pedagogical grammars and usually distinguishes between three different types of conditionals. These are defined by specific combinations of verb tenses and modals in the two clauses, and their associated meanings:

• Type 1: if + simple present // will + infinitive; used to talk about likely situations in the present or future. • Type 2: if + simple past // would + infinitive; used to talk about unlikely/hypothetical situations in the present or future. • Type 3: if + past perfect // would + have + infinitive; used to talk about unreal/hypothetical situations in the past.

1. The three basic textbook types do not occur nearly as frequently in natural language as teaching materials suggest [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF][START_REF] Römer | Comparing real and ideal language learner input: The use of an EFL textbook corpus in corpus linguistics and language teaching[END_REF][START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF]. 2. Many tense-aspect constructions and modal patterns that occur particularly frequently in British L1 English are underrepresented, not explicitly mentioned or, at best, treated as marginal cases in most textbooks [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF][START_REF] Römer | Comparing real and ideal language learner input: The use of an EFL textbook corpus in corpus linguistics and language teaching[END_REF][START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF]. 3. If-clauses in which the past tense form actually refers to past time instead of an imaginary present or future are much more frequent in British L1 English than textbook typologies imply [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF]. 4. Textbooks generally underrepresent the occurrence of modal verbs in the ifclause [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF]. 5. ELT grammars very rarely feature indirect conditionals, which are frequently used by native speakers to express pragmatic rather than real conditional meaning [START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF].

Additionally, [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF] and [START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF] addressed whether or notand, if so, to what extentthe teaching norm may influence learners' use of ifconditionals by comparing learner language with L1 data. For the learner data, [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF] explored the International Corpus of Learner English (ICLE; cf. [START_REF] Granger | The International Corpus of Learner English (Version 1.1)[END_REF] and a pilot version of the Lancaster-Trinity Corpus [START_REF] Gablasova | The Trinity Lancaster Corpus: Development, description and application[END_REF], whilst [START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF] examined the German component of the ICLE and Cologne-Hanover Advanced Learner Corpus (CHALK;cf. Römer, 2007). Both used samples from the BNC1994 as their native-speaker reference data: Gabrielatos focused on the academic subcorpus, whilst Römer analysed the written and spoken subcorpora of the BNC1994 separately. [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF] results suggest that the influence of the pedagogical norm on EFL teaching materials on learner production is only moderate, apart from learners' noticeable overuse of conditionals expressing degrees of likelihood rather than other modal senses. Learners' use of if-conditionals in Römer's (2007: 359-360) study, on the other hand, neither resembled the textbook norm nor native-speaker use. Instead, her learner corpora featured "many odd if-clauses with tense form sequences that are not (or hardly ever) used by native speakers" (Römer, 2007: 360), which Römer interpreted as a sign of the learners' confusion with regard to the choice of tense forms in conditionals, likely to be caused by both L1 interference and contradictory input from EFL textbooks and English encountered outside the classroom. Similar discrepancies were reported by [START_REF] Möller | From pedagogical input to learner output: Conditionals in EFL and CLIL teaching materials and learner language[END_REF] in her study comparing if-conditionals in EFL textbooks, Content and Language Integrated Learning (CLIL) materials, German L2 writing, and novice L1 writing. The results show that some conditional types that were underused by German learners were, as compared to novice L1 writing, in fact overrepresented in the teaching materials they worked with. Möller concluded that the observed differences between teaching materials and native speaker production may reflect textbook authors' attempt to counter L1 interferences (such as are apparent in her learner corpus) by specifically focusing on structures that learners seem to avoid or have difficulties with.

Thus far, descriptions of conditionals in naturally-occurring English have tended to be based on native-speaker reference corpora (foremost the BNC1994), which mostly comprise professionally written and edited texts. However, the use of such corpora as reference data can be argued to be at odds with the communicative aims of modern ELT curricula, which place a strong emphasis on spoken and informal communication, and no longer (explicitly) adhere to native-speaker norms. In addition, most studies refer only to the explicit grammatical descriptions of if-conditionals in textbook grammars and/or focus on EFL textbooks for higher or adult education. [START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF] examined these constructions in a corpus of dialogues from German secondary school textbooks, but did not cover the use of if-conditionals in other textbook registers. Moreover, relatively few studies have included learner corpora. Exceptions include [START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF], who focused exclusively on advanced learner English, and [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF], who explored texts produced by learners with mixed L1s. The latter approach, however, makes it difficult to disentangle the potential influences of national educational systems and/or L1 interferences.

Methodology

Based on the results of previous studies, we designed a study to examine and compare the use of if-conditionals in textbook, learner and "real-life" English data. Our first research question asks to which extent the traditional ELT typology of if-conditionals is taught and applied in French secondary school EFL textbooks, considering both the explicit grammar descriptions of conditionals and how they are used in context throughout the textbooks. We opted to examine "Textbook English" as a whole, rather than solely the textbooks' grammar sections, because we know that "what is explicitly taught is not necessarily, or solely, what is learned" (Gabrielatos, 2013: 164). Second, we examine the extent to which the ELT typology taught in EFL textbooks is applicable to the kind of "real-life", naturally occurring English that learners are likely to encounter outside the classroom. Third, we triangulate our results with an analysis of a sample of written production of French L1 learners of English, who are likely to have learnt English at school with textbooks similar to the ones we examine in order to find out whether the norms of the ELT typology continue to influence EFL learners once they have finished their formal schooling. Unlike [START_REF] Möller | From pedagogical input to learner output: Conditionals in EFL and CLIL teaching materials and learner language[END_REF] comparative study, however, the present study does not aim to observe the direct influence of specific school textbooks on learners; rather, we examine the similarities between the pedagogical norm and the range of ifconditionals produced by older and more advanced learners who, though they will no doubt have been exposed to this same pedagogical norm, will also have benefited from a wider range of English input from outside the classroom. Compared to [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF] studies, this exclusive focus on the French EFL context allows us to control for L1 interferences and thus avoids the distortion of results due to mixed L1 interferences and different national educational systems. Our study also differs from previous work in that we examine data from two reference corpora which allow us to explore conditionals in naturally occurring English in both British English and beyond the traditional British/American norms. For the latter, we draw on a large corpus of Web English that includes many different native and non-native varieties of English, as well as a wider range of registers, including non-edited pseudo-spoken language of the type that we can expect the learners of our Learner English sample to have been exposed to outside the classroom both during and after their school studies.

Corpus data

In an attempt to assess the usefulness of the current ELT typology and its potential impact on learner language, we therefore analysed and compared if-conditionals across four corpora representing Textbook, Learner, L1 and Web English. The following subsections briefly describe these four corpora.

Textbook corpus

For the textbook data, we draw on the Textbook English Corpus (TEC; cf. Le Foll, 2020, in press), which consists of the complete texts from nine modern textbook series (43 coursebooks) used at lower secondary school level in France, Spain and Germany (CEFR levels A1-B2). Totalling some 3.3 million words, the TEC includes all the texts, instructions and exercises printed in the textbooks, as well as the scripts/transcripts of the accompanying audio and video materials. In this study, we analyse the French subcorpus of the TEC (hereafter, TEC-Fr) which comprises three textbook series (corresponding to 14 textbook volumes) from three different publishers, published between 2010-2017, and totals some 769,200 words (see Table 1). These textbooks are among the most popular series currently used in the first five years of secondary education (collège [6 e to 3 e ] and the first year of lycée [2 e ]), thus corresponding to the period when if-conditionals are introduced and practised. The full coursebook materials, as well as the audio and video transcripts, were included in the analysis, thus capturing the full range of if-conditionals that students learning with these textbooks will encounter.

Learner corpus

Our learner data comes from the uncoded Open Cambridge Learner Corpus (OpenCLC; cf. Cambridge University Press, 2017), a large corpus of anonymised written student responses to Cambridge English exams. We focus on a subcorpus of the OpenCLC consisting of only the texts written by French nationals with French L1 (thereafter, OpenCLC-Fr). The resulting subcorpus of 239,600 words contains data from 141 intermediate (B1 and B2) and 235 proficient (C1 and C2) English learners aged 16 to 51+ (the vast majority being young adults). The exact numbers per proficiency and educational level are listed in Table 1.

Note that the majority of if-conditionals in the learner sample (72%) come from examination texts written by college or university students rather than secondary school pupils and that these exams took place between 1993-2012. Thus, the learners captured in this study are unlikely to have learnt with the exact same textbooks featured in the TEC-Fr (though perhaps with older editions thereof). Nevertheless, since in France the Ministry of National Education determines the contents of primary and secondary school syllabi, it can safely be assumed that ELT materials used in French schools bear many more similarities than differences, both with regard to the topics covered and their approaches to teaching grammar. More advanced EFL textbooks were not included in the TEC-Fr because if-conditionals are expected to be acquired at collège level (Ministère de l'éducation nationale, 2016) and textbooks are more sparingly used in the final years of ELT in lycées (Leroy, 2012: 72).

Reference corpora

Finding a reference corpus with comparable and learner-relevant text registers is always a challenge. This study therefore relies on two reference corpora: a stratified sample of the British National Corpus (BNC), and a random sample of a large Web English corpus. The BNC is one of the most frequently used reference corpora of Standard British English. Our BNC sample (BNC-S1 ) includes if-sentences from seven genres selected to best match the text types commonly featured in secondary school EFL textbooks and in our learner corpus (see Table 1). Given that the texts of the BNC1994 are more than twenty years old and that language change is known to be faster in spoken language, we draw our spoken data from the more recent Spoken BNC2014 (Love et al., 2017). 2 We decided to complement the BNC-S with a second sample of naturally occurring English drawn from the English Web Corpus 2015 (EnTenTen15) [START_REF] Jakubíček | The TenTen corpus family[END_REF] for two reasons. First, the written component of the BNC1994 mostly consists of professionally written and edited texts, which can be argued to only partially represent the kind of writing learners are expected to produce themselves. Web corpora, by contrast, contain a larger proportion of "interactional" language, i.e., texts from informal, pseudospoken registers, such as blog posts, forum discussions and social networking sites (Kilgarriff et al., 2010: 907-908). Second, the EnTenTen15 comprises texts drawn from a wide range of web domains, produced by both native and non-native speakers of English. The adequacy of "an idealized, somewhat generic, native speaker norm" (Keck & Kim, 2014: 141) is increasingly being questioned in ELT: many scholars now argue that the goal of EFL instruction should be successful lingua franca communication in international contexts. Since both an understanding of new media and internet registers, as well as an awareness of different sociocultural and geographical varieties of English feature on the French curriculum (Ministère de l'éducation nationale, 2015: 267), we consider the combination of the BNC-S and the EnTenTen15-S an appropriate and realistic reference for communicative ELT, combining both the traditional British nativespeaker standard norm and more varied, global English varieties.

Data extraction and processing

The analytical procedure was inspired by [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF], with a focus not just on the formal, but also on the semantic-pragmatic characteristics of conditional sentences. All four corpora are either publicly available on or were uploaded to the Sketch Engine platform [START_REF] Kilgarriff | The Sketch Engine: Ten years on[END_REF] for querying. First, all concordance lines containing the word if were retrieved from both the TEC-Fr and the OpenCLC-Fr.

For the larger reference corpora, it was not feasible to manually filter all occurrences of if; therefore, random samples of 1,000 concordance lines were downloaded using Sketch Engine's randomisation function. Subsequently, all non-conditional uses of if in these downloaded samples were manually filtered out. In line with Gabrielatos (2003: 7), the following constructions were also excluded: as if, instances of if used as a synonym for whether and unintelligible sentences. Even if-constructions were only counted as conditionals if they could be paraphrased as 'even in case', as opposed to 'even though', in which case they can be said to function as concessives, rather than conditionals.3

This procedure resulted in 620 instances of conditional if-sentences in the TEC-Fr and 718 in the OpenCLC-Fr. For ease of comparability, the corpus samples were then reduced to 620 randomly selected conditionals each. This randomisation procedure was achieved by generating a column of random numbers in the spreadsheet documents used for the manual annotation procedure and then selecting the first 620 if-conditionals when ordering the spreadsheet according to these random numbers. For the BNC-S, a stratified randomisation approach was followed in order to maintain a good balance between the seven selected genres (see Table 1). Ensuring that all four samples contain exactly the same number of conditionals allows for the comparison of raw numbers rather than relative frequencies, which we believe makes our method more transparent. Next, all four sets of 620 if-sentences were manually annotated for:

• Tense forms, grammatical aspect and modal verbs in each clause;

• Fixed idiomatic constructions such as if not, if only, if any, even if etc.;

• Time unit each clause refers to;

• Corresponding ELT type, if applicable (see 3.2.1);

• Meaning-based type, using an adapted version of [START_REF] Athanasiadou | Typology of if-clauses[END_REF][START_REF] Ford | Speaking conditionally: Some contexts for if-clauses in conversation[END_REF][START_REF] Athanasiadou | Pragmatic conditionals[END_REF] framework of conditionals (see 3.2.2). Note that if-conditionals found in gap-filling exercises in the textbook sample (TEC-Fr) were annotated according to the expected student answer as found in the textbooks' accompanying teacher book.

Annotation according to ELT types

ELT materials can differ slightly with regard to the formal flexibility of the basic threetype pedagogical norm briefly outlined in section 2, both in terms of the number of types included and the choice of "allowed" modals. Many, but not all EFL textbooks distinguish a fourth type that expresses general truths, often referred to Type 0. We therefore decided to distinguish between ELT types in the strict sense and in a wider sense. Table 2 provides an overview of our classification criteria of both the strict and the inclusive versions of the ELT typology. In our annotation scheme, conditional sentences need to conform to the ELT typology in both form (tense and modals) and meaning (degrees of likelihood / general validity) to qualify as representative of an ELT type (cf. [START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF]Gabrielatos, : 10, 2019: 17): 17). Since the textbooks of the TEC-Fr explicitly instruct learners to use simple tenses in the protasis (if-clause) and a modal followed by a verb in its base form in the apodosis (main clause), conditionals with progressives were not counted as conforming to any of the textbook types. If-clauses with can for Types 0 and 1 and could for Types 2 and 3 were considered to be in agreement with the strict interpretation of the typology because all of the textbooks of the TEC-Fr treat them like any other present or past tense verb in conditionals and frequently include them in examples and cloze exercises. For the same reason, semi-modals (have to, be able to, etc.) were treated like ordinary lexical verbs in their respective tense and therefore also deemed to conform to the strict ELT typology. The only exception to this rule is the BE going to + infinitive construction, which is explicitly contrasted with will + infinitive in virtually every textbook. Our inclusive typology additionally allows may in the if-clause of Type 1 conditionals, as well as might and could in Types 2 and 3 because, in all of the textbooks examined, modals that can refer to possibilities are described in terms of the degree of probability they express, e.g.:

COULD est le passé de CAN ; MIGHT est le passé de MAY ; WOULD le passé de WILL. La forme passée du modal exprime souvent l'irréel, c'est-à-dire ce qui est moins certain. Par exemple, MIGHT exprime une possibilité plus incertaine que MAY. ['COULD is the past form of CAN; MIGHT is the past form of MAY; WOULD the past form of WILL. A modal's past form often expresses the unreal, i.e., what is less certain. For example, MIGHT expresses a more uncertain possibility than MAY.'] (New Bridges 2 de : 178; original emphasis)

Annotation according to meaning

In order to annotate the meaning of each if-conditional sentence, we adopted a simplified version of the typology of conditionals introduced by [START_REF] Athanasiadou | Typology of if-clauses[END_REF][START_REF] Ford | Speaking conditionally: Some contexts for if-clauses in conversation[END_REF][START_REF] Athanasiadou | Pragmatic conditionals[END_REF], which focuses on meanings rather than on tense form / modal verb combinations. The original typology distinguishes three main types: "course of events conditionals" (CECs), "hypothetical conditionals" (HCs) and "marginal" or, in a revised version of the framework, "pragmatic conditionals" (PCs) [START_REF] Athanasiadou | Typology of if-clauses[END_REF]: 611, 1997: 61). Each type is further subdivided into various subcategories. We simplified the framework for the purposes of our analysis. Thus, the subcategories of CECs and HCs were not taken into account. In the category of PCs, we only distinguished between logical and conversational conditionals, not between their respective subcategories.

Table 3 summarises the resulting meaning-based typology that we used to annotate all 2,480 if-sentences in our four samples. [START_REF] Athanasiadou | Typology of if-clauses[END_REF][START_REF] Ford | Speaking conditionally: Some contexts for if-clauses in conversation[END_REF][START_REF] Athanasiadou | Pragmatic conditionals[END_REF] Course of events conditionals (CECs) Example:

• If the tonsils are removed, the adenoids are sometimes cut out, too. [START_REF] Athanasiadou | Typology of if-clauses[END_REF]: 619) • If there is more than one contributor, either sort out separate responsibilities or pool the family income. (Athanasiadou & Dirven 1996: 626) Meaning/function:

• General and habitual states and events, timelessness, natural courses of events Link between the clauses:

• Direct: one generally occurring event/situation (if-clause) entails the realisation of another • The negation of the protasis entails the negation of the apodosis (Comrie, 1986: 78-79;Quirk et al., 1985: 1088) Possible paraphrases:

• If = 'when / whenever; provided that' [START_REF] Athanasiadou | Typology of if-clauses[END_REF]: 617, 1997 • Specific predicted, assumed, uncertain, imagined, or counterfactual situations* • The speaker takes a certain "epistemic stance" towards the actuality of the events (cf. [START_REF] Fillmore | Epistemic stance and grammatical form in English conditional sentences[END_REF]) Link between the clauses:

• Direct: the realisation of one hypothetical event (main clause) depends on the realisation of another (if-clause) • The negation of the protasis entails the negation of the apodosis (Comrie, 1986: 78-79;cf. Quirk et al.: 1985cf. Quirk et al.: , 1088) Possible paraphrases:

• If = 'provided that, assuming that, supposing' (Athanasiadou & Dirven, 1997: 82)

Logical pragmatic conditionals (LPCs)

Example:

• If termites are the equivalent of an antelope, army ants are the equivalent of a beast of prey. [START_REF] Athanasiadou | Typology of if-clauses[END_REF]: 640) • If birds can fly, why shouldn't man? (Athanasiadou & Dirven, 2000: 13) Meaning/function:

• Inference or conclusion, often to achieve some kind of rhetorical effect (cf. [START_REF] Biber | Longman grammar of spoken and written English[END_REF]: 819) • The truth of the proposition in the protasis is taken for granted or assumed to be believed by someone else [START_REF] Iatridou | Topics in conditionals[END_REF]) Link between the clauses:

• Indirect, based on a mental process of inference Possible paraphrases:

• "if a is b, then c is d" / "if a, then because of b" (Athanasiadou & Dirven, 2000: 6, 9) • "If I know [protasis], then I conclude [apodosis]" (Sweetser, 1990: 121)

Conversational pragmatic conditionals (CPCs)

Example:

• If anyone wants me, I'm downstairs. (Athanasiadou & Dirven, 2000: 14) • I've come to offer my congratulations, if that's the right word. (Athanasiadou & Dirven 2000: 19) Meaning/function:

• Explanation of relevance, clarification, politeness, hedging, etc.

• Pragmatic enrichment is required to understand the implied speech act Link between the clauses:

• Indirect, situated on the speech act level Possible paraphrases:

• "in case that...(A), let me inform you that...(B)" (Funk, 1985: 369) • Deleting the if-clause is theoretically possible, but would result in a "possibly irrelevant, infelicitous or in some other sense non-optimal" utterance (Franke, 2007: 6) * Thus, the if-clause can express either what Biber et al. (1999: 819) refer to as an "open condition", whose truth value is unspecified, or what they call a "hypothetical condition", which is definitely not fulfilled.

Critics of the framework have noted that the category of PCs is very heterogeneous, as it comprises all cases in which the link between the protasis and the apodosis is absent or only very weak, including explanations as to why the content of the apodosis is relevant, politeness formulas, and metalinguistic comments on (the wording of) the speech act itself (Declerck & Reed, 2001: 5-6). This criticism is certainly justified, which is why we distinguish between the two subtypes of PCs (logical and conversational), which represent two different basic pragmatic uses. A second point of criticism concerns the criteria by which the three major types of conditional are distinguished: whereas CECs and HCs are characterised by the relationship between the protasis and the apodosis, PCs are differentiated from the other two on the basis of their discourse function (Declerck & Reed, 2001: 6). This issue is common to other typologies. It led [START_REF] Gabrielatos | A corpus-based examination of if-conditionals through the lens of modality[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF][START_REF] Gabrielatos | If-conditionals: Corpus-based classification and frequency distribution[END_REF] to propose an alternative classification scheme in which all conditionals are defined by two criteria: the nature of the link between the protasis and the apodosis (direct or indirect), and the semantic function ("modality") of the construction as a whole. This results in at least eight different types (not including subtypes). While Gabrielatos' typology undoubtedly gives a more specific account of the different kinds of modalities expressed by conditionals, we believe that our simplified classification based on Athanasiadou and Dirven's framework is more transparent and accessible, thus lending itself well to a pedagogically-driven study (cf. Ferguson, 2001: 66). Furthermore, it allows for a more direct comparison with the ELT typology since its HC category essentially subsumes the three traditional ELT types into one, treating them as different possibilities on a scale of likelihood or hypotheticality [START_REF] Athanasiadou | Typology of if-clauses[END_REF]: 630-631, 1997: 70-74).

Reliability and statistical analysis

The full annotation scheme, which requires six fields per if-sentence to be manually annotated, was evaluated by both authors independently coding three sets of 50 ifsentences each from the TEC-Fr, the OpenCLC-Fr and the BNC-S. This resulted in the comparison of 900 double-blind annotated fields. Inter-rater agreement rate on this sample (which makes up around 6% of our data) was found to be satisfactorily high (94.55%). Aside from a few inattention errors, the rare disagreements concerned the application of the ELT typology and the meaning-based typology. Apart from the "unclear" label, which was originally applied more liberally by the second author, no single category was found to be particularly problematic. All disagreements were easily resolved in discussion and helped to guarantee consistency throughout the rest of the single-coded samples. The label "unclear" was ultimately applied to one if-sentence each in the Textbook and Learner English samples (0.16%) and 17 each in the OpenCLC-Fr and the BNC-S (2.76%).

Due to the relatively small sample sizes involved and the large number of possible comparisons as a result of analysing four corpora across many different variables, we do not report p-values. However, we report all results with two-sided 95% confidence intervals. These were calculated in R using the BinomCI function of the DescTools package [START_REF] Le Foll | DescTools. Tools for descriptive statistics (Version R package version 0.99[END_REF]. The Wilson interval with continuity correction method was used [START_REF] Wallis | Binomial confidence intervals and contingency tests: Mathematical fundamentals and the evaluation of alternative methods[END_REF]. Whilst we appreciate that learner data is ideally analysed at the learner level [START_REF] Paquot | Quantitative research methods and study quality in learner corpus research[END_REF], this was not feasible in the context of this exploratory study since most learners featured in the OpenCLC-Fr only contributed one or two if-conditionals. For reasons of space, aggregated corpus results are reported except where significant differences between the learner proficiency levels, textbook series, or registers of the BNC-S were observed.

Results

This section presents the results of the four corpus analyses and their subsequent comparisons. Section 4.1 focuses on the ELT typology, i.e., the way the four types are explicitly described in the textbooks' grammar sections and their frequencies and distribution in the textbook, learner and reference corpora. The remaining sections explore the formal (4.2) and semantic-pragmatic features (4.3) of if-conditionals that diverge from this explicitly taught ELT typology.

Coverage of the ELT typology

The ELT typology in the grammar sections of the TEC-Fr

The grammatical descriptions of if-conditionals in the three textbook series examined correspond to the common three-type typology found in the majority of EFL textbooks and pedagogical grammars. Note that, although all three textbook series use this classification, only Piece of Cake explicitly applies the Type 1-3 terminology. The other series opt for labels such as "condition simple/incertaine/non-réalisée" ('simple/uncertain/unrealised condition'), or refer to the types by their formal constructions only.

According to the French textbooks under study, the conditional Type 1 presents the condition and consequence as possible and likely to be real in the present, or to be realised in the future. Formally, it is characterised by the simple present tense in the if-clause and the modal will followed by an infinitive in the main clause (1).

(1) If they increase their sales, they will become world leaders. (TEC-Fr, New Missions 2 de ) Type 2, by contrast, expresses a present or future condition that is still possible but "moins probable" ('less likely') (New Missions 2 de )' "incertaine" ('uncertain') or "nonréalisée" ('unrealised') (New Bridges 2 de ). Here, the simple past tense is used in the ifclause to refer to a hypothetical present or future condition, and the main clause contains the modal would plus an infinitive (2).

(2) If I went on a digital detox holiday, I would probably spend more time looking around me.

(TEC-Fr, Hi There 3 e ) Type 3 conditionals refer to unrealised hypothetical past conditions and consequences. In this type, the verb in the protasis is in the past perfect tense, while the apodosis features a would + have + past participle construction, e.g., (3).

(3) If Romeo had seen Juliet move, he wouldn't have killed himself. (TEC-Fr, Piece of Cake 3 e ) Among the textbook series examined, only one mentions if-conditionals expressing conditions that are "généralement nécessaire à la réalisation d'une action" ('generally necessary for the realisation of an event') and explicitly link this type to the present + present tense pattern (Hi There 3 e ). This type corresponds to the Type 0 found in some ELT typologies.

Although not all of the textbooks examined in this study include an explicit metalinguistic description of the tenses and modals to be used, they do link each conditional type to specific grammatical forms by providing examples. Note the typographical highlighting of the verb form combinations in the example sentences (1)-( 3), which appears to stress that conditional meaning is inherently connected to a specific formal pattern. In terms of the modal marking of conditionals, textbook grammars largely focus on the central modals will and would, while other modal verbs are, if at all, only mentioned in passing (e.g., could, should, may and might). One textbook series even refers to if-sentences with would as "'pure conditional[s]" (Piece of cake 3 e ), conveying the impression that if-conditionals with other modals are special or marginal cases.

Levels of coverage of the ELT typology in the textbook, learner and reference

samples Table 4 shows the proportions of conditionals from each corpus sample that conform, both in form and meaning, to one of the ELT types exemplified in Table 2. Strikingly, if we interpret the ELT typology in its strict, narrow sense, i.e., as consisting of only three types featuring either the modal will or would in the main clause (see 3.2.1), less than half of the conditionals featured in the textbooks themselves conform to the textbook typology (47% [43-51%], see Table 4). In the OpenCLC-Fr, it is only about a fifth (22% [19-25%]), with no significant difference between learner proficiency levels (B1/B2: 24% [18-30%]; C1/C2: 22% [18-27%]). Critically, the overwhelming majority (80% [76-83%]) of if-conditionals produced by native speakers in the BNC-S are not accounted for by the basic textbook typology of conditionals (strict interpretation). The rate is even higher for the if-conditionals analysed in the Web English sample (88% [85-90%]). Remarkably, even the more inclusive ELT typology (Type 0-3 and allowing for a wider range of modals; see 3.2.1) covers just 57% [53-61%] of if-sentences in the textbook corpus and only accounts for around a third of all if-conditionals in the BNC-S [31-39%] and the EnTenTen15-S [23-30%].

Distribution of Types 0-3

A closer look at the ELT type distributions reveals more fine-grained differences between the samples. Fig. 1, which is based on the more inclusive version of the ELT typology, clearly shows that French EFL textbooks overrepresent Types 1 and 2 as compared to our reference corpus samples. Taken together, they account for 43% [39-47%] of all conditionals in the textbooks, but only 21% [18-24%] in the BNC-S and 13% [10-16%] in the EnTenTen15-S. With 23% [20-26%], the proportion of Types 1 and 2 in the OpenCLC-Fr is very similar to that in the BNC-S. Type 0, the general conditional, accounts for just 7% [6-10%] of all if-sentences in the TEC-Fr, whereas it accounts for almost twice as many in the two reference corpus samples (BNC-S: 11% [9-14%]; EnTenTen15-S: 13% [10-16%]). This underrepresentation of Type 0 in the TEC-Fr corresponds to the rather marginal status it is granted in French EFL textbooks. These usually focus on conditionals expressing different degrees of likelihood. Nonetheless, the proportion of Type 0 sentences in the OpenCLC-Fr corresponds roughly to that of the two reference corpora (12% [10-15%]). Type 3 is very infrequent in both reference corpora (BNC-S: 3% [2-5%]; EnTenTen15-S: 1% [0-2%]) and the OpenCLC-Fr (1% [1-2%]). In the TEC-Fr, however, its proportional use is comparatively large (7% [5-9%]).

Form

The fine-grained analysis of verb form patterns revealed a great formal diversity of if-conditionals: out of 620 if-conditionals per sample, 95 unique combinations were identified in the BNC-S and 88 in the EnTenTen15-S. By way of comparison, 61 and 67 such patterns were found in the TEC-Fr and OpenCLC-Fr samples, respectively. Given this large range of possible constructions, it is clear that pedagogical materials can only focus on the most frequent and salient verb form patterns. The second most frequent form in the Web English sample is present + imperative (13% [10-16%]), typically found in instructions, advice, warnings and offers. Hence, one might have expected to see more in school EFL textbooks, where these functions are very frequent; yet these are rarely expressed with if-sentences. While comparatively rare in the TEC-Fr, both the present + present and the present + imperative patterns are frequently produced by the learners in our sample, i.e., 22% [19-25%] and 8% [6-10%], respectively, independent of proficiency. They use the present + imperative pattern most often in offers, especially in semi-fixed phrases such as (4)-( 6). The same applies to the EnTnTen15-S and if-sentences from the emails and letters of the BNC-S. In addition, learners frequently hedge their advice by using the modal can to express tentativeness [START_REF] Le Foll | DescTools. Tools for descriptive statistics (Version R package version 0.99[END_REF] and use pragmatic semi-fixed formulas such as I would be grateful/pleased/happy if you could... (8), which is reflected in their relatively frequent use of the present + can and could + would patterns (see Fig. 2). The distributions of the verb patterns in Fig. 2 confirm the comparatively high frequency of the three verb form combinations which correspond to Type 1 (present + will), Type 2 (past + would), and Type 3 (past perfect + would have) in the TEC-Fr (45% [41-49%]). Interestingly, learners' frequency of use of these structures is closer to actual English usage than that propagated in EFL textbooks (23% [20-26%]). The only exception is the Type 1 present + will pattern, which, although less frequently used by learners (15% [12-18%]) than textbook authors (20% [17-24%]), is still more frequently encountered than in our reference data (12% [9-15%] the BNC-S and 10% [8-13%] in the EnTenTen15-S). The meanings of this verb form pattern are further examined in 4.3.2.

Both the reference and the OpenCLC-Fr samples feature many conditionals with modalised if-clauses, which do not correspond to the teaching norm. The textbook grammars suggest that if-clauses are either never modalised, or that the only acceptable modals in if-clauses are can or could. None of the textbooks examined explicitly mention or give examples of if-clauses with other modals in the grammar sections. Thus, it is not surprising that the TEC-Fr features high proportions of can and could in if-clauses, whilst other (semi-)modalsespecially be to, the second most frequent if-clause modal both in the BNC-S and in the EnTenTen15-Sare largely absent. In this regard, the distribution of the learner data is similar to that of the textbooks since the learners of the OpenCLC-Fr also use comparatively few modals in if-clauses. Our analyses of the reference corpora confirm [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF]Gabrielatos' ( : 14-15, 2006: 14) : 14) findings from the written BNC1994: namely that a variety of other primary and secondary modals are frequently used in conditional protases, e.g., ( 9)-( 10). Two verb form patterns that rarely occur in the reference or textbook samples but are relatively frequently found in the OpenCLC-Fr are present + would (5% [3-7%]) and present + could (3% [2-4%]). The corresponding concordance lines from the learner data often point to unidiomatic usage of these patterns, e.g., ( 11).

(11) If only nowadays children make a lot of sport, they wouldn't become so fat. (OpenCLC-Fr, B2) Furthermore, our analysis of fixed if constructions revealed that the French EFL learners of the OpenCLC-Fr appear to considerably overuse even if conditionals, including in non-idiomatic contexts, e.g., (12). ( 12) Work in England it's the best way to learn English! However I don't want to be exploited even if I learn English. (OpenCLC-Fr, B2)

Semantics and pragmatics

Types of if-conditionals according to meaning

The distributions of meaning-based types of conditionals (see 3.2.2) across the four corpus samples are presented in Fig. 3.

Fig. 3. Meaning-based types of if-conditionals

As they comprise Types 1-3 of the ELT typology, it is not surprising that hypothetical conditionals (HCs) are by far the most frequent semantic type of conditionals in the TEC-Fr (69% [65-72%]). HCs are also the most represented semantic type in the remaining three corpora. As shown in Fig. 3, however, the dominance of HCs in the textbook sample means that other semantic and pragmatic functions of if-conditionals are underrepresented compared to our reference samples. This is especially true of courseof-events conditionals (CECs). In the EnTenTen15-S and the OpenCLC-Fr, CECs are frequently found in texts giving general advice, often in conjunction with an imperative form in the main clause (see 4.2). In the BNC-S and the EnTenTen15-S, they are even more common in instructional and informational texts and legal language (e.g., general policies, terms and conditions, user manuals). Thus, their higher proportional frequencies in the BNC-S (25% [21-28%]) and the EnTenTen15-S (30% [27-34%]) compared to the TEC-Fr (14% [12-17%]) may, at least in part, be due to register differences.

Similarly, conversational pragmatic conditionals (CPCs) are least frequent in the TEC-Fr (9% [7-11%]); when featured, they are mostly found in the transcripts of the listening materials. The high proportion of CPCs in the OpenCLC-Fr (21% [18-24%]) as compared to the two reference corpus samples (12% [9-14%] in the BNC-S; 14% [12%-17%] in the EnTenTen15-S) is more surprising given that CPCs do not express stereotypical conditional meaning. Here, too, this may be partly due to the text types featured in the OpenCLC-Fr. Indeed, many of the examination questions ask examinees to convince or give advice, make suggestions or recommendations, or write letters of complaint: such texts naturally lend themselves to CPCs. [START_REF] Ford | Speaking conditionally: Some contexts for if-clauses in conversation[END_REF] identified several important conversational functions for CPCs, many of which can also be found in the learner texts of the OpenCLC-Fr: e.g., adding relevance to what is being said by making the utterance fit in the conversation (13); hedging to avoid direct disagreement or to soften the impact of a potentially dispreferred turn ( 14), and making polite suggestions and offers by presenting the proposed action or idea as dependent on the addressee's willingness (15).

(13) On the other hand, if you want something else to photograph, you'll have a wide range of interesting buildings such as museum, castle and so on. (OpenCLC-Fr, C1) ( 14) And if you agree, I'd rather take this job than the other one. (OpenCLC-Fr, C1) (15) According to me, we could find a good place to live in zone two, not too expensive and, if you don't mind, we could rent a sharing-room together. (OpenCLC-Fr, B1)

Thus, although conversational conditionals are comparatively rare and never explicitly mentioned in French EFL textbooks, the learners of the OpenCLC-Fr seem to understand the pragmatics of conditional sentences and are able to employ them accordingly.

The second type of pragmatic conditional, logical pragmatic conditionals (LPCs), is used in a very similar way across all four corpus samples, both in terms of frequency and functions. In the TEC-Fr, LPCs mostly occur in the textbooks' dialogues and audio/video transcripts and fulfil pragmatic functions, just like they do in natural communication: e.g., strengthening an argument by producing a rhetorical effect (16), prompting a reaction from the addressee, or justifying a statement or question by referring to some known fact (17).

(16) And governor of California! Man, if he can do it, we can do it ourselves. (TEC-Fr, Piece of Cake 3 e ) (17) But if she had been dead for hours, who said "I'm in the kitchen"? (TEC-Fr, New Missions 2 de )

Meanings of the "present // will + infinitive" pattern

As already mentioned, some conditionals whose verb form combinations conform to the teaching typology could nevertheless not be assigned to any of the ELT types because they do not express genuine or hypothetical predictions. The most frequent example of this is the case of conditionals with a present tense verb in the if-clause and will in the main clause. According to the textbook grammars, this verb pattern sequence is to be interpreted as a prediction of a possible or likely future event (see Table 2). However, in the BNC-S and the EnTenTen15-S, this formal pattern also frequently expresses general validity (BNC-S: 27% [18-39%]; EnTenTen15-S: 39% [27-51%]) and therefore, following Athanasiadou & Dirven's meaning-based typology (see 3.2.2), belongs to the category of CECs, e.g., (18).

(18) Whenever we're out together they won't go near a food shop, even if we're out for the whole day. (BNC-S, non-academic prose)

In the TEC-Fr, by contrast, the large majority of such if-sentences express hypothetical or predictive meaning (91% [85-95%]). In contrast to what is portrayed in EFL textbooks, French learners of EFL appear to be aware of the versatility of this construction. As Fig. 4 shows, however, here, we observe a stark contrast between B1/B2 and C1/C2 speakers: while the former rarely use present + will conditionals as CECs (11% [4-28%]), the more proficient learners use this pattern for general reference in 47% [34-60%] of cases.

Meanings of the simple past in the if-clause

Similarly, if-clauses with verbs in the simple past tense do not always refer to a hypothetical future or an alternative present reality (cf. [START_REF] Ferguson | If you pop over there: A corpus-based study of conditionals in medical discourse[END_REF][START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Maule | Sorry, but if he comes, I go': Teaching conditionals[END_REF]. There are considerable differences between the four corpora with regard to the meaning expressed by such clauses. It would appear that both textbook authors and the EFL learners of our samples follow the convention corresponding to the meaning associated with Type 2 of the ELT typology (see Table 2). Consequently, the frequency of past tenses referring to the actual past rather than a hypothetical present or future is much lower in both the TEC-Fr (9% [6-15%]) and the OpenCLC-Fr (7% [3-13%]) than in the BNC-S (25% [18-32%]) or the EnTenTen15-S (23% [16-33%]). Indeed, the definitions and descriptions of the Type 2 conditional in EFL textbooks insinuate that hypothetical meaning is somehow inherent to the past + would (or past + modal) pattern, while frequent cases in naturally occurring English such as ( 19)-( 20 The examples above also illustrate that a past tense in the protasis can refer to either general past situations (19) or a particular past event (uncertain or factual) (20). In this respect too, there are notable qualitative differences between the corpora examined. In the textbooks, almost all of the if-clauses that do refer to the past concern general situations, whereas the specific past meaning is most frequent in the other three corpora.

Apart from denoting general and specific past events, there is, in fact, a third kind of past meaning that results from tense backshifting, which can be found in narrative texts and instances of reported speech or thought (21). In our study, backshifted clauses are most frequent in the BNC-S (19% [14-26%]), the large majority of which occur in fictional texts:

(21) Bigwig told Hawkbit and Speedwell that he'd scratch them to pieces if they didn't obey him.

(BNC-S, fiction)

It can be argued, of course, that the past tense in backshifted clauses does not really refer to the past but rather to some kind of hypothetical "future-in-the-past" (Dirven & Putseys, 1989: 350;Fenn, 2010: 337-338). However, even if we regard instances of reported speech and narrative past not as temporal, but rather as modal uses of the past tense, significant differences can still be observed between the four corpora: the temporal sense remains more than twice as frequent in the two reference corpus samples than in the TEC-Fr, and more than three times as frequent as in the OpenCLC-Fr (Fig. 5). Finally, we turn our attention to the use of the indicative was as opposed to the subjunctive were in if-clauses that refer to hypothetical conditions. Both forms can be used when the subject of the if-clause is in the first or third person singular, but, in ELT grammars, were is generally considered the "grammatically correct" form. It is certainly characteristic of a more formal (written) style (Quirk et al., 1985(Quirk et al., : 1094)). The EFL textbooks in the TEC-Fr also favour the use of subjunctive were instead of was in conditional clauses: in 18 out of 25 if-clauses in which this alternation is possible, the textbooks use were. Most of these are instances of the trigram if I were..., where the use of the subjunctive has been argued to be largely conventionalised (Quirk et al., 1985: 158). However, subjunctive uses of were are also found in textbook dialogues supposedly portraying spontaneous spoken language, e.g., ( 22 In the BNC-S, the distribution of was and were is more even, with were occurring in 13 out of 29 possible cases. Interestingly, the if-sentences from the spoken register do not contain any instances of subjunctive were and instead always feature indicative was (23), confirming the claim that subjunctive were is primarily a feature of written language.

(23) I think I'd benefit more from the situation if I was working rather than just studying (BNC-S, spoken)

Considering that the spoken data is more recent than the rest of the BNC-S, the absence of subjunctive were may also indicate an ongoing change from were to was in hypothetical clauses. This would corroborate the findings of diachronic studies on these structures (e.g., Leech et al., 2009: 64-67).

Our second reference corpus, the EnTenTen15-S, by contrast, shows a higher frequency of the more standard form were (11 out of 18 cases). This may partly be due to the higher proportion of American English, which is known to be more conservative with regard to the use of subjunctive were versus indicative was (Leech et al., 2009: 63-69). Like in the BNC-S, the learners in the OpenCLC-Fr use both variants to an equal extent: were occurs in 11 out of 21 of all possible cases, with no significant differences between the proficiency groups.

Discussion

The present results point to many mismatches between how if-conditionals are presented in EFL textbooks and how they are used in naturally occurring English, showing that the current treatment of conditionals in ELT materials cannot adequately prepare learners for what they are likely to need and encounter outside the classroom. In sum, our findings corroborate those of previous studies, supporting Gabrielatos' claim (2006: 2) that the typology explicitly taught in textbooks "provides learners with an incomplete, and in some cases distorted, picture of if-conditionals".

First, we have seen that even the more inclusive version of the textbook typology only covers about a third of all if-sentences in our reference corpora, which largely corresponds to the level of coverage reported by [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF]Gabrielatos ( : 10, 2006: 11) : 11) and [START_REF] Römer | Comparing real and ideal language learner input: The use of an EFL textbook corpus in corpus linguistics and language teaching[END_REF]Römer ( : 159, 2007: 358): 358). Second, the three conditional types outlined in most ELT grammars (Types 1-3) are overrepresented in textbooks, whereas Type 0 and its characteristic verb form pattern are strongly underrepresented compared to naturally occurring English (cf. [START_REF] Römer | Comparing real and ideal language learner input: The use of an EFL textbook corpus in corpus linguistics and language teaching[END_REF]Römer, : 159-160, 2007: 358-359): 358-359). In addition, textbooks feature only few instances of modalised if-clausesand when they do, mostly with only can or could. If-clauses with other commonly used modals are largely absent. Conditionals expressing the notion of likelihood or hypotheticality (HCs) largely dominate, while general (CECs) and pragmatic conditionals (PCs) are underrepresented. Moreover, textbooks omit instances of conditionals in which the present + will pattern does not refer to possible present or future events but rather to general truths. The fact that more advanced learners use this pattern with general (CEC) meaning more frequently that intermediate learners suggests that the former will have had more exposure to the present + will construction with general meaning from sources other than EFL textbooks. Similarly, the overwhelming majority of past tense if-clauses in textbooks express hypothetical Type 2 meaning, whereas they more frequently refer to the actual past time in our reference samples.

Despite the strong focus on if-sentences with hypothetical meaning (HCs) observed in the TEC-Fr, by no means do all textbook conditionals neatly fit into the typology described in the textbooks' own grammar sections. In fact, conditionals that do not conform to it still make up around 43% [39-47%] of the TEC-Fr, a much larger proportion than in [START_REF] Römer | Comparing real and ideal language learner input: The use of an EFL textbook corpus in corpus linguistics and language teaching[END_REF][START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF] corpus of German EFL textbook series. 4 Hence, even though the typology outlined in the textbooks' grammar section is very restricted, French EFL textbooks nevertheless present learners with a variety of conditional structures other than the traditional Types 1-3 in their text passages. There appears to be somewhat of a gap between what EFL learners are expected to produce in grammar exercises aimed at the systematic reproduction of specific tense form or modal combinatory patterns (almost exclusively corresponding to Types 1-3) and what they are exposed to in other textbook-based reading and listening activities. In particular, we noted that a large proportion of Type 3 conditionals featured in the TEC-Fr were found in decontextualised gap-filling exercises, e.g., ( 24)-( 25). Our analysis of the if-conditionals in the OpenCLC-Fr shows that the influence of the pedagogical norm on intermediate and advanced French EFL learners is evident in some, but not all of the aspects mentioned above. For a start, the fact that the explicit typology only covers some 36% [33-40%] of conditionals in the OpenCLC-Fr makes clear that the learners captured in this study are able to use a much greater variety of conditional types than those they were likely exposed to in their formal school education. For instance, although French EFL textbooks tend to overrepresent Type 3 whilst largely underrepresenting Type 0 conditionals, the French EFL learners examined used both these types with approximately the same frequencies as they occur in our reference corpora. With regard to Type 0, it can be assumed that the learners who contributed to the OpenCLC-Fr are likely to have been exposed to Type 0 conditionals outside the English classroom. However, we may also hypothesise that French learners' affinity to this construction in spite of low exposure in EFL instructional contexts is at least partially due to the presence of a congruent construction in French ( 26).

(26) si + présent / présent (phrase générique) : Si on chauffe l'eau à 100 degrés, elle bout (= quand, toutes les fois que) ['If you heat water to 100 degrees, it boils. (= when, whenever)] (Riegel, Pellat, & Rioul, 2009: 854) In the case of Type 3 conditionals, however, we noted that some learners seemingly attempted Type 3 conditionals but failed to produce the correct form, e.g., ( 27).

(27) We had to stop many times and we arrived in the nick of time but it would be easier if the meeting point was not so far. (OpenCLC-Fr, C2)

Although the learners of the OpenCLC-Fr produce Type 1 and 2 conditionals slightly more frequently than native speakers, similarities between the ELT typology based on degrees of likelihood/hypotheticality and the production of intermediate and advanced French EFL learners are not as striking as those found by [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF]Gabrielatos ( : 161, 2019: 38) : 38) (see section 2). Similarly, learners of the OpenCLC-Fr use conditionals with the present + will pattern just as flexibly as observed in the BNC-S and the EnTenTen15-S, i.e., to refer to both hypothetical and generally valid situations, despite the latter meaning being vastly underrepresented in the TEC-Fr. Nor does the textbooks' underrepresentation of CPCs seem to discourage learners from using conditionals that communicate more pragmatic kinds of meaning, as indicated by the relatively high proportion of CPCs in the OpenCLC-Fr (cf. [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF]Gabrielatos, : 161, 2019: 34): 34). This limited influence of the pedagogical norm on the learners of the OpenCLC-Fr may be partly due to the fact that more advanced learners tend to benefit from a wider range of language input and are thus proportionally less exposed to EFL textbook language than beginner learners.

That said, the learners of the OpenCLC-Fr do make extensive use of if-sentences with can and could, which confirms Gabrielatos' (2019: 38) observation that learners tend to overuse conditionals expressing the notion of ability -possibly because "can is always one of the modals given as a possible choice" in textbooks. For learners struggling with the choice of the correct verb forms in conditionals, can and its corresponding past form could might therefore also represent a "safe option" in the context of an examination. By contrast, learners rarely produce conditionals with imperative main clauses, although these are relatively frequent in our reference data (see 4.2).

The strongest influence of the pedagogical norm observed, however, concerns the function of the past tense in if-clauses: as in the TEC-Fr, it almost always expresses modal meaning in the OpenCLC-Fr, while the temporal meaning is rarely produced by learners, whatever their English proficiency level. This also confirms a tendency that was previously observed by [START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF]Gabrielatos ( : 162-163, 2019: 40): 40). A closer look at if + past occurrences in the OpenCLC-Fr shows that, when French EFL learners do use the simple past tense with temporal meaning, they often do so in contexts where the past perfect would have been expected, making these utterances rather hard to interpret ( 27). This suggests that some learners struggle with the form of the Type 3 conditional.

Needless to say, the present results are based on a relatively small sample of nine textbooks used in French secondary schools, as well as a small sample of French L1 learner English (620 if-conditionals). Whilst this study does not claim to observe direct textbook-based influence on learner English, we can nevertheless quantify the extent to which (mostly young adult) French EFL learners still adhere to the pedagogical norms commonly propagated in EFL textbooks for French secondary schools, even after having been presumably exposed to a wider range of English input on leaving school. Whilst it is unlikely that the learners of the OpenCLC-Fr learned English with exactly the textbooks represented in the TEC-Fr, given "the textbook industry's strong resistance to change" (Keck & Kim, 2014: 49) and the centralised nature of the French education system, we can safely assume that they will have been exposed to teaching materials very similar to those included in the TEC-Fr.

Pedagogical implications and conclusion

Our analysis confirms the need to adaptif not completely revisethe traditional ELT typology to allow for the inclusion of frequently occurring types that are currently not covered (cf. Gabrielatos, 2019: 52-54). In particular, we propose that the highly frequent Type 0 ought to be much more prominently featured than is currently the case. By contrast, we argue that the inclusion of the conditional Type 3 in the basic ELT typology is unjustified considering its infrequency in naturally occurring English (cf. Leech, 2011: 18). It could be argued that textbooks' strong focus on this type is necessary to meet EFL learners' productive needs, considering the above-mentioned difficulties that some learners seem to have with its formal aspects. Möller (2020: 118) argues that the prioritisation of particular structures in EFL textbooks (in her case: the Type 2 conditional) is appropriate as it can "help learners minimize L1 influence via underrepresentation and maximize L2 influence via overrepresentation". The case of the Type 3 conditional, however, may be understood as an example of negative washback: it appears to be mostly taught in order to successfully navigate tasks and exercises that have themselves been constructed to elicit and therefore assess learners' ability to correctly produce Type 3 forms. Whilst Type 3 conditionals are, of course, necessary to make counterfactual statements about the past, we believe that they need not be introduced, at least in productive contexts, at the proficiency levels represented by the textbooks examined (see 3.1.1). In the first years of study, it may be wiser to focus on more frequent conditional form-meaning pairings. In particular, production tasks and exercises can emphasise the use of idiomatic formulaic structures, such as if I may, if I were you, if you don't mind, etc., that can help learners improve both their accuracy and fluency. Furthermore, we agree with [START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF]Gabrielatos ( : 17, 2019: 53) : 53) and Kormos and Gabrielatos (2014: 33-34), who point out that it is important to ensure that learners have a sound understanding of the system of tense-aspect marking before expecting them to produce more complex conditional forms. This is especially relevant for Type 3 conditionals, which require full mastery of the perfect aspect. Considering that modality and tenseaspect marking tend to be introduced at the same time as (or, in some cases, even after) if-conditionals (cf. Gabrielatos, 2006: 15), presenting (low) intermediate learners with a predefined formal pattern for Type 3 might even risk having an adverse effect on learner production by creating inhibitions.

Rather than asking students to study rigid formal rules, we believe that the pedagogical focus should shift to the range of meanings communicated by conditionals. An intervention study by Dolgova Jacobsen (2018) suggests that this could be achieved by presenting learners with a cognitive linguistic model of conditionals, which emphasises the components of meaning that determine their linguistic form, notably the discourse context, the co-text and the speaker's perspective (i.e. the relation between the time of speaking and the events in the two clauses, the speaker's background knowledge and attitude towards the situation referred to). We therefore suggest adapting the typology put forth by Athanasiadou & Dirven (see 3.2.2) for EFL instruction. It bears the advantage of being simple yet comprehensive enough to familiarise learners with the diverse communicative functions associated with conditionals and, critically, does not make form, but rather meaning, its primary classification criterion. Evidently, a meaning-first approach to conditionals cannot be achieved with the kind of decontextualised, exclusively form-focused gap-filling exercises, which are currently the norm in French EFL textbooks. We therefore argue that any ELT typology should be complemented by real-life examples, contextualised exercises and relevant communicative tasks developed on the basis of corpus data (cf. Dolgova Jacobsen, 2018).

In addition, our study has once again shown that EFL textbook authors can draw on learner corpus insights to "design pedagogical tools which meet the realities of the teaching and learning context" (Granger, 2009: 13), for instance, to pre-empt typical unidiomatic uses of particular verb form patterns such as those highlighted in 4.2. In the context of secondary school ELT where country-specific textbooks are the norm, it is possible to focus on L1/school language interferences in addition to more general EFL issues. For example, our analysis confirmed Paquot's (2007: 407-408) and Gilquin's (2008: 19-20) observations that French EFL learners overuse even if-constructions due to cross-linguistic from the analogous même si construction in French, which is much more frequent than even if in English (126.36 per million words in the FrTenTen17 vs. 53.08 in the full EnTenTen15). In and of itself an overuse of even ifconstructions would not be problematic were it not for the fact that même si carries a stronger sense of concessivity than even if (cf. Gilquin 2008: 19-20). In some cases, e.g., ( 28)-( 29), French learners' use of even if does not create the intended effect (i.e., to signal concessive meaning) because it implies that there is more conditionality involved than the learner most likely intended to express. Corpus-informed cross-linguistic L1 vs. 'reallife' English comparisons of such constructions in EFL textbooks can therefore help raise learners' awareness of both their frequencies, as well as their contextual and pragmatic uses in English.

(28) As a conclusion, I think we should stop driving and start walking even if it entails some sacrifices: it is good for our environment, our planet, but also for us. (OpenCLC-Fr, C2) (29) Even if this comparison may be considered as simplistic, I still believe that children must have a general understanding […] (OpenCLC-Fr, C2)

In conclusion, given that they largely corroborate the results of previous studies (e.g. [START_REF] Gabrielatos | Conditional sentences: ELT typology and corpus evidence[END_REF][START_REF] Gabrielatos | Corpus-based evaluation of pedagogical materials: If-conditionals in ELT coursebooks and the BNC[END_REF][START_REF] Gabrielatos | If-conditionals in ICLE and the BNC: A success story for teaching or learning[END_REF][START_REF] Gabrielatos | If-conditionals and modality: Description and pedagogy[END_REF][START_REF] Römer | Comparing real and ideal language learner input: The use of an EFL textbook corpus in corpus linguistics and language teaching[END_REF][START_REF] Römer | Learner language and the norms in native corpora and EFL teaching materials: A case study of English conditionals[END_REF], the trends observed in the present analysis appear to be fairly robust. Future research avenues could include the exploration of alternative structures to express conditions, e.g., subject-auxiliary inversion, conjunctions other than if and whether-or constructions. The present study could also be extended to other learner groups, e.g., by comparing learners with different L1s, from different educational backgrounds, or with different levels of L2 exposure outside the English classroom.

Fig. 1 .

 1 Fig. 1. Distribution of ELT types in the four corpora

Fig. 2

 2 Fig.2depicts the distribution of the most frequent verb form combinations found in the four corpus samples examined. By far the most frequent verb form pattern in the two reference corpora is present + present (BNC-S: 21% [18-24%]; EnTenTen15-S: 22% [19-26%]), which corresponds to the typical form of the "general" Type 0 conditional. By contrast, this form is, with 11% [9-14%], only the third most frequent combination in the TEC-Fr, after the formal patterns corresponding to Types 1 and 2.

  (4)[...] so please feel free to contact me if you find my proposal interesting! (OpenCLC-Fr, C1) (5) If you have any thoughts, please let me know. (EnTenTen15-S, livingwell.org.au) (6) Please don't hesitate to contact me if you have any questions. (BNC-S, letters)

  (9) I should be grateful if you would investigate this as a matter of importance and urgency and let me know your findings. (BNC-S, letters) (10) If you'll pardon the awful pun -I really do love Lucy. (EnTenTen15-S, insideuniversal.net)

Fig. 4 .

 4 Fig. 4. Meanings of the present // will + infinitive pattern

Fig. 5 .

 5 Fig. 5. Meaning of the past tense in the if-clause

( 24 )

 24 Paul [would not have bought] (buy) that video game if he had known it was so bad. (TEC-Fr, Join the Team 3 e ) (25) If I [had] (have/had) practised my guitar, I might have (become/became) a rock star. (TEC-Fr, Join the Team 3 e )

Table 1 . Overview of data English variety Corpus / subcorpus Registers Composition of samples Textbook English

 1

	• Textbook English Corpus	• Instructions and explanations	Textbook series:
	(TEC)	• Exercises	• Hi There / New Missions (Bordas, 2012-2015):
	• Subcorpus: Textbooks	• Dialogues, transcripts of spoken English in	228 conditionals
	published in France (TEC-	accompanying audio and video materials	• Join the Team / New Bridges (Nathan, 2010-
	Fr) (769,200 words)	• Informative texts	2013): 248 conditionals
		• Fiction	• Piece of Cake (Le livre scolaire, 2017): 144
		• E-mails, letters, diary entries	conditionals
		• Poetry and songs
	Learner English • Open Cambridge Learner	Written examinations:	376 learners of French nationality with French as
	Corpus (OpenCLC)	• Personal correspondence / informal letters	L1:
	• Subcorpus: French learners	• Blog posts	Educational level (no. of learners; no. of
	(OpenCLC-Fr) (239,600	• Argumentative essays	conditionals):
	words)	• Narrative writing	• College/university (273; 447)
		• Reviews / reports	• Secondary school (61; 102)
			• Unknown (42; 71)
			Proficiency levels (no. of learners, no. of
			conditionals):
			• B1 (49; 75)
			• B2 (92; 153)
			• C1 (123; 210)
			• C2 (112; 182)

Table 2 .

 2 ELT typologies

	Meaning	Form (strict)	Form (inclusive)
		If-clause	Main clause	If-clause	Main clause
	Type 0			Simple present;	Simple
	Meaning: Informative: generally	-	-	only modal allowed: can	present; only modal
	valid cause-effect-				allowed: can
	relationships / situations
	known to be true
	Type 1	Simple present;	will +	Simple present;	will/may +
	Meaning:	only modal	infinitive	only modal	infinitive
	Predictive: possible/likely	allowed: can		allowed: can
	present or future events	If global warming causes this ice to	You may get a promotion if you
		melt, it will affect all of our lives.	work hard enough. (TEC-Fr, New
		(TEC-Fr, Hi There 4 e )	Bridges 2 de )
	Type 2	Simple past; only	would +	Simple past; only	would/could/m
	Meaning:	modal allowed:	infinitive	modal allowed:	ight +
	Speculative: hypothetical	could		could	infinitive
	or theoretically possible	I would utilize public transport if it	If you were rich you could just buy
	but uncertain/unlikely	were available in my area. (TEC-Fr,	up carbon in cash. (TEC-Fr, New
	present or future events	New Missions 2 de )		Missions 2 de )
	Type 3	Past perfect	would + have	Past perfect	Would/could/
	Meaning:		+ past		might + have
	Counterfactual:		participle		+ past
	unreal/hypothetical				participle
	situations in the past	If she had called me, I would have	If you had given me your address, I
		talked to her. (TEC-Fr, New	could have helped you. (TEC-Fr,
		Bridges 2 de )		Join the Team 3 e )

-If you turn a picture of someone upside down, you can give them a headache. (TEC-Fr, Piece of Cake 3 e )*

Table 3 .

 3 Meaning-based typology used in the present study, based on

Table 4 .

 4 Levels of coverage of the ELT typology (strict and inclusive interpretations, see Table2)

		TEC-Fr	OpenCLC-Fr	BNC-S	EnTenTen15-S
	Strict ELT	292 (47% [43-	135 (22% [19-	125 (20% [17-	76 (12% [10-
	typology	51%])	25%])	24%])	15%])
	(Types 1-3)
	Inclusive ELT	354 (57% [53-	225 (36% [33-	215 (35% [31-	164 (26% [23-
	typology (Types 0-	61%])	40%])	39%])	30%])
	3)

  Finally, I think It can be a good idea if the cinema provides reduced prices for students who usually doesn't earn a lot of money by their own. (OpenCLC-Fr, C1) (8) I would be pleased if you could change the wrong informations. C1)

	(7)
	present//present
	present//will+infinitive
	past//would+infinitive
	present//can+infinitive
	present//imperative
	could+infinitive//would+infinitive
	past perfect//would+have+participle
	0%	5%	10%	15%	20%	25%
	EnTenTen15-S	BNC-S	OpenCLC-Fr	TEC-Fr

  ) are not mentioned. He would always lean into a kiss if we asked him for one, but never pucker up and smooch. After a few months of attachment therapy, he now hugs us back and gives us kisses. (EnTenTen15-S, a4everfamily.org) (20) If you missed Sir Gordon's speech and wish to hear a recorded version, press this button.(BNC-S, news)

	(19)
	100%
	80%
	60%
					HC
					CEC
	40%
					other
					meanings
	20%
	0%
	TEC-Fr	OpenCLC-Fr:	OpenCLC-Fr:	EnTenTen15-S	BNC-S
		B1/B2	C1/C2

  ): (22) "Who is going to believe me? It would have been different if he were here now, if he came back." (TEC-Fr, New Bridges 2 de )

S: short for "sample".

At the time of writing, only the spoken component of the BNC2014 was available.

We are aware that the first sense of even if also implies a certain degree of concessivity since it implies a (potential) conflict between what is said in the two clauses. However, what even if in the sense of 'even in case' contradicts is the presupposed assumption that the truth of the apodosis is dependent on the hypothetical condition in the protasis, which is why we consider these as conditionals (cf.Dancygier, 1988: 120).

* Note that school years are counted backwards in France: 6 e is the first year and 3 e the last year of collège, followed by 2 de , the first year of lycée.

Note, however, that Römer's (2004, 2007) textbook corpus only contained texts representing spoken language, whereas the TEC-Fr analysed in this study represents textbook language in its entirety (which also includes written text genres, instructions, exercises, etc.).